"The Method of Transport for Systems of Hyperbolic Conservationlaws"

Abstract

In 1992 M. Fey introduced the method of transport for the Euler equations of gasdynamics. We shall derive this method for the Euler equations using the advection form. In this form one sees more easily the characteristic propagation directions inherent in the differential equation. A straightforward decomposition and linearisation of this advection form leads to a genuinely multi-dimensional method. This method is robust, but of first order only. It is indicated how one can obtain a second order scheme. It is then shown that the method can be applied not only to the Euler equations of gas dynamics but also to the shallow water equation, MHD, Navier-Stokes and equations to model elasto-plastic waves in solids. We discuss briefly the treatment of boundary conditions and mesh adaptations as well as parallelisations for MIMD computers.