On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. (English) Zbl 0565.65051

Harten, Amiram; Lax, Peter D.; van Leer, Bram

SIAM Rev. 25, 35-61 (1983).

Summary: 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.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws

Keywords:

upstream difference schemes; Godunov-type schemes; Riemann problem; collisionless Boltzmann equation

Software:

HLLE