Artificial viscosity-based shock capturing scheme for the Spectral Difference method on simplicial elements.

An artificial viscosity-based shock capturing scheme is extended to the context of high-order triangular Spectral Difference method for solving gas dynamics problems featuring discontinuities and shock waves. The equations are regularised thanks to an artificial diffusivity method combined with a shock sensor based on dilatation and vorticity fields valid for any polynomial order of approximation. The methodological novelty of this paper is an L 2 projection based iterative Restriction Prolongation filtering operation introduced for high-order triangular elements. This filtering operation applied to the artificial bulk viscosity and thermal conductivity stabilises the simulations and improves the quality of the shock capturing approach. The methodology is validated on various canonical relevant compressible test cases. Numerical results demonstrate the performance and the flexibility of the triangular high-order Spectral Difference method for solving simultaneously compressible flows and shock waves. [ABSTRACT FROM AUTHOR]