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. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. The simulation results are validated by comparing with those of other numerical methods as well as experimental data. This meshfree method is based on a partition of unity concept and formulated for geometrically non-linear problems. 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.

Meshfree methods in solid mechanics