Numerical studies of laminar flame propagation in spherical bombs

Abstract

A reaction-diffu sion equation which has an exact traveling wave solution is used to characterize the accuracy of nine finite difference schemes. These schemes are then applied to study the propagation of a laminar flame in a spherical bomb where chemistry is modeled by a one-step Arrhenius-type reaction. The numerical schemes evaluated include an implicit predictor-corrector method, a quasilinear algorithm, a majorant operator splitting technique, two methods of lilies, a linear block tridiagonal procedure, and the standard explicit, implicit, and Crank-Nicolson methods. The numerical results indicate that the most accurate scheme is the fourth-order method of lines whose efficiency is comparable to that of the most efficient explicit algorithm.