A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

Abstract

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM). The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.