Convection algorithms based on a diagonalization procedure for the multidimensional Euler equations

Abstract

Convection algorithms for the multidimensional Euler equations are presented based on characteristic propagation properties, with the aim of following closely the physical transfer of information. As opposed to the one dimensional case, information in two or three dimensional Euler flows is propagated in infinitely many directions, each one corresponding to an arbitrary wave front normal. It is shown that a complete decoupling (diagonalization) of the Euler equations can be obtained by an appropriate choice of wave front propagation directions. Actually,two directions are sufficient, one related to the pressure gradient and another related to the local strain tensor. This new formulation allows the definition of numerical schemes with upwind properties depending only on the local flow properties and not on the mesh geometry.