On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws

On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws

This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes. Special attention is given to the Godunov-type schemes that result from using an approximate solution of the Riemann problem....

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Veröffentlicht in:SIAM review 1983-01, Vol.25 (1), p.35-61
Hauptverfasser: Harten, Amiram, Lax, Peter D., Van Leer, Bram
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Approximation
Cauchy problem
Conservation laws
Constant coefficients
Eigenvalues
Eigenvectors
Entropy
Inequality
Mathematical discontinuity
Partial differential equations
Rectangles
Shock discontinuity
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Beschreibung
Zusammenfassung:This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes. Special attention is given to the Godunov-type schemes that result from using an approximate solution of the Riemann problem. For schemes based on flux splitting, the approximate Riemann solution can be interpreted as a solution of the collisionless Boltzmann equation.
ISSN:0036-1445
1095-7200
DOI:10.1137/1025002