A multislope MUSCL method on unstructured meshes applied to compressible Euler equations for axisymmetric swirling flows
Résumé
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. In this one, convective fluxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical flux and geometric source terms are discretized by the explicit Euler method. Extension to the second-order space approximation using a multislope MUSCL method is derived. 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 the Riemann problem. Effectiveness of the multislope MUSCL scheme is demonstrated for strongly shocked axially symmetric flows as the forward-facing step and the spherical bubble compression problems.
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