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A multidimensional fluctuation splitting scheme for the three-dimensional Euler equations. (English) Zbl 0968.76034
Summary: First, we recall the fluctuation splitting scheme formalism. Then we present the hyperbolic/elliptic decomposition of three-dimensional Euler equations. This decomposition leads to an acoustic subsystem and two scalar advection equations, one of them being the entropy advection. Thanks to this decomposition, the two scalar equations can be treated with the well-known PSI scalar fluctuation splitting scheme, and the acoustic subsystem can be treated with the Lax-Wendroff matrix fluctuation splitting scheme. We introduce an additional viscous term in order to reduce the oscillatory behavior of the Lax-Wendroff scheme. An implicit form leads to a robust scheme which enables computations over a large range of Mach number. This fluctuation splitting scheme, called the Lax-Wendroff-PSI scheme, produces little spurious entropy, thus leading to accurate drag predictions. Numerical results obtained with this Lax-Wendroff-PSI scheme are presented and compared to a reference Euler code, based on a Lax-Wendroff scheme.
MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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