MULTIDIMENSIONAL UPWINDING - PART I - THE METHOD OF TRANSPORT FOR SOLVING THE EULER EQUATIONS

The aim of this paper is to show a new approach towards the discretiza tion of multidimensional conservation laws. The idea of transport asso ciated with the solution of a scalar equation is used for the convecti ve part of the compressible Euler equations. A multidimensional wave s tructure is derived to model the acoustic part of this non-linear syst em, that allows infinitely many propagation directions in the numerica l method. This provides the basic knowledge to construct a numerical m ethod that does not rely on Riemann solvers. A more general definition of the waves, together with the concept of consistency. enables the d esign of a number of effective, genuinely multidimensional, methods. ( C) 1998 Academic Press.