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Annual Review of Fluid Mechanics top

► Large-Scale Eddy-Mean Flow Interaction in the Earth's Extratropical Atmosphere
  19 Jan, 2024

Large-scale circulation of the atmosphere in the Earth's extratropics is dominated by eddies, eastward (westerly) zonal winds, and their interaction. Eddies not only bring about weather variabilities but also help maintain the average state of climate. In recent years, our understanding of how large-scale eddies and mean flows interact in the extratropical atmosphere has advanced significantly due to new dynamical constraints on finite-amplitude eddies and the related eddy-free reference state. This article reviews the theoretical foundations for finite-amplitude Rossby wave activity and related concepts. Theory is then applied to atmospheric data to elucidate how angular momentum is redistributed by the generation, transmission, and dissipation of Rossby waves and to reveal how an anomalously large wave event such as atmospheric blocking may arise from regional eddy-mean flow interaction.

► Interfacial Dynamics Pioneer Stephen H. Davis (1939–2021)
  19 Jan, 2024

Stephen H. Davis (1939–2021) was an applied mathematician, fluid dynamicist, and materials scientist who lead the field in his contributions to interfacial dynamics, thermal convection, thin films, and solidification for over 50 years. Here, we briefly review his personal and professional life and some of his most significant contributions to the field.

► Fluid Dynamics of Airtanker Firefighting
  19 Jan, 2024

Airtanker firefighting is the most spectacular tool used to fight wildland fires. However, it employs a rudimentary large-scale spraying technology operating at a high speed and a long distance from the target. This review gives an overview of the fluid dynamics processes that govern this practice, which are characterized by rich and varied physical phenomena. The liquid column penetration in the air, its large-scale fragmentation, and an intense surface atomization give shape to the rainfall produced by the airtanker and the deposition of the final product on the ground. The cloud dynamics is controlled by droplet breakup, evaporation, and wind dispersion. The process of liquid deposition onto the forest canopy is full of open questions of great interest for rainfall retention in vegetation. Of major importance, but still requiring investigation, is the role of the complex non-Newtonian viscoelastic and shear-thinning behavior of the retardant dropped to stop the fire propagation. The review describes the need for future research devoted to the subject.

► The Early Days and Rise of Turbulence Simulation
  19 Jan, 2024

This review highlights major developments and milestones during the early days of numerical simulation of turbulent flows and its use to increase our understanding of turbulence phenomena. The period covered starts with the first simulations of decaying homogeneous isotropic turbulence in 1971–1972 and ends about 25 years later. Some earlier history of the progress in weather prediction is included if relevant. Only direct simulation, in which all scales of turbulence are accounted for explicitly, and large-eddy simulation, in which the effect of the smaller scales is modeled, are discussed. The method by which all scales are modeled, Reynolds-averaged Navier–Stokes, is not covered.

► Multiscale Velocity Gradients in Turbulence
  19 Jan, 2024

Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities.

► Flows Over Rotating Disks and Cones
  19 Jan, 2024

Rotating-disk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.

► Bubble Plumes in Nature
  19 Jan, 2024

Bubble plumes are ubiquitous in nature. Instances in the natural world include the release of methane and carbon dioxide from the seabed or the bottom of a lake and from a subsea oil well blowout. This review describes the dynamics of bubble plumes and their various spreading patterns in the surrounding environment. We explore how the motion of the plume is affected by the density stratification in the external environment, as well as by internal processes of dissolution of the bubbles and chemical reaction. We discuss several examples, such as natural disasters, global warming, and fishing techniques used by some whales and dolphins.

► Turbulent Drag Reduction by Streamwise Traveling Waves of Wall-Normal Forcing
  19 Jan, 2024

We review some fundamentals of turbulent drag reduction and the turbulent drag reduction techniques using streamwise traveling waves of blowing/suction from the wall and wall deformation. For both types of streamwise traveling wave controls, their significant drag reduction capabilities have been well confirmed by direct numerical simulation at relatively low Reynolds numbers. The drag reduction mechanisms by these streamwise traveling waves are considered to be the combination of direct effects due to pumping and indirect effects of the attenuation of velocity fluctuations due to reduced receptivity. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts at experimental validation are also intensively ongoing toward their practical implementation.

► Building Ventilation: The Consequences for Personal Exposure
  19 Jan, 2024

Ventilation is central to human civilization. Without it, the indoor environment rapidly becomes uncomfortable or dangerous, but too much ventilation can be expensive. We spend much of our time indoors, where we are exposed to pollutants and can be infected by airborne diseases. Ventilation removes pollution and bioaerosols from indoor sources but also brings in pollution from outdoors. To determine an appropriate level of ventilation and an appropriate way of providing it, one must understand that the needs for ventilation extend beyond simple thermal comfort; the quality of indoor air is at least as important. An effective ventilation system will remove unwanted contaminants, whether generated within the space by activities or by the simple act of breathing, and ensure that the ventilation system does not itself introduce or spread contaminants from elsewhere. This review explores how ventilation flows in buildings influence personal exposure to indoor pollutants and the spread of airborne diseases.

