Improvement in Computational Efficiency of Euler Equations Via a Modified Sparse Point Representation Method

Abstract

A modified Sparse Point Representation (SPR) method is proposed to enhance the computational efficiency of Euler equations. A SPR dataset adapted to a solution is constructed through interpolating wavelet decomposition and thresholding. The fluxes are evaluated only at the points within a SPR dataset, which reduces the total computing time. In order to improve the overall efficiency and accuracy of the SPR method in a steady-state calculation, the following three techniques are applied: First, the threshold method is modified so as to maintain the spatial accuracy of a conventional solver by switching between a threshold value and the order of magnitude of a spatial truncation error. Second, a stabilization technique is added to improve the compression ratio of the SPR method by keeping numerical errors due to the thresholding from being inserted into the computational domain. Third, if the variations of flow variables in a time integration step are below the order of a threshold value at the points excluded from a SPR dataset, then the tiny variations are restricted by adopting a weighting factor. The modified SPR method was applied to two-dimensional steady Euler equations and it was confirmed that their efficiency and convergence were greatly enhanced without compromising the accuracy of the solution when compared to a conventional solver.