Approximation Schemes for convective term - structured grids - What we need: Please help
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A. Harten (1984), "On a class of high resolution total-variation stable finite difference schemes", SIAM J. Num. Analysis, 21, p1.
A. Harten (1983), "High resolution schemes for hyperbolic conservation laws", J. Comput. Phys., 49:357-393, 1983.
P. K. Sweby (1984), "High resolution schemes using flux-limiters for hyperbolic conservation laws", SIAM J. Num. Analysis, 21, p995.
B. P. Leonard (1988), "Simple high-accuracy resolution program for convective modelling of discontinuities", International Journal for Numerical Methods in Fluids, 8:1291–1318, 1988.
B. P. Leonard (1988), "Universal limiter for transient interpolation modelling of the advective transport equations", Technical Memorandum TM-100916 ICOMP-88-11, NASA, 1988.
B. P. Leonard (1991), "The ULTIMATE conservative difference scheme applied to unsteady one–dimensional advection", Computer Methods in Applied Mechanics and Engineering, 88:17–74, June 1991.
ULTRA-SHARP : Universal Limiter for Thight Resolution and Accuracy in combination with the Simple High-Accuracy Resolution Program (also ULTRA-QUICK)
B. P. Leonard and S. Mokhtari (1990), "Beyond first-order upwinding: the ULTRA-SHARP alternative for non-oscillatory steady state simulation of convection.", International Journal of Numerical Methods in Engineering, 30:729–766, 1990..
B. P. Leonard and S. Mokhtari. (1990), "ULTRA-SHARP nonoscillatory convection schemes for highspeed steady multidimensional flow", Technical Memorandum TM-102568 ICOMP-90-12,NASA, April 1990..
UTOPIA - Uniformly Third Order Polynomial Interpolation Algorithm
B. P. Leonard, M. K. MacVean, and A. P. Lock. (1993), "Positivity-preserving numerical schemes for multidimensional advection.", Technical Memorandum TM-106055 ICOMP-93-05, NASA, March 1993..
NIRVANA - Non-oscilatory Integrally Reconstructed Volume-Avaraged Numerical Advection scheme
B. P. Leonard, A. P. Lock, and M. K. MacVean. (1995), "The NIRVANA scheme applied to one–dimensional advection.", International Journal of Numerical Methods in Heat and Fluid Flow,5:341–377, 1995..
ENIGMATIC - Extended Numerical Integration for Genuinely Multidimensional Advective Transport Insuring Conservation
B. P. Leonard, A. P. Lock, and M. K. MacVean. (1995), "Extended numerical integration for genuinely multidimensional advective transport insuring conservation.", In C. Taylor and P. Durbetaki, editors, Numerical Methods in Laminar and Turbulent Flow, volume 9, pages 1–12. Pineridge Press, 1995..
MACHO : Multidimensional Advective - Conservative Hybrid Operator
B. P. Leonard, A. P. Lock, and M. K. MacVean. (1996), "Conservative explicit unrestricted-timestep multidimensional constancy-preserving advection schemes.", Monthly Weather Review,124:2588–2606, November 1996..
COSMIC : Conservative Operator Splitting for Multidimensions with Internal Constancy
B. P. Leonard , A. P. Lock, and M. K. MacVean. (1996), "Conservative explicit unrestricted-timestep multidimensional constancy-preserving advection schemes.", Monthly Weather Review, 124:2588–2606, November 1996..
QUICKEST - Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms
B. P. Leonard (1988), "Elliptic systems: Finite-difference method IV.", In W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, and R. H. Pletcher, editors, Handbook of Numerical Heat Transfer, pages 347–378. Wiley, New York, 1988..
AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection
B. P. Leonard (1981), "A survey of finite differences with upwinding for numerical modelling of the incompressible convective diffusion equation.", In C. Taylor and K. Morgan, editors, Computational Methods in Transient and Turbulent Flow, pages 1–35. Pineridge Press, Swansea, 1981..
EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation
B. P. Leonard (1981), "A survey of finite differences with upwinding for numerical modelling of the incompressible convective diffusion equation", In C. Taylor and K. Morgan, editors, Computational Methods in Transient and Turbulent Flow, pages 1–35. Pineridge Press, Swansea, 1981..
van Leer limiter
G.D. Van Albada, B.Van Leer, W.W.Roberts
A comparative study of computational methods in cosmic gas dynamics
Astron. Astrophysics, Vol. 108, p.76, 1982
A unified approach to the design and application of bounded higher-order convection schemes
In C. Taylor and P.Durbetaki, editors, Proc. Ninth Int. Conf. on Numer. Method. Laminar and Turbulent Flow, pages 203-214, Pineridge Press, Swansea, 1995
Sweby - limiter
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
van Leer harmonic
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
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)
smooth, bounded cubic upwind interpolation, analogous to van Leer Harmonic limiter
A unified approach to the design and application of bounded high-order convection schemes
In C. Taylor and P.Durbetaki, editors, Proc. Ninth Int. Conf. on Numerical Methods in Laminar and Turbulent Flow, pages 203-214, Pineridge Press, Swansea, 1995.
Evaluation of a bounded high-resolution scheme for combustor flow computations
AIAA J., vol. 30, No. 1, p.64 (1992)