Spatiotemporal Compound Wavelet Matrix Framework for Multiscale/Multiphysics Reactor Simulation: Case Study of a Heterogeneous Reaction/Diffusion System

We present a mathematical method for efficiently compounding information from different models of species diffusion from a chemically reactive boundary. The proposed method is intended to serve as a key component of a multiscale/multiphysics framework for heterogeneous chemically reacting processes. An essential feature of the method is the merging of wavelet representations of the different models and their corresponding time and length scales. Up-and-downscaling of the information between the scales is accomplished by application of a compounding wavelet operator, which is assembled by establishing limited overlap in scales between the models. We show that the computational efficiency gain and potential error associated with the method depend on the extent of scale overlap and wavelet filtering used. We demonstrate the method for an example problem involving a two-dimensional chemically reactive boundary and first order reactions involving two species.