Extending the Riemann-Solver-Free High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme (DG-CVS) to Solve Compressible Magnetohydrodynamics Equations
Technical Report,01 Mar 2013,31 Mar 2016
JACKSON STATE UNIV MS JACKSON United States
Pagination or Media Count:
In this project, we continue our development of our Riemann-solver-free spacetime discontinuous Galerkin method for general conservation laws to solve compressible magnetohydrodynamics MHD equations. The method is first applied to solve the 3 by 3 MHD model system in the phase space which exactly preserves the MHD hyperbolic singularities. Numerical results show that the method is able to solve the model system correctly, which makes the method very promising in solving the complete ideal MHD equations. The method is then extended to solve the 1-D 7 by7 and 2-D 8 by 8 MHD equations. The Powells approach by adding appropriate source terms is adopted to handle the divergence-free magnetic field condition. Again, the numerical results show that the present method is able to resolve the complex MHD waves without the need of any type of Riemann solvers or other flux functions. The success of solving MHD equations further strengthens our belief that the DG-CVS is an effective approach in solving systems where accurate and reliable Riemann solvers are difficult to design.
- Plasma Physics and Magnetohydrodynamics
- Operations Research