Flux splitting schemes for the Euler equations

In this paper we consider two aspects of flux splitting, one at the level of the differential equations and another concerned with numerical methods to discretize the resulting problems. In this framework there are various choices for the splitting at the level of the PDEs and many choices for their numerical discretization. Some of the existing flux splitting schemes fall within this framework. For the Euler equations we propose a new flux splitting and study the associated two systems of differential equations, called the advection system and the pressure system. For each of the splittings studied we analyse the resulting two systems of differential equations and propose discretization schemes of the Godunov type. These schemes are simple, robust and accurate when compared with existing methods. Moreover, they enjoy a most desirable property: recognition of contact discontinuities and shear waves.

► Present a framework for constructing flux-splitting procedures.
► For the Euler equations this gives rise to two sub-systems.
► New splitting for the Euler equations is presented.
► Numerical methods result from fluxes for each subsystem.
► The new methods are thoroughly tested on problems with reference solutions.