Efficiency enhancement in high order accurate euler computation via AWM

Abstract

An adaptive wavelet method is proposed to achieve an efficient algorithm with maintaining numerical accuracy of a conventional solver in case of high order accurate Euler computations. Due to wavelet transformation including wavelet decomposition and thresholding, dataset is automatically adapted to local features of a solution. Then, the flux values are calculated only at the adapted dataset, which enables the enhancement of the computational efficiency. For maintaining the higher order accuracy of a conventional solver, threshold value is adjusted to consider the spatial and temporal accuracies. Through this threshold value, the deterioration of the numerical accuracy due to thresholding is obstructed and the wavelet method can present high order accurate solutions. The adaptive wavelet method was successfully applied to high order accurate Euler flow computation. In consequence, computational efficiency was enhanced while maintaining the higher order numerical accuracy of a solution. © 2011 Springer-Verlag Berlin Heidelberg.