Application of moving grid control volume finite element method to ablation problems

This article presents the solution of two-dimensional axisymmetric ablation problems with unstructured grids. The energy equation is formulated and solved using the control volume finite element method. The exterior shape of the ablating body is determined from a surface energy balance with the interior mesh displaced in response to the surface ablation as if the body was a linear elastic solid. Boundary condition matrices are formulated for both heat of ablation and generalized thermochemical ablation boundary conditions. Computed recession rates are compared to an analytical solution to demonstrate the accuracy and convergence of this approach. Additionally, the practical application of this approach to the ablation of a re-entry vehicle nose tip is presented.