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Comparative study of pressure-correction and Godunov-type schemes on unsteady compressible cases

Abstract : Two pressure-correction algorithms are studied and compared to an approximate Godunov scheme on unsteady compressible cases. The first pressure-correction algorithm sequentially solves the equations for momentum, mass and enthalpy, with sub-iterations which ensure conservativity. The algorithm also conserves the total enthalpy along a streamline, in a steady flow. The second pressure-correction algorithm sequentially solves the equations for mass, momentum and energy without sub-iteration. This scheme is conservative and ensures the discrete positivity of the density. Total enthalpy is conserved along a streamline, in a steady flow. It is numerically verified that both pressure-correction algorithms converge towards the exact solution of Riemann problems, including shock waves, rarefaction waves and contact discontinuities. To achieve this, conservativity is compulsory. The two pressure-correction algorithms and the approximate Godunov scheme are finally compared on cases with heat source terms: all schemes converge towards the same solution as the mesh is refined.
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Frédéric Archambeau, Jean-Marc Hérard, Jérôme Laviéville. Comparative study of pressure-correction and Godunov-type schemes on unsteady compressible cases. Computers and Fluids, Elsevier, 2009, 38, pp.1495-1509. ⟨10.1016/j.compfluid.2008.12.005⟩. ⟨hal-01265395⟩

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