WAVELET ADAPTIVE MULTIRESOLUTION REPRESENTATION: APPLICATIONS TO VISCOUS MULTISCALE FLOW SIMULATIONS

摘要

We present a new wavelet-based adaptive multiresolution representation (WAMR) algorithm for the numerical solution of multiscale evolution problems, Key features of the algorithm are fast procedures for grid rearrangement, computation of derivatives, as well as the ability to minimize the degrees-of-freedom for a prescribed solution accuracy. To demonstrate the efficiency and accuracy of the algorithm, we use it to solve the two-dimensional benchmark problem of incompressible fluid-flow in a lid-driven cavity at large Reynolds numbers. The numerical experiments demonstrate the great ability of the algorithm to adapt to different scales at different locations and at different times so as to produce accurate solutions at low computational cost. Specifically, we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees-of-freedom.