A pressure-correction method for incompressible flows using unstructured meshes

Abstract

A pressure-correction method is presented to solve incompressible viscous flows. The development of this method is aimed at dealing with unstructured grids, which are made of control volumes with arbitrary topology. To enhance the robustness of the method, all variables are collocated on the cell centers. The divergence theorem of Gauss is employed for discretization, and vector forms are used throughout the formulation. In this way the method is equally applicable to two- and three-dimensional problems. An overrelaxed approach is adopted for the approximation of the cross-diffusion flux to deal with "skew" grids. It can he seen that this approach is equivalent to some other approximations available in the literature. However, the present approach is more suitable for three-dimensional calculations without causing complication. This overrelaxed approach is also employed in the pressure-correction equation derived from the continuity constraint. Most prevailing "methods simply ignore the cross-derivative term of the pressure-correction equation, which not only causes instability but also slows down convergence rate if the grid is skew. This cross-derivative term is taken into account in the present calculations by using a successive correction procedure. The application of the methodology to flows in lid-driven cavities and diffusers shows that no more than two pressure-correction steps are enough to obtain fast and stable convergence. The method is also applied to a three-dimensional flow in an impeller-stirred tank.