Improved Computational Efficiency of Unsteady Flow Problems via the Modified Wavelet Method

Abstract

A newly modified adaptive wavelet method is proposed to enhance the computational efficiency and to maintain a level of accuracy in unsteady flow calculations that is similar to the conventional schemes. The slim and compressed data set is well adapted to the local features of a solution, and fluxes are only calculated according to this adaptive data set, which results in shorter total computation time. While retaining this advantage, the following methods are applied to the wavelet method. First, residual interpolation is applied and entire residual values are calculated before time integration, and it is therefore not necessary to add several cells to a data set, which were definitely necessary in previous wavelet methods. Second, the threshold value is modified to consider the temporal accuracy as well as the spatial accuracy of the conventional schemes. This modification ensures that the errors caused by the thresholding method do not damage the numerical accuracy of the conventional schemes. The modified wavelet method is successfully applied to the unsteady flow problems and compared with the results of the conventional solvers. In consequence, computing efficiency is enhanced without the deterioration of the solution accuracy.