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 homogenous isotropic turbulence. The simulation results show that the method can conserve the total amount of kinetic energy regardless of the time interval, clarifying the usefulness of the method. In addition, the solution methods for the nonlinear simultaneous equations which are obtained from the discretized equations are investigated. The results show that the SOR method is much faster than the Jacobian-free Newton-Krylov method with the GMRES method for the Krylov iteration.
