Abstract
In this study, we aim to construct a finite difference method, which spatially and temporally conserves the kinetic energy, for the vorticity equation on the two-dimensional flow field. In order to achieve the temporal kinetic energy conservation, a space-time staggered grid is used for the discretization of governing equations and implicit mid-point rule is applied to the time integration. The method is applied to simulate a two-dimensional viscous flow, known as a lid-driven cavity flow, under the non-periodic boundary condition. The solution methods for the Krylov iteration in the Jacobian-Free Newton-Krylov method are investigated. The results show that the Jacobian-free Newton-Krylov method with SOR method is much faster than the method with the GMRES method for the Krylov iteration.
