关键词: 间断有限元, 高阶格式, Euler方程, 稀疏网格, Newton-GMRES

Abstract:

A high-order discontinuous galerkin (DG) method is used to solve the 2-D Euler equations on unstructured grids. Numerical results indicate that highly accurate solutions can be obtained using high-order DG and real solid boundary conditions even on very coarse grids. Besides, preconditioning is not necessary when using high-order DG for very low Mach flows. Since a good initial guess is required when Newton-generalized minimal residual method (Newton-GMRES) is used, a hierarchic iteration procedure is developed to improve the robustness of relaxation.

Key words: discontinuous galerkin, high-order scheme, Euler equations, coarse grids, Newton-GMRES