上风式LRPIM求解对流占优问题影响因素分析

为处理对流扩散问题中对流项占优时的数值稳定性问题,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对比,发现ULRPIM能够得到比较好的结果.通过一维对流占优问题实例对比了不同影响因素下ULRPIM计算结果的相对误差,研究了影响因素对数值结果的稳定性的影响规律,给出了ULRPIM方法求解对流占优问题求解过程中的参数选取的参考值.结果表明:权函数的偏置量需要随着对流程度而变化,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ac、Gauss积分点数量对计算结果的影响相对较小.因此,为获得稳定的数值计算结果,应首先考虑权函数偏置量的选取,然后根据具体计算实例选取合适的支持域尺寸、RBF参数和Gauss积分点数量.

Upwinding LRPIM for Convection Dominated Problems

In order to deal with the numerical stability of convection dominated problems, using the local upwinding weight function, the upwinding local radial point interpolation method (ULRPIM) is proposed based on the local radial point interpolation method (LRPIM), and were then compared with those numerical results of the LRPIM. The ULRPIM gives very good results. Moreover, some examples in one-dimension were performed to reveal the influence of parameters on relative error. The results indicate that, the optimal offset of weight function increase with the increase of Peclet number, the parameter of the radial basis functions (RBF) q and the size of the support influence the results greatly. It is thus concluded that prior consideration for suitable offset of weight function helps to obtain stable numerical results , the other parameter is chosen accordant to the actual situation.