A time discretization for conservation laws. (English) Zbl 0604.65062
Numerical methods for the Euler equations of fluid dynamics, Proc. INRIA Workshop, Rocquencourt/France 1983, 108-120 (1985).
[For the entire collection see Zbl 0596.00018.]
We introduce a time discretization for non linear hyperbolic systems of conservation laws unifying many recent numerical schemes, each of them being obtained by a different full discretization. Among them we recognize the Osher scheme, the Roe scheme and its generalization by Le Veque for large Courant numbers. By using a non classical technique of full discretization suggested to us by the works of Chorin we also obtain a particle scheme. The time discretization described here is closely related to the Boltzmann type schemes considered by A. Harten, P. Lax and B. Van Leer [SIAM Rev. 25, 35-61 (1983; Zbl 0565.65051)].
We introduce a time discretization for non linear hyperbolic systems of conservation laws unifying many recent numerical schemes, each of them being obtained by a different full discretization. Among them we recognize the Osher scheme, the Roe scheme and its generalization by Le Veque for large Courant numbers. By using a non classical technique of full discretization suggested to us by the works of Chorin we also obtain a particle scheme. The time discretization described here is closely related to the Boltzmann type schemes considered by A. Harten, P. Lax and B. Van Leer [SIAM Rev. 25, 35-61 (1983; Zbl 0565.65051)].
MSC:
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
