Abstract
This study concerns conservative properties of the kinetic energy in two-dimensional incompressible flow simulations using the vorticity equation. A procedure which derives the conservation equation for the kinetic energy from the inviscid vorticity equation is analytically considered and then the procedure is formulated discretely. In the procedure, the vorticity equation multiplied by stream-function is integrated (or summed discretely) over the computational domain under the periodic boundary condition and the Green's second identity and the Gauss's divergence theorem are applied to deform the equation. When the identity and the theorem are formed discretely, the total amount of kinetic energy is conserved discretely in time. Hence formulations of fully consistent discretized forms (referred to as "appropriate" form) for the identity and the theorem are necessary. In this study, the appropriate forms for the identity and theorem are proposed and then the discretized conservation equation for the total amount of kinetic energy is appropriately formulated.
