SOLUTION OF INCOMPRESSIBLE NAVIER‐STOKES EQUATIONS ON UNSTRUCTURED GRIDS USING DUAL TESSELLATIONS

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.