A Voronoi-based ALE solver for the calculation of incompressible flow on deforming unstructured meshes

Abstract

An Arbitrary Lagrangian–Eulerian method for the calculation of incompressible Navier–Stokes equations in deforming geometries is described. The mesh node connectivity is defined by a Delaunay triangulation of the nodes, whereas the discretized equations are solved using finite volumes defined by the Voronoi dual of the triangulation. For prescribed boundary motion, an automatic node motion algorithm provides smooth motion of the interior nodes. Changes in the connectivity of the nodes are made through the use of local transformations to maintain the mesh as Delaunay. This allows the nodes and their associated Voronoi finite volumes to migrate through the domain in a free manner, without compromising the quality of the mesh. An MAC finite volume solver is applied on the Voronoi dual using a cell-centred non-staggered formulation, with cell-face velocities being calculated by the Rhie–Chow momentum interpolation. Advective fluxes are approximated with the third-order QUICK differencing scheme. The solver is demonstrated via its application to a driven cavity flow, and the flow about flapping aerofoil geometries.