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TitleMultislope MUSCL method for unstructured meshes applied to the compressible axisymmetric Euler equations for swirling flows
Author(s)Clain, Stéphane
Rochette, D.
Touzani, R.
KeywordsEuler system
MUSCL method
Issue dateJul-2010
JournalJournal of Computational Physics
Citation"Journal of Computational Physics". ISSN 0021-9991. 229:10 (July 2010) 4884-4906.
Abstract(s)A finite volume method for the numerical solution of axisymmetric inviscid swirling flows is presented. The governing equations of the flow are the axisymmetric compressible Euler equations including swirl (or tangential) velocity. A first-order scheme is introduced where the convective fluxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical flux while the geometric source terms are discretizated to provide a well-balanced scheme {\it i.e.}, the steady-state solutions with null velocity are preserved. Extension to the second-order space approximation using a multislope MUSCL method is then derived. To test the numerical scheme, a stationary solution of the fluid flow following the radial direction has been established with a zero and non-zero tangential velocity. Numerical and exact solutions are compared for classical Riemann problems where we employ different limiters and effectiveness of the multislope MUSCL scheme is demonstrated for strongly shocked axially symmetric flows like in spherical bubble compression problem. Two other tests with axisymmetric geometries are performed: the supersonic flow in a tube with a cone and the axisymmetric blunt body with a free stream.
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Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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