Accuracy analysis of super compact scheme in non-uniform grid with application to parabolized stability equations

摘要

A brief derivation of the super compact finite difference method (SCFDM) in non-uniform grid points is presented. To investigate the accuracy of the SCFDM in non-uniform grid points the Fourier analysis is performed. The Fourier analysis shows that the grid aspect ratio plays a crucial role in the accuracy of the SCFDM in a non-uniform grid. It is also found that the accuracy of the higher order relations of the SCFDM is more sensitive to grid aspect ratio than the lower order relations. In addition, to obtain a mathematical representation of the accuracy and making clear the role of the aspect ratio in the accuracy of the SCFDM in non-uniform grids, the modified equation approach is used. For the sake of demonstrating the analytical results obtained from the Fourier analysis and the modified equation approach, the super compact finite difference method is applied to solve the Blasius boundary layer and the non-linear parabolized stability equations as numerical examples indicating the difficulty with non-uniform grid spacing using the super compact scheme. Copyright (C) 2004 John Wiley Sons, Ltd.