WAMR: An adaptive wavelet method for the simulation of compressible reacting flow. Part I. Accuracy and efficiency of algorithm

The Wavelet Adaptive Multiresolution Representation (WAMR) method provides a robust method for controlling spatial grid adaptation — fine grid spacing in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Subsequently, a wide range of spatial scales, often demanded in challenging continuum physics problems, can be efficiently captured. Furthermore, the wavelet transform provides a direct measure of local error at each collocation point, effectively producing automatically verified solutions.The method is applied to the solution of unsteady, compressible, reactive flow equations, and includes detailed diffusive transport and chemical kinetics models. Accuracy and performance of the method are examined on several test problems. The sparse grids produced by the WAMR method exhibit an impressive compression of the solution, reducing the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution.