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

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.