Finite element simulation of the transonic-supersonic inviscid circleflow field and MHD flow field

In this paper, we use Streamline-Upwind/ Petrov-Galerkin (SUPG) finite element method and isotropic diffusion method with the ability of capturing shock to solve the compressible Euler equations. The adaptive mesh refinement technique in this simulation improves the accuracy of calculation. Numerical experiments verify the feasibility of the method. Using the above method for MHD (Magnetohydrodynamics)equations, we introduce hyperbolic divergence cleaning technique to overcome the difficulties of numerical calculation for magnetic field divergence on unstructured grid. Finally, we propose good numerical simulation for the MHD shock tube. (authors)