A new multidimensional Euler scheme

A new idea is presented to solve the multidimensional Euler equations numerically. The aim of this idea is to obtain a robust shock capturing method without the use of dimensional splitting. The starting point is the idea of the one-dimensional flux vector splitting and the homogeneity of the Euler equations. Using this concept it is shown that a different interpretation of the one-dimensional waves and the use of some physical properties lead to a decomposition of the state vector into three multidimensional waves. This idea includes most of the physical properties of the Euler equations and allows infinitely many propagation directions. Assuming a Cartesian grid and constant states within each cell a numerical scheme is derived and some test calculations are shown