Modeling the Motion of Pyrolysis Gas Through Charring Ablating Material Using Discontinuous Galerkin Finite Elements

Abstract

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.

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

“…Our initial attempt was at getting the analytical expressions of the Jacobians. We have already demonstrated complexity and limitations that abound analytical approach to evaluate jacobians in [24] and [28]. To summarize, approach of evaluating analytical expressions is very cumbersome, and has convergence and stability problems for thermal ablation.…”

“…The properties are expressed as a function of temperature and gas density. Further details on thermo-chemical modeling used in CANTERA were already discussed in our earlier paper, [24]. We have used two curve fits for internal energy, e g (see Fig.…”