ZusammenfassungGodunovs Methode, und besonders deren Erweiterung auf höhere Ordnung, approximiert die Gleichungen der Gasdynamik genau und löst Unstetigkeiten scharf auf. Diese Methoden basieren auf der Lösung von Riemann-Problemen an den Zellrändern. Aufbauend auf einem globalen Existenzbeweis wird eine neue Methode zur numerischen Lösung des Riemann-Problems vorgestellt. Diese Methode erweist sich als sehr zuverlässig und numerisch effizient.AbstractGodunov's method, and especially its extensions to higher order accuracy, can approximate the equations of gas dynamics accurately and resolve discontinuities sharply. These methods are based on solving Riemann problems at the interface between cells. A new method is proposed for solving the Riemann problem based on a global existence proof for the solution of the Riemann problem. This method is found to be very reliable and computationally efficient.
[1]
P. Lax.
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
,
1987
.
[2]
Alexandre J. Chorin,et al.
Random choice solution of hyperbolic systems
,
1976
.
[3]
J. Marsden,et al.
A mathematical introduction to fluid mechanics
,
1979
.
[4]
Richard Courant,et al.
Supersonic Flow And Shock Waves
,
1948
.
[5]
J. Smoller.
Shock Waves and Reaction-Diffusion Equations
,
1983
.
[6]
G. Sod.
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
,
1978
.
[7]
I. Bohachevsky,et al.
Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics
,
1959
.