Simulation of incompressible flows around moving bodies using meshless finite differencing

Abstract

A scheme using the mesh-free generalized finite differencing (GFD) on flows past moving solid bodies is proposed. The aim is to devise a method which can be applied to simulate flows past immersed moving bodies with reduced computational effort by eliminating the need to perform remeshing for every time step and the intense interpolation procedures. The generalized finite difference method (GFD) with weighted least squares approximation was used to solve the incompressible Navier Stokes equations under the arbitrary Lagrangian-Eulerian (ALE) formulation, on a stationary background set of Cartesian nodes and a cloud of nodes following each moving solid boundary to simulate flows near the solid-fluid interface. A combination of standard central-spaced finite differencing and GFD is applied to the background region and cloud region respectively as spatial discretization. The second-ordered Crank Nicolson time discretization is applied in the projection method, which computes an intermediate set of velocities and uses the pressure Poisson equation to obtain the divergence-free velocity field. Test cases were performed for workability and accuracy of the method, and satisfactory results were obtained for the driven cavity, the decaying vortex, the flow past circular cylinder and a flapping elliptic body in a square enclosed space.