On the Use of Wavelets in Computational Combustion

The numerical simulation of combustion remains a challenging task. Flames are often thin and occupy a relatively small volume within the domain of interest. Nevertheless all of the combustion chemistry and much of the associated molecular transport takes place within the flame itself, giving rise to a structure that must be resolved if the simulated flame response is to be captured accurately. The present work examines the use of a wavelet-based method in this context. A spatial discretisation scheme using biorthogonal wavelets is presented and is applied to a test problem involving flame propagation in a representative fuel?air mixture, in which the chemistry is treated using a standard four-step reduced reaction mechanism. A novel and elegant boundary treatment is adopted in the wavelet scheme to enable the implementation of physically realistic boundary conditions. Results show that the wavelet scheme is stable and accurate and, moreover, is able to exploit the natural data-compression properties of wavelets to represent the solution using a fraction of the storage required for more conventional methods.