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

Abstract

A diagonal Cartesian method is proposed for the simulation of incompressible fluid flows over complex boundaries in Cartesian coordinates. A structured grid is utilized for the sake of simplicity. The method approximates complex boundaries using both Cartesian grid lines and diagonal line segments. The grid is generated automatically, and the geometry approximation is shown to be more accurate than the traditional sawtooth method. Mass conservation on complex boundaries is enforced with an appropriate pressure boundary condition. The method, which utilizes cell-centered nodes on a nonstaggered grid, uses boundary velocity information to avoid the specification of pressure values on boundaries, An enlarged control-volume method is introduced for mass conservation and pressure boundary conditions on complex boundaries. The conservation of momentum on complex boundaries is enforced through the finite analytic (FA) method, using nine-point and five-point FA elements. Velocity boundary conditions at moving boundaries are analyzed. The proposed diagonal Cartesian method is verified with the solution of a rotated lid-driven cavity flow. It is shown that this diagonal method predicts the fluid flow very well and improves the accuracy of the numerical simulation compared to the traditional sawtooth method. The application of this method to a grooved channel flow is also presented.

Notes

Address correspondence to Prof. Ching Jen Chen, Department of Mechanical Engineering, FAMU-FSU College of Engineering, Florida A&M University and Florida State University, 2525 Pottsdamer St., Tallahassee, FL 32310-2175, USA, E-mail: [email protected] or [email protected]