上风式LRPIM求解对流占优问题的影响因素分析

为提高对流扩散问题中对流项占优时的数值稳定性,采用局部上风式权函数,在局部径向基点插值无网格法(LRPIM)基础上构建了上风式局部径向基点插值无网格法(ULRPIM).将其与LRPIM方法的对流占优问题计算结果进行比较,发现ULRPIM能够得到更好的结果.通过对比不同参数时ULRPIM计算结果的相对误差,研究了各个参数对数值结果稳定性的影响规律.结果表明:权函数的偏置量需要随着对流强弱而变化,径向基函数(RBF)参数q、支持域尺寸对计算结果的影响比较大,RBF参数a_c、Gauss积分子域数对计算结果的影响相对较小.

Analysis of Factors Influencing the Solving of Convection-Dominated Problems by Means of Upwinding LRPIM

In order to improve the numerical stability during the solving of convection-dominated convection-diffusion problems, an upwinding local radial point interpolation method (ULRPIM) is proposed based on the local radial point interpolation method (LRPIM) and the local upwinding weight function. The proposed method is then compared with the LRPIM through some numerical calculations, finding that ULRPIM achieves better results. Moreover, the influences of different parameters on the stability of calculation results are investigated by comparing the relative errors of ULRPIM results at different parameters. It is found that the offset of weight function should change with the Peclet number, and that both the parameter q of radial basis functions (RBF) and the size of the support domain have a greater influence on the calculation results than the RBF parameter a_c and the quantity of Gauss integral points.