DIAGONAL CARTESIAN METHOD FOR NUMERICAL-SIMULATION OF INCOMPRESSIBLE FLOWS OVER COMPLEX BOUNDARIES

A diagonal Cartesian method is proposed for the simulation of incompre ssible fluid flows over complex boundaries in Cartesian coordinates. A structured grid is utilized for the sake of simplicity. The method ap proximates complex boundaries using both Cartesian grid lines and diag onal line segments. The grid is generated automatically, and the geome try approximation is shown to be more accurate than the traditional sa wtooth method. Mass conservation on complex boundaries is enforced wit h an appropriate pressure boundary condition. The method, which utiliz es cell-centered nodes on a nonstaggered grid uses boundary velocity i nformation to avoid the specification of pressure values on boundaries . An enlarged control-volume method is introduced for mass conservatio n and pressure boundary conditions on complex boundaries. The conserva tion of momentum on complex boundaries is enforced through the finite analytic (FG) method, using nine-point and five-point FA elements. Vel ocity boundary conditions at moving Boundaries are analyzed. The propo sed diagonal Cartesian method is verified with the solution of a rotat ed lid-driven cavity flow. It is shown that this diagonal method predi cts the fluid flow very wed and improves the accuracy of the numerical simulation compared to the traditional sawtooth method. The applicati on of this method to a grooved channel flow is also presented.