A new stability parameter in streamline upwind meshless Petrov–Galerkin method for convection–diffusion problems at large Peclet number

Abstract

The numerical oscillation will occur in convection–diffusion equations as special linear problems at large Peclet number (Pe) in the numerical calculation process. In this article, we propose a new definition of the stability parameter in streamline upwind meshless Petrov–Galerkin (SUMLPG) method. The most important feature of the proposed method is that the test function in the stabilization term is taken into the differential operator-like form $v^{*}=v+\tau L_{\text{adv}}v.$ The stability parameter $\tau$ is designed to adjust the convection strength to achieve accurate and stable numerical solutions. Several classical examples are adopted to assessment the accuracy and stability of the proposed stability parameter. It is proven that the proposed method is especially suitable for convection–diffusion problems with large Pe.

Additional information

Funding

This work is supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 51721004) and the 111 Project of China (B16038).