Evaluating the Accuracy of a Grid Singularity Strategy using External Verification Analysis

摘要

Computational Aeroacoustics codes require highly accurate numerical schemes to resolve and propagate acoustics disturbances over long distances. Because of the relative ease with which high-order and optimized schemes can be developed for it, the finite difference method is frequently used in CAA. To apply the finite difference method to complex geometry and to promote good parallel performance, grids used with the finite difference method are decomposed into blocks. This often results in the formation of grid singularities. Grid singularities are grid points in the calculation with an "abnormal" number of adjacent points, i.e., points that do not have four (for two dimensions) or six (for three dimensions) neighbors. The correct way of evaluating the spatial derivatives of the governing equations at and near grid singularities is an open question. This work proposes to use External Verification Analysis, a code-independent verification technique, to evaluate the error of a nonlinear Euler CAA code solver using singular grids. Two-dimensional results are presented for three-way and five-way grid singularities and two spatial differencing schemes.