The Application of Adaptive Wavelet Method to Multi-Dimensional Limiting Process for Enhancement of Computational Efficiency

An adaptive wavelet method is applied in order to enhance the computational efficiency of enhanced Multi-dimensional Limiting Process (e-MLP) without deterioration of the numerical accuracy of original Computational Fluid Dynamics (CFD) scheme. For this purpose, higher order of adaptive wavelet method is constructed including higher order of wavelet decomposition and modified thresholding. Besides, the locations of crucial features such as shock, vortex core, etc. are automatically and accurately searched in the CFD dataset through wavelet transformation. Only on these locations, high order spatial interpolation scheme with e-MLP are performed; in the other locations, interpolation method is utilized to compute residual values, which reduces the computational time of flux evaluation. This high order adaptive wavelet method was applied to unsteady Euler flow computations such as shock-vortex interaction problem. Throughout these processes, it was verified that computational efficiency was enhanced with preservation of numerical accuracy of CFD solver.