It works perfectly well for irregular nodes using only local quadrature cells for nodes on the natural boundary, which can be generated without any difficulty. Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. An overview on the SPH method and its recent developments is presented, including the need for meshfree particle methods, and advantages of SPH, and several important numerical aspects.

The simulation results are validated by comparing with those of other numerical methods as well as experimental data. The MWS method is then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions.

In this method, the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries the local Petrov-Galerkin weak form is applied only to the nodes on the natural boundaries of the problem domain. This paper formulates the MWS method for the incompressible Navier-Stokes equations that is non-linear in nature. A meshfree weak-strong (MWS) form method has been proposed by the authors' group for linear solid mechanics problems based on a combined weak and strong form of governing equations.

G.r liu 2005 meshfree