An adaptive algorithm for compressible reacting flows using interpolating wavelets

Abstract

A new wavelet-based method for the simulation of reacting flows on adaptive meshes is presented. The method is based on the removal of grid points whose wavelet coefficients are small with reference to some user-specified threshold. Unlike some other collocation methods, 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. The wavelet transformis based on a subtraction algorithm, and circumvents the hanging node problem associated with other adaptive strategies. Interpolating wavelets are applied to a compressible one-dimensional laminar flame problem with time dependent boundary conditions. We find that the resolution of the chemistry distribution is comparatively straightforward. The same is not true of the pressure field, which demonstrates sensitivity to the imposed threshold level. Conclusions and directions for future work are presented based on these findings.