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 stencil to define the vorticity boundary condition (whether boundary condition is defined on time step n+1 or n+1/2) does not affect the simulation results. However, the initial value of vorticity strongly affects the simulation results when the vorticity boundary condition is defined on time step n+1/2 and the initial value of vorticity set to zero over whole computational domain. As the countermeasure, the necessary of the boundary condition imposed to the vorticity at initial time is clarified. In addition, the results of the evaluations for numerical stability of time integration show higher stability of time integration scheme which uses a space-time staggered grid and implicit mid-point rule, demonstrating the stabile calculations at high diffusion numbers.
