Numerical simulation of edge flames initiation and propagation using an adaptive wavelet collocation method

Abstract

We use an adaptive wavelet collocation method to estimate the number of space computational modes, N, necessary to describe the initiation and propagation of hydrogen edge flames, considering detailed chemistry. Indeed, it has been shown in the literature that the temporal behavior of the projection of exact solutions of dissipative evolution equations on the finite-dimensional space of interpolant polynomials determines the time behavior of the solution itself, provided that the spatial mesh is sufficiently fine. The adaptive wavelet method, based on interpolating wavelets, provides a means to directly adjust the spatial resolution according with the local demands of the physical solution and the desired accuracy. The results show that the computational modes provided by the wavelet method properly describe the spatial and temporal evolution of the flame structure. They also show that the data-compression properties of the wavelet scheme yields verified solutions with large savings in storage requirements.