Other Schemes (unclassified) - structured grids
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Chakravarthy-Osher limiter
Sweby - limiter
Superbee limiter
R-k limiter
MINMOD - MINimum MODulus
Harten A. High resolution schemes using flux limiters for hyperbolic conservation laws. Journal of Computational Physics 1983; 49: 357-393
A. Harten
High Resolution Schemes for Hyperbolic Conservation Laws
J. Comp. Phys., vol. 49, no. 3, pp. 225-232, 1991
Identical to SOUCUP
Normalized variables - uniform grids
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Normalized variables - non-uniform grids (NVSF)
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SOUCUP - Second-Order Upwind Central differnce-first order UPwind
Zhu J. (1992), "On the higher-order bounded discretization schemes for finite volume computations of incompressible flows", Computational Methods in Applied Mechanics and Engineering. 98. 345-360.
J. Zhu, W.Rodi (1991), "A low dispersion and bounded convection scheme", Comp. Meth. Appl. Mech.&Engng, Vol. 92, p 225.
Normalized variables - uniform grids
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Normalized variables - non-uniform grids
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where
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ISNAS - Interpolation Scheme which is Nonoscillatory for Advected Scalars
Third-order flux-limiter scheme
M. Zijlema , On the construction of a third-order accurate monotone convection scheme with application to turbulent flows in general domains. International Journal for numerical methods in fluids, 22:619-641, 1996.
COPLA - COmbination of Piecewise Linear Approximation
Seok Ki Choi, Ho Yun Nam, Mann Cho
Evaluation of a High-Order Bounded Convection Scheme: Three-Dimensional Numerical Experiments
Numerical Heat Transfer, Part B, 28:23-38, 1995
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where
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and
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HLPA - Hybrid Linear / Parabolic Approximation
Zhu J. Low Diffusive and oscillation-free convection scheme // Communications and Applied Numerical Methods. 1991. 7, N3. 225-232.
Zhu J., Rodi W. A low dispersion and bounded discretization schemes for finite volume computations of incompressible flows // Computational Methods for Applied Mechanics and Engineering. 1991. 92. 87-96
In this scheme, the normalized face value is approximated by a combination of linear and parabolic charachteristics passing through the points, O, Q, and P in the NVD. It satisfies TVD condition and is second-order accurate
Usual variables
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Normalized variables - uniform grids
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Normalized variables - non-uniform grids
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where
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Implementation
Using the switch factors:
for
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for
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and taken all the possible flow directions into account, the un-normalized form of equation can be written as
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where
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LODA - Local Oscillation-Damping Algorithm
J. Zhu and M.A. Leschziner
A local oscillation-damping algorithm for higher-order convection schemes
Comput. Methods Appl. Mech. Engnrng 67 (1988) 355-366
CLAM - Curved-Line Advection Method
Van Leer B. , Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme. Journal of Computational Physics 1974; 14:361-370
identical to HLPA
normalised variables - uniform grids
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normalised variables - non-uniform grids (NVSF - compare with HLPA - here is used another variant of notation)
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van Leer harmonic
BSOU
G. Papadakis, G. Bergeles.
A locally modified second order upwind scheme for convection terms discretization.
Int. J. Numer. Meth. Heat Fluid Flow, 5.49-62, 1995
MSOU - Monotonic Second Order Upwind Differencing Scheme
Sweby
Koren
bounded CUS
B. Koren
A robust upwind discretisation method for advection, diffusion and source terms
In: Numerical Mthods for Advection-Diffusion Problems, Ed. C.B.Vreugdenhil& B.Koren, Vieweg, Braunscheweigh, p.117, (1993)
H-CUS
bounded CUS
N.P.Waterson H.Deconinck
A unified approach to the design and application of bounded high-order convection schemes
VKI-preprint, 1995-21, (1995)
MLU
B. Noll
Evaluation of a bounded high-resolution scheme for combustor flow computations
AIAA J., vol. 30, No. 1, p.64 (1992)
LPPA - Linear and Piecewise / Parabolic Approximasion
Normalized variables - uniform grids
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Normalized variables - non-uniform grids
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where
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GAMMA
Jasak H., Weller H.G., Gosman A.D.
High resolution NVD differencing scheme for arbitrarily unstructured meshes
International Journal for Numerical Methods in Fluids
1999, 31: 431-449
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CUBISTA - Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection
M.A. Alves, P.J.Oliveira, F.T. Pinho, A convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection // International Lournal For Numerical Methods in Fluids 2003, 41; 47-75
normalised variables - uniform grid
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normalised variables - non-uniform grid (NVSF)
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