CALCULATIONS OF INCOMPRESSIBLE FLOW ON A STAGGERED TRIANGULAR GRID, PART I: MATHEMATICAL FORMULATION

Abstract

Abstract A novel staggered triangular grid system and the associated solution procedure to simulate incompressible flow field is proposed in this article. In this grid system, pressure is calculated at the centroid of the triangular cell and velocity components at the faces. The difference governing equations are derived using a general finite-volume procedure, which is based on term-by-term consideration of flow convection, diffusion, and source contributions. These terms are cast to reflect the physical meaning of various flow processes, thus resulting in a highly comprehensible solution procedure. A standard SIMPLE pressure correction method is employed. From the solution procedure described, it is seen that the present formulation can be easily extended to apply on meshes with arbitrarily convex polygons.