► Gas Microfilms in Droplet Dynamics: When Do Drops Bounce?
  19 Jan, 2024

In the last ten years, advances in experimental techniques have enabled remarkable discoveries of how the dynamics of thin gas films can profoundly influence the behavior of liquid droplets. Drops impacting onto solids can skate on a film of air so that they bounce off solids. For drop–drop collisions, this effect, which prevents coalescence, has been long recognized. Notably, the precise physical mechanisms governing these phenomena have been a topic of intense debate, leading to a synergistic interplay of experimental, theoretical, and computational approaches. This review attempts to synthesize our knowledge of when and how drops bounce, with a focus on () the unconventional microscale and nanoscale physics required to predict transitions to/from merging and () the development of computational models. This naturally leads to the exploration of an array of other topics, such as the Leidenfrost effect and dynamic wetting, in which gas films also play a prominent role.

Computers & Fluids top

► Non-intrusive reduced order models for the accurate prediction of bifurcating phenomena in compressible fluid dynamics
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Niccolò Tonicello, Andrea Lario, Gianluigi Rozza, Gianmarco Mengaldo

► A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Mathilde Tavares, Christophe Josserand, Alexandre Limare, José Ma Lopez-Herrera, Stéphane Popinet

► Influence of material property on semi-sealed cylindrical shell during high-speed vertical water entry
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Shengsheng Xia, Yingjie Wei, Cong Wang

► Bathymetry reconstruction from experimental data using PDE-constrained optimisation
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Judith Angel, Jörn Behrens, Sebastian Götschel, Marten Hollm, Daniel Ruprecht, Robert Seifried

► A locally redistributed level-set method for numerical simulation of thin interface structures
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Jaehee Chang, Kiyoung Kim, Haecheon Choi

► Investigation of physics-informed deep learning for the prediction of parametric, three-dimensional flow based on boundary data
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Philip Heger, Daniel Hilger, Markus Full, Norbert Hosters

► A systematic analysis of three-dimensional Riemann problems for verification of compressible-flow solvers
    

Publication date: 30 June 2024

Source: Computers & Fluids, Volume 278

Author(s): Nils Hoppe, Nico Fleischmann, Benedikt Biller, Stefan Adami, Nikolaus A. Adams

► An explicit primitive conservative solver for the Euler equations with arbitrary equation of state
    

Publication date: Available online 14 June 2024

Source: Computers & Fluids

Author(s): Giuseppe Sirianni, Alberto Guardone, Barbara Re, Rémi Abgrall

► A comparative study of Newtonian and non-Newtonian blood flow through Bi-Leaflet Mechanical Heart Valve
    

Publication date: Available online 10 June 2024

Source: Computers & Fluids

Author(s): Nandan Sarkar, Siddharth D. Sharma, Suman Chakraborty, Somnath Roy

► A face-centred finite volume method for laminar and turbulent incompressible flows
    

Publication date: Available online 15 June 2024

Source: Computers & Fluids

Author(s): Luan M. Vieira, Matteo Giacomini, Ruben Sevilla, Antonio Huerta

International Journal of Computational Fluid Dynamics top

► Angular Momentum Conserving Limiters for the Euler Equations
  10 Jun, 2024
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► Parallel Immersed Boundary Method for Two-Phase Flows on DCU Clusters
    5 Jun, 2024
Volume 37, Issue 8, September 2023, Page 711-728
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► A CFD-Based Design of S-Shaped Nozzle Attachment for Aircraft Cabin Gaspers
    4 Jun, 2024
Volume 37, Issue 8, September 2023, Page 729-745
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► Flow Around a Pile Under Highly Non-linear Waves Using an Unstructured Finite-Volume Technique
  28 May, 2024
Volume 37, Issue 8, September 2023, Page 693-710
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► A Large Time Step Wave-Adding Simple Scheme for Unsteady Compressible Flows
    9 May, 2024
Volume 37, Issue 8, September 2023, Page 675-692
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► Erratum
  18 Aug, 2014
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International Journal for Numerical Methods in Fluids top

► A general pressure equation based method for incompressible two‐phase flows
  11 Jun, 2024
A general pressure equation based method for incompressible two-phase flows

A fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows is presented. This computationally efficient algorithm combines the general pressure equation (GPE), modified switching technique for advection and capturing of surfaces (MSTACS) which is an algebraic volume-of-fluid approach for interface capturing and the operator-split (OS) method. It can accurately handle problems involving a range of density and viscosity ratios and surface tension effects. Since it is fully-explicit, the algorithm is highly scalable for parallel computing.


Summary

We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure equation which is solved explicitly. In addition, a less diffusive algebraic volume-of-fluid approach is used as the interface capturing technique and in order to facilitate improved parallel computing scalability, the technique is discretised temporally using the operator-split methodology. Our method is fully-explicit and stable with simple local spatial discretization, and hence, it is easy to implement. Several two- and three-dimensional canonical two-phase flows are simulated. The qualitative and quantitative results prove that our method is capable of accurately handling problems involving a range of density and viscosity ratios and surface tension effects.

