The meshless local Petrov-Galerkin method for simulating unsteady incompressible fluid flow

This article presents a numerical algorithm using the Meshless Local Petrov-Galerkin (MLPG) method for the incompressible Navier–Stokes equations. To deal with time derivatives, the forward time differences are employed yielding the Poisson’s equation. The MLPG method with the moving least-square (MLS) approximation for trial function is chosen to solve the Poisson’s equation. In numerical examples, the local symmetric weak form (LSWF) and the local unsymmetric weak form (LUSWF) with a classical Gaussian weight and an improved Gaussian weight on both regular and irregular nodes are demonstrated. It is found that LSWF1 with a classical Gaussian weight order 2 gives the most accurate result.