Convergence of a two-layer scheme for equations of gas dynamics in Eulerian variables with geo-physical applications

Abstract

This paper deals with the convergence of a completely conservative, two-layer difference scheme for equations of gas dynamics in Eulerian variables. The convergence of the difference solution to the smooth solution of the original periodic Cauchy problem of order τ²+h ² at layer-by-layer norm L ₂ is proved, provided that the mesh step sizes are sufficiently small and that τ=h ^1+ϵ (ϵ=constant>0). Several modifications of the proposed method were used for the numerical solution of a one-dimensional mathematical model (on the basis of the shallow water theory), which describes crash events produced by dam collapse.

Keywords:

• Cauchy problem
• Eulerian variables
• difference scheme
• partial differential equations
• shallow water theory

2000 AMS Subject Classification :

• 65L12 (finite difference methods)
• 65D25 (numerical differentiation)