A TWO-DIMENSIONAL VERSION OF THE GODUNOV SCHEME FOR SCALAR BALANCE LAWS

A Godunov scheme is derived for two-dimensional scalar conservation laws without or with source terms following ideas originally proposed by Boukadida and LeRoux [Math. Comput., 63 (1994), pp. 541–553] in the context of a staggered Lax–Friedrichs scheme. In both situations, the numerical fluxes are...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:SIAM journal on numerical analysis Ročník 52; číslo 2; s. 626 - 652
Hlavní autor: GOSSE, LAURENT
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2014
Témata:
Approximation
Cauchy problem
Conservation laws
Decomposition
Elastic waves
Entropy
Error rates
Gas dynamics
Hypotheses
Mathematics
Numerical Analysis
Scalars
Wave interaction
Wave propagation
Kruzkov entropy solution
Well-Balanced 2D Godunov scheme
External wave
Helmholtz decomposition and Curl-free field
Approximate 2D Riemann solver
ISSN:0036-1429, 1095-7170
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:A Godunov scheme is derived for two-dimensional scalar conservation laws without or with source terms following ideas originally proposed by Boukadida and LeRoux [Math. Comput., 63 (1994), pp. 541–553] in the context of a staggered Lax–Friedrichs scheme. In both situations, the numerical fluxes are obtained at each interface of a uniform Cartesian computational grid just by means of the "external waves" involved in the entropy solution of the elementary two-dimensional (2D) Riemann problems; in particular, all the wave-interaction phenomena are overlooked. This restriction of the wave pattern suffices for deriving the exact numerical fluxes of the staggered Lax–Friedrichs scheme, but it furnishes only an approximation for the Godunov scheme: we show that under convenient assumptions, these flux functions are smooth and the resulting discretization process is stable under nearly optimal CFL restriction. A well-balanced extension is presented, relying on the Curl-free component of the Helmholtz decomposition of the source term. Several numerical tests against exact 2D solutions are performed for convex, nonconvex, and inhomogeneous equations and the time-evolution of the L1 truncation error is displayed.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/130925906