► A modified fifth‐order WENO‐Z scheme based on the weights of the reformulated adaptive order WENO scheme
    5 Jun, 2024
A modified fifth-order WENO-Z scheme based on the weights of the reformulated adaptive order WENO scheme

A modified fifth-order WENO-Z scheme is developed by modifying the non-normalized nonlinear weights of a reformulated fifth-order adaptive order WENO scheme. The modified scheme has significantly higher resolution compared with the existing WENO-Z+ and WENO-Z+M schemes with a little more computational overhead per time step.


Abstract

A modified fifth-order WENO-Z scheme is proposed by analogy with the non-normalized weights of the reformulated fifth-order adaptive order (AO) WENO scheme. We show that if the original fifth-order WENO-AO scheme is rewritten as the form of the conventional WENO combination, the resulting non-normalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENO-Z scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifth-order WENO-Z scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with small-scale structures compared with the recently developed WENO-Z+ and WENO-Z+M schemes.

► A data‐driven turbulence modeling for the Reynolds stress tensor transport equation
    5 Jun, 2024
A data-driven turbulence modeling for the Reynolds stress tensor transport equation

A data-driven turbulence model that solves the Reynolds stress transport equation along with the momentum balance is developed, the model is fueled by a source-term that combines the unclosed terms in the Reynolds stress tensor equation. Using neural networks, trained with direct numerical simulations data, we were able to predict this source-term and correct the Reynolds averaged Navier–Stokes flow in the square-duct. This is the first time that machine learning corrections of turbulent flows are driven by a coupled transport equation combined with the momentum equations.


Abstract

The long lasting demand for better turbulence models and the still prohibitively computational cost of high-fidelity fluid dynamics simulations, like direct numerical simulations and large eddy simulations, have led to a rising interest in coupling available high-fidelity datasets and popular, yet limited, Reynolds averaged Navier–Stokes simulations through machine learning (ML) techniques. Many of the recent advances used the Reynolds stress tensor or, less frequently, the Reynolds force vector as the target for these corrections. In the present work, we considered an unexplored strategy, namely to use the modeled terms of the Reynolds stress transport equation as the target for the ML predictions, employing a neural network approach. After that, we solve the coupled set of governing equations to obtain the mean velocity field. We apply this strategy to solve the flow through a square duct. The obtained results consistently recover the secondary flow, which is not present in the baseline simulations that used the κ−ϵ$$ \kappa -\epsilon $$ model. The results were compared with other approaches of the literature, showing a path that can be useful in the seek of more universal models in turbulence.

► On robust boundary treatments for wall‐modeled LES with high‐order discontinuous finite element methods
    5 Jun, 2024
On robust boundary treatments for wall-modeled LES with high-order discontinuous finite element methods

The auxiliary boundary condition must be specified for the discontinuous finite element methods (e.g., DG, SD, FR/CPR) to evaluate the solution gradients. Since the velocity gradient near the wall is not fully resolved in the WMLES grid, we recommend a looser auxiliary condition than the usual no-slip condition. Superior performance of the proposed WMLES framework was confirmed for a benchmarking non-equilibrium periodic hill flow with curvilinear walls compared to the results of an algebraic WMLES and a DDES.


Summary

To robustly and accurately simulate wall-bounded turbulent flows at high Reynolds numbers, we propose suitable boundary treatments for wall-modeled large-eddy simulation (WMLES) coupled with a high-order flux reconstruction (FR) method. First, we show the need to impose an auxiliary boundary condition on auxiliary variables (solution gradients) that are commonly introduced in high-order discontinuous finite element methods (DFEMs). Auxiliary boundary conditions are introduced in WMLES, where the grid resolution is too coarse to resolve the inner layer of a turbulent boundary layer. Another boundary treatment to further enhance stability with under-resolved grids, is the use of a modal filter only in the wall-normal direction of wall-adjacent cells to remove the oscillations. A grid convergence study of turbulent channel flow with a high Reynolds number (Reτ≈5200$$ R{e}_{\tau}\approx 5200 $$) shows that the present WMLES framework accurately predicts velocity profiles, Reynolds shear stress, and skin friction coefficients at the grid resolutions recommended in the literature. It was confirmed that a small amount of filtering is sufficient to stabilize computation, with negligible influence on prediction accuracy. In addition, non-equilibrium periodic hill flow with a curved wall, including flow separation, reattachment, and acceleration at a high Reynolds number (Reh≈37,000$$ R{e}_h\approx 37,000 $$), is reported. Considering stability and the prediction accuracy, we recommend a loose auxiliary wall boundary conditions with a less steep velocity gradient for WMLES using high-order DFEMs.

► Enhanced conservative phase field method for moving contact line problems
    5 Jun, 2024
Enhanced conservative phase field method for moving contact line problems

This paper develops a three dimensional phase field model, based on a recently improved Allen–Cahn phase field model. The model was discretized using a finite difference method on a half-staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.


Abstract

The traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvature-driven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a half-staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.

► Simulation of fluid‐structure interaction using the boundary data immersion method with adaptive mesh refinement
    5 Jun, 2024
Simulation of fluid-structure interaction using the boundary data immersion method with adaptive mesh refinement

The boundary data immersion method smears the fluid-structure interface in the smoothing region and incurs deviations. The proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss.


