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FULLY DISCRETE HIGH‐RESOLUTION SCHEMES FOR HYPERBOLIC CONSERVATION LAWS
Author(s) -
SHI J.,
TORO E. F.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960830)23:4<309::aid-fld410>3.0.co;2-z
Subject(s) - conservation law , euler equations , upwind scheme , extension (predicate logic) , mathematics , euler's formula , total variation diminishing , hyperbolic partial differential equation , computer science , mathematical analysis , partial differential equation , discretization , programming language
The present paper is a sequel to two previous papers in which rigorous, up to fourth‐order, fully discrete (FD) upwind TVD schemes have been presented. In this paper we discuss in detail the extension of these schemes to solutions of non‐linear hyperbolic systems. The performance of the schemes is assessed by solving test problems for the time‐dependent Euler equations of gas dynamics in one and two space dimensions. We use exact solutions and experimental data to validate the results.