Positive schemes and shock modelling for compressible flows
Author:
- 30 April 1995
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Fluids
- Vol. 20 (8-9) , 743-776
Abstract
A unified theory of non‐oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presented which confirm the properties of these schemes.Keywords
This publication has 35 references indexed in Scilit:
- On central-difference and upwind schemesJournal of Computational Physics, 1992
- Computation of unsteady transonic flows by the solution of Euler equationsAIAA Journal, 1988
- On the convergence of difference approximations to scalar conservation lawsMathematics of Computation, 1988
- Multigrid solution of monotone second-order discretizations of hyperbolic conservation lawsMathematics of Computation, 1987
- Numerical viscosity and the entropy condition for conservative difference schemesMathematics of Computation, 1984
- High resolution schemes for hyperbolic conservation lawsJournal of Computational Physics, 1983
- Upwind difference schemes for hyperbolic systems of conservation lawsMathematics of Computation, 1982
- Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methodsJournal of Computational Physics, 1981
- Numerical viscosity and the entropy conditionCommunications on Pure and Applied Mathematics, 1979
- Fully multidimensional flux-corrected transport algorithms for fluidsJournal of Computational Physics, 1979