Assessment of two pressure-velocity coupling strategies for local meshless numerical method

Abstract

The performance of two pressure-velocity coupling strategies, associated with the primitive variable solution of incompressible Newtonian fluid with the meshless Local Radial Basis Function Collocation Method (LRBFCM), is compared with respect to computational efficiency, stability, accuracy and spatial convergence. The LRBFCM is structured with multiquadrics on five noded support domains. The explicit time stepping is used. The Backward- Facing Step problem (BFS) has been selected as a benchmark problem, previously tackled by several numerical methods. The semi-local fractional step method (FSM) and completely local pressure-velocity couplings (LPVC) are compared. The numerical results are validated against previously published data. The results are represented and compared in terms of a convergence plot of the reattachment position. We show that both approaches provide reasonable results; however, LVPC is less computationally complex and less stable in comparison to FSM. © 2012 WIT Press.