Pyrolysis gas flow in thermally ablating media using time- implicit discontinuous Galerkin methods

In this work, we apply time-implicit discontinuous Galerkin methods to the problem of thermal ablation, where we solve for the dynamics of flow of pyrolysis gas in a charring ablating media. We have benchmarked our results with the published data. The protective coating of thermal protection system over the space vehicle is of the order of a few centimeters, and high flow speed of gas and dominant source terms in the problem put very restrictive CFL limit necessitating the use of implicit time integration methods. Good convergence of these methods is ensured by use of #ewton method, where the required jacobians are calculated numerically for accurate evaluations. Analytical approach to evaluate the jacobians, especially for thermal ablation problems, is very cumbersome, and causes serious convergence issues. We have also tested our development of DG capability for 2-D double Mach reflection problem for extending the code to 2-D thermal ablation in future.