A characteristic-based split meshless local Petrov–Galerkin method for unsteady three-dimensional incompressible fluid flow

Abstract

A meshless local Petrov–Galerkin (MLPG) method has been developed for solving 3D incompressible isothermal laminar flow problems. It is derived from the local weak form of the Navier–Stokes equations by using the general MLPG concept. By incorporating the multi quadrics radial basis function (MQ-RBF) approximations for trial functions, the local weak form is discretized, and is integrated over the local subdomain for the unsteady incompressible fluid flow analysis. The present numerical technique uses characteristic-based split algorithm to solve Navier–Stokes equations in terms of primitive variables. A test case of lid-driven cavity flow is presented. The numerical procedure produces stable solutions with results comparable to those of other conventional methods.