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

Stéphane Clain (1) , David Rochette (2) , Rachid Touzani (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAEPT - Laboratoire arc électrique et plasmas thermiques
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Swirling flow; Axisymmetric compressible Euler equations; MUSCL method; Unstructured mesh; Finite volumes

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]

Stéphane Clain, David Rochette, Rachid Touzani. A multislope MUSCL method on unstructured meshes applied to compressible Euler equations for axisymmetric swirling flows. Journal of Computational Physics, 2010, 229 (13), pp.4884-4906. ⟨10.1016/j.jcp.2010.03.004⟩. ⟨hal-00340087⟩