Summary

The fluid-structure interaction is simulated using the boundary data immersion method. As the fluid-structure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma =2.67$$ =2.67 $$ and Re =1482$$ =1482 $$, which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake.

► Local discontinuous Galerkin method coupled with the implicit‐explicit Runge–Kutta method for the time‐dependent micropolar fluid equations
    5 Jun, 2024
Local discontinuous Galerkin method coupled with the implicit-explicit Runge–Kutta method for the time-dependent micropolar fluid equations

In this article, the implicit-explicit RK time discretization coupled with LDG spatial discretization numerical algorithm for the micropolar fluid equations are presented. Moreover, the stability of the first-order and second-order fully discrete method are proved. Finally, the numerical experiments are given to verify the theoretical order and effectiveness of the presented method.


Abstract

In this article, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal implicit-explicit Runge–Kutta (RK) evolution for the micropolar fluid equations are adopted to construct the discretization method. To avoid the incompressibility constraint, the artificial compressibility strategy method is used to convert the micropolar fluid equations into the Cauchy–Kovalevskaja type equations. Then the LDG method based on the modal expansion and the implicit-explicit RK method are properly combined to construct the expected third-order method. Theoretically, the unconditionally stable of the fully discrete method are derived in multidimensions for triangular meshs. And the numerical experiments are given to verify the theoretical and effectiveness of the presented methods.

► Development of a cascaded lattice Boltzmann model for two‐layer shallow water flows
    5 Jun, 2024
Development of a cascaded lattice Boltzmann model for two-layer shallow water flows

Cascaded collision operator is adapted to multilayer shallow water flows. Two sets of particle distribution function (PDF) are solved separately, with external forces modeling the mutual actions between the two layers. The model is able to reproduce ideal dam break flows and gravity currents.


Summary

Many environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the ‘shallow approach’. A multi-layer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multi-layer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multi-layer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a two-layered liquid Lattice-Boltzmann model (CaLB-2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks.

► Comparative analysis of nondimensionalization approaches for solving the 2‐D differentially heated cavity problem
    5 Jun, 2024
Comparative analysis of nondimensionalization approaches for solving the 2-D differentially heated cavity problem

We report the effect of three nondimensionalization approaches on the solution of the 2-D differentially heated cavity problem. The governing equations were discretized using orthogonal collocation and solved via the Newton–Raphson method with LU factorization. Approach II was found to be the most suitable for nondimensionalization.


Abstract

This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2-D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 103 and 108, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.

► Issue Information
    5 Jun, 2024
International Journal for Numerical Methods in Fluids, Volume 96, Issue 7, July 2024.

Journal of Computational Physics top

► A Lawson-time-splitting extended Fourier pseudospectral method for the Gross-Pitaevskii equation with time-dependent low regularity potential
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Bo Lin, Ying Ma, Chushan Wang

► A new very high-order finite-difference method for linear stability analysis and bi-orthogonal decomposition of hypersonic boundary layer flow
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Zihao Zou, Xiaolin Zhong

► A skew-symmetric energy stable almost dissipation free formulation of the compressible Navier-Stokes equations
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Jan Nordström

► An unfitted high-order HDG method for two-fluid Stokes flow with exact NURBS geometries
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Stefano Piccardo, Matteo Giacomini, Antonio Huerta

► Graph network surrogate model for subsurface flow optimization
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Haoyu Tang, Louis J. Durlofsky

► Centralized gradient-based reconstruction for wall modeled large eddy simulations of hypersonic boundary layer transition
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Natan Hoffmann, Amareshwara Sainadh Chamarthi, Steven H. Frankel

► Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret

► A nodal based high order nonlinear stabilization for finite element approximation of Magnetohydrodynamics
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Tuan Anh Dao, Murtazo Nazarov

► Probabilistic graph networks for learning physics simulations
    

Publication date: 15 September 2024

Source: Journal of Computational Physics, Volume 513

Author(s): Sakthi Kumar Arul Prakash, Conrad Tucker

► A preconditioned Riemannian conjugate gradient method for computing the ground states of arbitrary-angle rotating Bose-Einstein condensates
    

Publication date: 1 September 2024

Source: Journal of Computational Physics, Volume 512

Author(s): Qingzhou Shu, Qinglin Tang, Shaobo Zhang, Yong Zhang

Journal of Turbulence top

► Challenges and perspective on the modelling of high-Re, incompressible, non-equilibrium, rough-wall boundary layers
    5 Jun, 2024
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► Errors and uncertainties in CFD validation for non-equilibrium turbulent boundary layer flows at high Reynolds numbers
  30 May, 2024
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► Effects of roughness on non-equilibrium turbulent boundary layers
  29 May, 2024
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► Evaluation of flow and flame characteristics of turbulent bluff-body CH4-H2 flame using LES-FPV approach
  11 May, 2024
Volume 25, Issue 4-6, April - June 2024
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► Large eddy simulations of sheet-to-cloud cavitation transitions with special emphasis on the simultaneous existence of the re-entrant jet and shock waves
    8 May, 2024
Volume 25, Issue 4-6, April - June 2024, Page 157-180
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► Theory and simulations of confined periodic turbulence
    3 May, 2024
Volume 25, Issue 4-6, April - June 2024, Page 145-156
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Physics of Fluids top

