Abstract: The discontinuous finite element method with first, second and third order accuracy on triangular meshes on two-dimensional domain is applied to simulate hydrodynamic equations. The calculation results are compared with those from difference methods. It is reckoned that the discontinuous finite element method has advantages in solving hydrodynamic problems with complicated boundary conditions or a domain with a complicated boundary.

Key words: triangular mesh, discontinuous finite element method, wind tunnel with a step, double Mach reflection of a strong shock