Spectral difference method with a posteriori limiting: application to the Euler equations in one and two space dimensions

We present a new numerical scheme which combines the Spectral Difference (SD) method up to arbitrary high order with \emph{a-posteriori} limiting using classical MUSCL-Hancock as fallback scheme. It delivers very accurate solutions in smooth regions of flow, while capturing sharp discontinuities without spurious oscillations. exploit strict equivalence between SD and Finite-Volume (FV) based on control volumes enable straightforward strategy. At end each stage our high-order time-integration ADER scheme, we check if solution is admissible under number physical criteria. If not, replace fluxes troubled cells by from robust second-order MUSCL apply suite test problems for 1D 2D Euler equations. demonstrate that this combination provides virtually accuracy, at same time preserving good sub-element shock capabilities.