Numerical prediction of one-dimensional ablation using a finite control volume procedure with exponential differencing
The exponential differencing scheme of Spalding, which has been used for convection problems, is adapted to solve one-dimensional ablation problems by using a grid attached to the receding surface. Using the finite control volume approach, element conduction, convection, and storage matrices are developed. The method is applied to a steady-state ablation problem for which an analytical solution is known; comparisons are also made with upwind differencing for the convection terms and central differencing for the conduction terms. An example of a realistic ablation problem is presented.