High-order composite finite volume schemes with arbitrary order physically admissible non linear reconstruction

  • Hoch, Philippe (CEA)

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We deal with extension of the finite volume classical ARS (Approximate Riemann Solver) for two dimensionnal conservation laws: ∂t U + div F (U ) = 0. The flux F is considered as a linear or a nonlinear function of the conservative states U. We have proposed a nodal definition of some of classical ARS (Roe, VFFC, Rusanov, ..) defined at edge. Each of such nodal/composite scheme is consistent and locally conservative. The definition of composite flux at edges is the same than the classical edge solver. We propose an arbitrary order composite finite volume scheme with a nonlinear physically admissible (arbitrary order) reconstruction. For Euler equations of compressible gas dynamics (with a perfect gas law), the limitation of density and internal energy induced the limitation for the velocity. We show some comparison on second, third and fourth order schemes to asses the accuracy and robustness of the approach.