► A sharp interface immersed edge-based smoothed finite element method with extended fictitious domain scheme
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
This paper proposes a versatile and robust immersed edge-based smoothed finite element method with the mass conservation algorithm (IESFEM/Mass) to solve partitioned fluid–structure interaction (FSI). A gradient smoothing technique was used to solve the system governing equations, which can improve the calculated capability of the linear triangular elements in two phases. Based on the quadratic sharp interface representation of immersed boundary, an extended fictitious domain constructed by a least squares method approximately corrected the residual flux error. The compatibility for boundary conditions on moving interfaces was satisfied, thus eliminating spurious oscillations. The results from all numerical examples were consistent with those from the existing experiments and published numerical solutions. Furthermore, the present divergence-free vector field had a faster-converged rate in the flow velocity, pressure, and FSI force. Even if in distorted meshes, the proposed algorithm maintained a stable accuracy improvement. The aerodynamics of one- and two-winged flapping motions in insect flight has been investigated through the IESFEM/Mass. It can be seen that the wing–wake interaction mechanism is a vital factor affecting the lift. The applicability of the present method in the biological FSI scenario was also well-demonstrated.
► Enhanced and reduced solute transport and flow strength in salt finger convection in porous media
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
We report a pore-scale numerical study of salt finger convection in porous media, with a focus on the influence of the porosity in the non-Darcy regime, which has received little attention in previous research. The numerical model is based on the lattice Boltzmann method with a multiple-relaxation-time scheme and employs an immersed boundary method to describe the fluid–solid interaction. The simulations are conducted in a two-dimensional, horizontally periodic domain with an aspect ratio of 4, and the porosity [math] is varied from 0.7 to 1, while the solute Rayleigh number [math] ranges from [math] to [math]. Our results show that, for all explored [math], solute transport first enhances unexpectedly with decreasing [math] and then decreases when [math] is smaller than a [math]-dependent value. On the other hand, while the flow strength decreases significantly as [math] decreases at low [math], it varies weakly with decreasing [math] at high [math] and even increases counterintuitively for some porosities at moderate [math]. Detailed analysis of the salinity and velocity fields reveals that the fingered structures are blocked by the porous structure and can even be destroyed when their widths are larger than the pore scale, but become more ordered and coherent with the presence of porous media. This combination of opposing effects explains the complex porosity dependencies of solute transport and flow strength. The influence of porous structure arrangement is also examined, with stronger effects observed for smaller [math] and higher [math]. These findings have important implications for passive control of mass/solute transport in engineering applications.
► On the instability of the magnetohydrodynamic pipe flow subject to a transverse magnetic field
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
The linear stability of a fully developed liquid–metal magnetohydrodynamic pipe flow subject to a transverse magnetic field is studied numerically. Because of the lack of axial symmetry in the mean velocity profile, we need to perform a BiGlobal stability analysis. For that purpose, we develop a two-dimensional complex eigenvalue solver relying on a Chebyshev–Fourier collocation method in physical space. By performing an extensive parametric study, we show that in contrast to the Hagen–Poiseuille flow known to be linearly stable for all Reynolds numbers, the magnetohydrodynamic pipe flow with transverse magnetic field is unstable to three-dimensional disturbances at sufficiently high values of the Hartmann number and wall conductance ratio. The instability observed in this regime is attributed to the presence of velocity overspeed in the so-called Roberts layers and the corresponding inflection points in the mean velocity profile. The nature and characteristics of the most unstable modes are investigated, and we show that they vary significantly depending on the wall conductance ratio. A major result of this paper is that the global critical Reynolds number for the magnetohydrodynamic pipe flow with transverse magnetic field is Re = 45 230, and it occurs for a perfectly conducting pipe wall and the Hartmann number Ha = 19.7.
► The turbulence development at its initial stage: A scenario based on the idea of vortices decay
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
In this paper, a model of the development of a quantum turbulence in its initial stage is proposed. The origin of the turbulence in the suggested model is the decay of vortex loops with an internal structure. We consider the initial stage of this process, before an equilibrium state is established. As result of our study, the density matrix of developing turbulent flow is calculated. The quantization scheme of the classical vortex rings system is based on the approach proposed by the author earlier.
► Interstage difference and deterministic decomposition of internal unsteady flow in a five-stage centrifugal pump as turbine
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
A five-stage centrifugal pump is utilized to investigate the interstage flow characteristics of the multistage centrifugal pump as turbine (PAT). The simulation results of performance are verified by comparing with the experimental results. Owing to the distinct structural attributes, significant differences in flow occur between the first stage and the other stages of the multistage PAT. To enhance the understanding of these disparities and explore their repercussions, this study focuses on analyzing the flow within the impellers in the first and second stages by a deterministic analysis. The main conclusions are as follows: The discrepancies in the inflow conditions are the major reason for the dissimilarities in the flow of impellers between stages. The impact loss generated by the misalignment between the positive guide vane outlet angle and the impeller inlet angle leads to flow deviation between impeller passages and affects the internal flow pattern. The unsteadiness under low flow rates is mostly produced by the spatial gradient of the blade-to-blade nonuniformities, which is relevant to the relative position between blades and the positive guide vanes. At high flow rates, especially in the second-stage impeller, the pure unsteady term is the primary cause of flow unsteadiness as a result of the flow separation induced by interactions between the blades and the positive guide vanes. This study can provide some references for the practical operation and performance optimization of the multistage PATs in the future.
► Effect of gravity on phase transition for liquid–gas simulations
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
