A meshless local Petrov-Galerkin approach for solving the convection-dominated problems based on the streamline upwind idea and the variational multiscale concept

摘要

A meshless local Petrov-Galerkin (MLPG) approach based on the streamline upwind (SU) idea and the variational multiscale (VMS) concept, called as VMS-SUMLPG method, is herein proposed to solve the convectiondominated problems. In the present VMS-SUMLPG method, the streamline upwind is constructed in the test function to solve the non-self-adjoint matrix. Meanwhile, the VMS concept as a stability term is adopted to alleviate the numerical instability such as spurious oscillations, overshoots, and undershoots. Its numerical accuracy and stability are validated by comparing with the streamline upwind Petrov-Galerkin (SUMLPG) method and the finite volume method with high-order difference schemes for two classical convection-dominated problems at the Peclet number ranging from 106 to 108. It is shown that the numerical solutions of the present VMS-SUMLPG method are accuracy, smoothness, and stability.