Variational Multiscale Element-Free Galerkin Method and Precise Time Step Integration Method for Convection–Diffusion Problems

To simulate the convection-diffusion problems and improve the computational efficiency of Galerkin meshless methods, an explicit algorithm that combines variational multiscale element-free Gakerkin method with precise time step integration is presented. Variational multiscale element-free Gakerkin method is used to overcome the numerical spurious oscillations for convection-dominated problems; meanwhile in order to save the computational time, the precise time step integration method is adopted for the solution of the ordinary differential equations. Two numerical examples are considered to demonstrate the stability, accuracy, and computational efficiency of the method. The numerical results illustrate that the presented method not only has high calculation accuracy, but also brings a significant computational time saving for solving the unsteady convection-diffusion problems.