A multidimensional fluctuation splitting schemeforthe three dimensional Euler equations

Abstract

The fluctuation splitting schemes were introduced by Roe in the beginning of the80's and have been then developed since then, essentially thanks to Deconinck.In this paper, the fluctuation splittingschemes formalism is recalled. Then, the hyperbolic/elliptic decomposition of thethree dimensional Euler equations is presented. This decomposition leads to an acousticsubsystem and two scalar advection equations, one of them being the entropy advection.Thanks to this decomposition, the two scalar equations are treated with the well knownPSI scalar fluctuation splitting scheme, and the acoustic subsystem is treatedwith the Lax Wendroff matrix fluctuation splitting scheme. Anadditional viscous term is introduced in order to reduce the oscillatory behavior of theLax Wendroff scheme. An implicit form leadsto a robust scheme which enables computations over a large rangeof Mach number. This fluctuation splitting scheme, called the Lax Wendroff - PSI scheme, produceslittlespurious entropy, thus leading to accurate drag predictions.Numerical results obtained with this Lax Wendroff PSI scheme are presented and compared to areference Euler code, based on a Lax Wendroff scheme.