Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

Gao, Song and Habashi, Wagdi G. and Fossati, Marco and Isola, Dario and Baruzzi, Guido S.; (2017) Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids. In: 55th AIAA Aerospace Sciences Meeting. AIAA SciTech Forum . American Institute of Aeronautics and Astronautics Inc, AIAA, USA, pp. 1-28. ISBN 9781624104473 (https://doi.org/10.2514/6.2017-0085)

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Abstract

A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.

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