Direct simulations of phase-change and phase-ordering phenomena are becoming more common. Recently, qualitative simulations of boiling phenomena have been undertaken by a large number of research groups. One seldom discussed limitation is that large values of gravitational forcing are required to simulate the detachment and rise of bubbles formed at the bottom surface. The forces are typically so large that neglecting the effects of varying pressure in the system becomes questionable. In this paper, we examine the effect of large pressure variations induced by gravity using pseudopotential lattice Boltzmann simulations. These pressure variations lead to height dependent conditions for phase coexistence and nucleation of either gas or liquid domains. Because these effects have not previously been studied in the context of these simulation methods, we focus here on the phase stability in a one-dimensional system, rather than the additional complexity of bubble or droplet dynamics. Even in this simple case, we find that the different forms of gravitational forces employed in the literature lead to qualitatively different phenomena, leading to the conclusion that the effects of gravity induced pressure variations on phase-change phenomena should be very carefully considered when trying to advance boiling and cavitation as well as liquefaction simulations to become quantitative tools.
► Entrapment and mobilization dynamics during the flow of viscoelastic fluids in natural porous media: A micro-scale experimental investigation
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
Capillary desaturation process was investigated as a function of wetting phase rheological signatures during the injection of Newtonian and non-Newtonian fluids. Two sets of two-phase imbibition flow experiments were conducted on a water-wet sandstone core sample using brine and viscoelastic polymer solutions. During the experiments, a high-resolution micro-computed tomography scanner was employed to directly map pore-level fluid occupancies within the pore space. The results of the experiments revealed that at a given capillary number, the viscoelastic polymer was more efficient than the brine in recovering the non-wetting oil phase. At low capillary numbers, this is attributed to the improved accessibility of the viscoelastic polymer solution to the entrance of pore elements, which suppressed snap-off events and allowed more piston-like and cooperative pore-body filling events to contribute to oil displacement. For intermediate capillary numbers, the onset of elastic turbulence caused substantial desaturation, while at high capillary numbers, the superimposed effects of higher viscous and elastic forces further improved the mobilization of the trapped oil ganglia by the viscoelastic polymer. In the waterflood, however, the mobilization of oil globules was the governing recovery mechanism, and the desaturation process commenced only when the capillary number reached a threshold value. These observations were corroborated with the pore-level fluid occupancy maps produced for the brine and viscoelastic polymer solutions during the experiments. Furthermore, at the intermediate and high capillary numbers, the force balance and pore-fluid occupancies suggested different flow regimes for the non-Newtonian viscoelastic polymer. These regions are categorized in this study as elastic-capillary- and viscoelastic-dominated flow regimes, different from viscous-capillary flow conditions that are dominant during the flow of Newtonian fluids. Moreover, we have identified novel previously unreported pore-scale displacement events that take place during the flow of viscoelastic fluids in a natural heterogeneous porous medium. These events, including coalescence, fragmentation, and re-entrapment of oil ganglia, occurred before the threshold of oil mobilization was reached under the elastic-capillary-dominated flow regime. In addition, we present evidence for lubrication effects at the pore level due to the elastic properties of the polymer solution. Furthermore, a comparison of capillary desaturation curves generated for the Newtonian brine and non-Newtonian viscoelastic polymer revealed that the desaturation process was more significant for the viscoelastic polymer than for the brine. Finally, the analysis of trapped oil clusters showed that the ganglion size distribution depends on both the capillary number and the rheological properties of fluids.
► Impact of wettability on interface deformation and droplet breakup in microcapillaries
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
The objective of this research paper is to relate the influence of dynamic wetting in a liquid/liquid/solid system to the breakup of emulsion droplets in capillaries. Therefore, modeling and simulation of liquid/liquid flow through a capillary constriction have been performed with varying dynamic contact angles from highly hydrophilic to highly hydrophobic. Advanced advection schemes with geometric interface reconstruction (isoAdvector) are incorporated for high interface advection accuracy. A sharp surface tension force model is used to reduce spurious currents originating from the numerical treatment and geometric reconstruction of the surface curvature at the interface. Stress singularities from the boundary condition at the three-phase contact line are removed by applying a Navier-slip boundary condition. The simulation results illustrate the strong dependency of the wettability and the contact line and interface deformation.
► Drag increase and turbulence augmentation in two-way coupled particle-laden wall-bounded flows
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
The exact regularized point particle method is used to characterize the turbulence modulation in two-way momentum-coupled direct numerical simulations of a turbulent pipe flow. The turbulence modification is parametrized by the particle Stokes number, the mass loading, and the particle-to-fluid density ratio. The data show that in the wide region of the parameter space addressed in the present paper, the overall friction drag is either increased or unaltered by the particles with respect to the uncoupled case. In the cases where the wall friction is enhanced, the fluid velocity fluctuations show a substantial modification in the viscous sub-layer and in the buffer layer. These effects are associated with a modified turbulent momentum flux toward the wall. The particles suppress the turbulent fluctuations in the buffer region and concurrently provide extra stress in the viscous sub-layer. The sum of the turbulent stress and the extra stress is larger than the Newtonian turbulent stress, thus explaining the drag increase. The non-trivial turbulence/particles interaction turns out in a clear alteration of the near-wall flow structures. The streamwise velocity streaks lose their spatial coherence when two-way coupling effects are predominant. This is associated with a shift of the streamwise vortices toward the center of the pipe and with the concurrent presence of small-scale and relatively more intense vortical structures near the wall.
► Partial and complete wetting of thin films with dynamic contact angle
  17 Apr, 2023
Physics of Fluids, Volume 35, Issue 4, April 2023.
The wetting of thin films depends critically on the sign of the spreading coefficient [math]. We discuss the cases S < 0, S = 0, and S > 0 for transient models with contact line dissipation and find that the use of a dynamic contact angle solves problems for S > 0 that models might otherwise have. For initial data with a non-zero slope and S > 0, we show that there exists a finite time [math] at which the contact angle of the thin film goes to zero. Then, a molecular precursor emerges from the thin film and moves outward at a constant velocity.

