Positive schemes and shock modelling for compressible flows
作者:
Antony Jameson,
期刊:
International Journal for Numerical Methods in Fluids
(WILEY Available online 1995)
卷期:
Volume 20,
issue 8‐9
页码: 743-776
ISSN:0271-2091
年代: 1995
DOI:10.1002/fld.1650200805
出版商: John Wiley&Sons, Ltd
关键词: computational aerodynamics;shock capturing;positive schemes
数据来源: WILEY
摘要:
AbstractA 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 scheme
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