A numerical analysis of two dimensional lid driven cavity flow using cubic interpolated pseudo-particle method

Abstract

The Finite Different Navier Stokes equation (FDNSE) and Cubic Interpolated Pseudo-Particle Navier Stokes equation (CIPNSE) are applied to simulate the 2-D square lid driven cavity flow of water at Reynolds numbers 100, 400 and 1000. CIPNSE scheme solves hyperbolic type equations which is the vorticity transport equation In the CIPNSE, the gradient and the value of the vorticity at the nodes is determined and the stream function is then determined using the vorticity equation. It is discovered that the numerical simulation of CIPNSE provided a very good agreement with the established ‘benchmark’ results by Ghia et. al. but is slightly less accurate compare to FDNSE. The flow structure of 2-D shallow lid driven cavity flow of water at Reynolds numbers has been studied numerically using CIPNSE and compared with FDNSE and Ghia result which show good agreement. The location of the primary and secondary vortex also settled at the same place. For shallow cavity flow, both streamline pattern using FDNSE and CIPNSE show concluding remarks compare to CIPLBM. On top of that, the accuracy of CIPNSE and FDNSE are compared based on Ghia result within the midsection velocity profile where minor differences of accuracy are demonstrated for CIPNSE. On the other hand, both midsection velocity for CIPNSE and FDNSE show tiny differences compare to FDNSE and Constrained Interpolation Profile Lattice Boltzmann Method (CIPLBM). Yet CIPNSE is practical in simulating two dimensional lid driven cavity.