Solution of the heterogeneous thin flame problem using an exponential scale transformation

The scale transformation x=exp(Bx')-1 is implemented in the solution of the one dimensional heterogeneous thin flame problem. A preliminary analysis of the steady state problem indicates the possibility of adjusting the parameter B to the particular combustion configuration under study. Numerical solutions of steady states are computed for a wide range of operating conditions and physico-chemical properties of the burning material (solid rocket propellant); satisfactory agreement with the corresponding analytical solutions (if available) is found by selecting appropriate values of B. The initial value problem is numerically integrated in order to simulate extinction transients and self-sustained oscillatory combustion. Computations with exponential scaling are found to be superior in terms of efficiency (for comparable accuracy) to computations using linear scale. In particular, the required number of nodes in the space grid can be one order of magnitude smaller using exponential scale, with a corresponding reduction of both computer core and execution time.