Modeling the motion of pyrolysis gas through charring ablating material using Discontinuous Galerkin finite elements

A series of efforts were made to solve a simple ablation problem with gas motion through the porous media employing finite element based Galerkin and Discontinuous Galerkin methods. First, one-dimensional solutions of Euler and magneto-hydrodynamics (MHD) equations are presented for comparison with analytical results, to validate the code. The spurious oscillations of standard Galerkin approach were mitigated using Discontinuous Galerkin method. We have shown some preliminary results for the ablation problem using both explicit and implicit Discontinuous Galerkin methods in the paper. However an unresolved exit velocity fluctuations to pressure boundary condition, due to which we are not able to go to target time of 5 seconds for this problem. We plan to resolve these issues, and take this code for application of ablation problems in higher dimensions (2-D or 3-D), and bring in plasma application on the surface.