The theoretical development of wavelets in reacting flows

This paper focuses on the simulation of turbulent reacting flows via recent developments in wavelet-based analyses. The unique data compression properties of wavelet methods render them especially attractive for such simulations, in which the length and time-scales of interest originate from both physical and chemical processes and may span several orders of magnitude. The particular difficulties encountered when representing reacting flow problems on non-periodic domains, and how these difficulties have led to the adoption of a biorthogonal wavelet framework, are discussed. This leads to consideration of interpolating wavelet transforms based on second-generation wavelets, for which a fast transform algorithm is presented. Issues raised by the application of wavelet transform methods to the reacting Navier-Stokes equations, including the calculation of differential operators, the extension to two and three dimensions and the evaluation of non-linear terms, are examined. The implications of the wavelet approach for the representation of the turbulent energy cascade are explored briefly. Finally, some future directions for research into the extension of wavelet analysis as an underpinning technology for computational fluid dynamics are indicated.