Open Access

ARTICLE

On the Application of Wavelets to One Dimensional Flame Simulations with Non-Unit Lewis Numbers

R. Prosser¹

1 Department of MACE, University of Manchester, Manchester M60 1QD

Fluid Dynamics & Materials Processing 2009, 5(4), 411-424. https://doi.org/10.3970/fdmp.2009.005.411

Abstract

A novel wavelet-based method for the simulation of reacting flows on adaptive meshes is presented. The method is based on a subtraction algorithm, wherein the wavelet coefficients are calculated from the low resolution up (as opposed to the standard top-down approach). The advantage of this new method is that it allows the calculation of wavelet coefficients on sparse grids, and thus lends itself more readily to adaptive computational meshes than does the traditional wavelet algorithm. The approach is used to simulate a one-dimensional laminar pre-mixed flame with different Lewis numbers. The computational grid is adapted via the removal of grid points whose wavelet coefficients are small with reference to some user-specified threshold. To circumvent the difficulties associated with the strongly nonlinear reaction rate terms, the scheme simulates flow behaviour in the physical (i.e. not transformed) domain, and the wavelets thus provide the method by which the derivatives appearing in the transport equations are calculated. A number of simulations are presented which demonstrate the efficiency of the method.

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