Shock detection and limiting with discontinuous Galerkin methods for Euler equations on unstructured mesh

摘要

The purpose of this paper is to simulate therntransonic steady-state flows with therndiscontinuous Galerkin finite element methodrnwhich is very sensitive to the spuriousrnoscillations. In this article, a strategy forrncombining the discontinuous detector andrnlimiter is employed to suppress the spuriousrnoscillations near such discontinuities. Therndiscontinuous detector is based on physicicalrncharacters of shock waves which can effectivelyrndistinguish a smooth extremum and a shockrnwave; Limiter is followed by Barth andrnJespersen's monotonic limiter which is onlyrnused to modify the solutions slope of therndetected regions to ensure the solution beingrnmonotonic. Numerical simulation for both 2Drnand 3D Euler Equations are presented torndemonstrate the accuracy of the developedrndiscontinuous Galerkin method. The resultsrnshow that the detector can effectively identifyrnthe discontinuous regions and the limiter canrneffectively suppress the spurious numericalrnoscillations. Moreover, DG method has lessrnnumerical dissipation and excellent ability torncapture shocks compared with the finite volumernmethod with the same accuracy order.