Theoretical and Computational Fluid Dynamics top

► Resolvent analysis of swirling turbulent jets
  13 Jun, 2024

Abstract

This study explores coherent structures in a swirling turbulent jet. Stationary axisymmetric solutions of the Reynolds–Averaged Navier–Stokes equations at \(Re=200,000\) were obtained using an open source computational fluid dynamics code and the Spalart–Allmaras eddy viscosity model. Then, resolvent analysis with the same eddy viscosity field provided coherent structures of the turbulent fluctuations on the base flow. As in many earlier studies, a large gain separation is identified between the optimal and sub-optimal resolvent modes, permitting a focus on the most amplified response mode and its corresponding optimal forcing. At zero swirl, the results indicate that the jet’s coherent response is dominated by axisymmetric ( \(m=0\) ) structures, which are driven by the usual Kelvin–Helmholtz shear amplification mechanism. However, as swirl is increased, different coherent structures begin to dominate the response. For example, double and triple spiral ( \(|m|=2\) and \(|m|=3\) ) modes are identified as the dominant structures when the axial and azimuthal velocity maxima of the base flow are comparable. In this case, distinct co- and counter-rotating \(|m|=2\) modes experience vastly different degrees of amplification. The physics of this selection process involve several amplification mechanisms contributing simultaneously in different regions of the mode. This is analysed in more detail by comparing the alignment between the wavevector of the dominant response mode and the principal shear direction of the base flow. Additional discussion also considers the development of structures along the exterior of the jet nozzle.

Graphical abstract

► A balanced outflow boundary condition for swirling flows
    6 Jun, 2024

Abstract

In open flow simulations, the dispersion characteristics of disturbances near synthetic boundaries can lead to unphysical boundary scattering interactions that contaminate the resolved flow upstream by propagating numerical artifacts back into the domain interior. This issue is exacerbated in flows influenced by real or apparent body forces, which can significantly disrupt the normal stress balance along outflow boundaries and generate spurious pressure disturbances. To address this problem, this paper develops a zero-parameter, physics-based outflow boundary condition (BC) designed to minimize pressure scattering from body forces and pseudo-forces and enhance transparency of the artificial boundary. This “balanced outflow BC” is then compared against other common BCs from the literature using example axisymmetric and three-dimensional open swirling flow computations. Due to centrifugal and Coriolis forces, swirling flows are known to be particularly challenging to simulate in open geometries, as these apparent forces induce non-trivial hydrostatic stress distributions along artificial boundaries that cause scattering issues. In this context, the balanced outflow BC is shown to correspond to a geostrophic hydrostatic stress correction that balances the induced pressure gradients. Unlike the alternatives, the balanced outflow BC yields accurate results in truncated domains for both linear and nonlinear computations without requiring assumptions about wave characteristics along the boundary.

