A VIRTUAL FINITE VOLUME METHOD FOR COMPUTATIONAL FLUID DYNAMICS

Abstract

The virtual finite volume method (VFVM), based on Voronoi diagrams, is developed, and applied to two benchmark simulations of laminar and turbulent flows. The results of the VFVM are found to be closest to the benchmark for turbulent flow compared to all-quad and triangular meshes. Additionally, the VFVM produced the smallest RMS error for laminar flow on the coarsest mesh in comparison. The resources required to generate a high-quality mesh for computational fluid dynamics (CFD) computations may well exceed those required for CFD computations. Further, mesh-generation is a labor-intensive process that is difficult to automate. Meshless computing is therefore an active area of research. The article describes a finite volume method (FVM) that is mesh-less as far as the user is concerned. The mesh is generated from a cloud of distributed points automatically without any intervention by the CFD practitioner. We call this the virtual finite volume method. A key feature of the VFVM is that the mesh is generated from a point cloud that is converted into Voronoi diagrams. In the context of the FVM, Voronoi polygons (2D) or polyhedra (3D) have the important property that the line connecting two adjacent nodes is perpendicular to the common intervening face and is bisected by it. This orthogonality allows for very efficient computation of diffusion and convection terms and minimizes the numerical diffusion. The ANSWER^® CFD solver has been extended to generate these Voronoi mesh systems automatically and allow for adaptive gridding to yield a high accuracy solution with optimal computational resources.