A novel stabilized Galerkin meshless method for steady incompressible Navier–Stokes equations

Abstract

In the paper, a novel stabilized meshless method is presented for solving steady incompressible fluid flow problems. For this method, the standard Galerkin discretization is used to momentum equations, where the variational multiscale method is applied to mass conservation equation. Thus, the novel stabilized method can be regarded as a simplification of the variational multiscale element free Galerkin method, but it still retains the advantages of the variational multiscale element free Galerkin method. The present method allows equal linear basis approximation of both velocity and pressure and avoids the Ladyzhenskaya–Babuška–Breezi(LBB) condition. Meanwhile, it can automatically obtain the stabilization tensor. Three Stokes flow and two Navier–Stokes flow problems are applied to validate the accuracy and feasibility of the present method. It is shown that the present stabilized meshless method can guarantee the numerical stability and accuracy for incompressible fluid flow problems. Moreover, it can save computational cost evidently compared with variational multiscale element free Galerkin method.