A multislope MUSCL method on unstructured meshes applied to compressible Euler equations for swirling ows

A nite volume method for the numerical solution of axisymmetric inviscid swirling ows is presented. The governing equations of the ow are the axisymmetric compressible Euler equations including swirl (or tangential) velocity. A rst-order scheme is introduced. In this one, convective uxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical ux 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 uid ow 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 ows as the forward-facing step and the spherical bubble compression problems.