Meshfree point collocation method for the stream-vorticity formulation of 2D incompressible Navier-Stokes equations

Abstract

Meshfree point collocation method is developed for the stream-vorticity formulation of two-dimensional incompressible Navier-Stokes equations. Particular emphasis is placed on the novel formulation of effective vorticity condition on no-slip boundaries. The moving least square approximation is employed to construct shape functions in conjunction with the framework of point collocation method. The derivatives of an arbitrary function can be obtained by the linear combination of these shape functions, which enables the vorticity boundary condition to vary linearly with the boundary velocity and the stream function. Together with the second-order partial differential equations for the stream and vorticity functions, this boundary condition of vorticity provides the efficient meshfree point collocation scheme for the two-dimensional incompressible flow. The accuracy and stability for the proposed scheme are demonstrated through a new type of application problem with complex geometry, in addition to several typical examples of steady-state flow simulation.