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The Discontinuous Galerkin Method (DGM) is an important numerical method in computational fluid dynamics. The characteristics of DGM include its flexibility to construct high order schemes by using high order basis functions, and its compactness regardless of basis function order. In supersonic simulations, the DGM often produce severe oscillations in regions where strong discontinuity solutions appear, so the slope limiters become necessary. In this study, three slope limiters are considered: TVB limiter, WENO limiter and HWENO limiter. The performance of these limiters are compared and analyzed in two dimensional supersonic flows. The results of test problems show that all these limiters are able to stabilize the solution procedure, but the solutions show some differences between these limiters. Explanations as well as possible improvements are given.

computation; numerical methods; supersonic flow; discontinuous galerkin method