关键词: 对流占优, 上风式, 局部径向基点插值法, 稳定性

Abstract:

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. Mo- reover, 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 ac and the quantity of Gauss integral points.

Key words: convection domination, upwinding, local radial point interpolation method, stability