► Data assimilation and linear analysis with turbulence modelling: application to airfoil stall flows with PIV measurements
    4 Jun, 2024

Abstract

A combined data-assimilation and linear mean-flow analysis approach is developed to estimate coherent flow fluctuations from limited mean-flow measurements. It also involves Reynolds-Averaged Navier–Stokes (RANS) modelling to efficiently tackle turbulent flows. Considering time-averaged Particle Velocimetry Image (PIV) measurements of the near-stall flow past a NACA0012 airfoil at an angle of attack of \(10^{\circ }\) and in the chord-based Reynolds number range \(4.3 \cdot 10^4 \le Re \le 6.4 \cdot 10^4\) , data assimilation is first employed to correct RANS equations that are closed by the Spalart-Allmaras model. The outputs of this procedure are a full mean-flow description that matches the PIV data and a consistent turbulence model that provides not only a mean eddy-viscosity field but also the perturbations of the latter with respect to mean-flow modifications. Global stability and resolvent analyses are then performed based on the so-obtained mean flow and model to satisfactorily predict near-stall low-frequency phenomena, as confirmed through comparison with the Spectral Proper Orthogonal Decomposition (SPOD) of the PIV measurements. This comparison highlights the benefits in taking into account variations in the turbulent eddy-viscosity over a frozen approach for the correct estimation of the present coherent low-frequency oscillations.

Graphical abstract

► General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media
    2 Jun, 2024

Abstract

A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence.

Graphical abstract

► Acoustic resolvent analysis of turbulent jets
  20 May, 2024

Abstract

We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023).

Graphical abstract

► Eduction of coherent structures from schlieren images of twin jets using SPOD informed with momentum potential theory in the spectral domain
  20 May, 2024

Abstract

This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses.

Graphical abstract

► Efficient harmonic resolvent analysis via time stepping
  18 May, 2024

Abstract

We present an extension of the RSVD- \(\Delta t\)  algorithm initially developed for resolvent analysis of statistically stationary flows to handle harmonic resolvent analysis of time-periodic flows. The harmonic resolvent operator, as proposed by Padovan et al. (J Fluid Mech 900, 2020), characterizes the linearized dynamics of time-periodic flows in the frequency domain, and its singular value decomposition reveals forcing and response modes with optimal energetic gain. However, computing harmonic resolvent modes poses challenges due to (i) the coupling of all \(N_{\omega }\) retained frequencies into a single harmonic resolvent operator and (ii) the singularity or near-singularity of the operator, making harmonic resolvent analysis considerably more computationally expensive than a standard resolvent analysis. To overcome these challenges, the RSVD- \(\Delta t\)  algorithm leverages time stepping of the underlying time-periodic linearized Navier–Stokes operator, which is \(N_{\omega }\) times smaller than the harmonic resolvent operator, to compute the action of the harmonic resolvent operator. We develop strategies to minimize the algorithm’s CPU and memory consumption, and our results demonstrate that these costs scale linearly with the problem dimension. We validate the RSVD- \(\Delta t\)  algorithm by computing modes for a periodically varying Ginzburg–Landau equation and demonstrate its performance using the flow over an airfoil.

Graphical abstract

► Numerical simulations of dam-break flows of viscoplastic fluids via shallow water equations
  13 May, 2024

Abstract

This paper presents simulations of dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the shallow water equations (SWE). In particular, this study aims to assess the effects of rheological parameters: power-law index (n), consistency index (K), and yield stress ( \(\tau _{c}\) ), on flow height and velocity over different topographies. Three practical examples of dam-break flow cases are considered: a dam-break on an inclined flat surface, a dam-break over a non-flat topography, and a dam-break over a wet bed (downstream containing an initial fluid level). The effects of bed slope and depth ratios (the ratio between upstream and downstream fluid levels) on flow behaviour are also analyzed. The numerical results are compared with experimental data from the literature and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, peak height, and mean velocity decrease when any of the three rheological parameters are increased. However, based on a parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating fluid behaviour. Moreover, by increasing the bed slope and/or depth ratio, the wave-frontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction, which increases by increasing any of the three rheological parameters. This study is useful for an in-depth understanding of the effects of rheology on catastrophic gravity-driven flows of non-Newtonian fluids (like lava or mud flows) for risk assessment and mitigation.

Graphical abstract

► Contribution of wedge and bulk viscous forces in droplets moving on inclined surfaces
  17 Apr, 2024

Abstract

Employing direct numerical simulations, we investigate water and water-glycerol (85 wt%) droplets ( \(\sim \) 25 µL) moving on smooth surfaces, with contact angles of around 90 \(^{\circ }\) , at varying inclinations. Our focus is on elucidating the relative contribution of local viscous forces in the wedge and bulk regions in droplets to the total viscous force. We observe that, for fast-moving droplets, both regions contribute comparably, while the contribution of the wedge region dominates in slow-moving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk viscous forces in fast-moving droplets. Furthermore, we demonstrate that droplets with identical velocities can exhibit disparate viscous forces due to variations in internal fluid dynamics.

Graphical abstract

► Modal-based generalised quasilinear approximations for turbulent plane Couette flow
  15 Apr, 2024

Abstract

We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri and Nogueira (Phys Rev Fluids 7:102601, 2022), which considers controllability modes of the linearised Navier–Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by high-controllability modes and the other by low-controllability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised. We also consider a new GQL framework wherein the linearised equations for the low-controllability modes are driven by nonlinear interactions of modes in the first group, which are characterised by large-scale coherent structures. It is shown that GQL-ROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQL-ROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by large-scale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQL-ROMs, which can be valuable to extend these models to larger Reynolds numbers.

Graphical abstract


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