Three-dimensional diagonal Cartesian method for incompressible flows involving complex boundaries

A diagonal Cartesian method for the three-dimensional simulation of incompr essible fluid flows over complex boundaries is presented in this article, T he method is derived utilizing the superposition of the finite analytic sol utions of a linearized two-dimensional convection-diffusion equation in Car tesian coordinates. The complex boundary is approximated with a structured grid in a series of calculation planes which are perpendicular to the x, y, and z coordinate axis. In rite calculation plane, both Cartesian grid line s and diagonal line segments are used It is observed that this geometry app roximation is more accurate than the traditional sawtooth method Mass conse rvation on complex boundaries is enforced with an appropriate pressure boun dary condition. The method, which utilizes cell-vertex nodes on a staggered grid uses boundary velocity information to avoid the specification of pres sure values on boundaries, An enlarged control-volume merited is introduced for the mass conservation and the pressure boundary condition on complex b oundaries. The conservation of momentum on complex boundaries is enforced t hrough the use of three-dimensional 19, 15, 11, or 7-point finite analytic elements. The proposed diagonal Cartesian method is verified by the solutio n of a rotated lid-driven cavity flow. It is shown that this diagonal Carte sian method predicts the fluid flow very well.