3D lid driven cavity flow by mixed boundary and finite element method

Abstract

A numerical algorithm for the solution of the velocity-vorticity formulation of Navier-Stokes equations is presented. This formulation results in splitting of fluid flow into its kinematic and kinetic aspect. The Boundary Element Method (BEM) used for the solution of flow kinematics results in an implicit calculation of vorticity values at the boundary, whereas all transport equations are solved using Finite Element Method (FEM). The combination of both numerical techniques is proposed in order to increase the accuracy of computation of boundary vorticities, a weak point for a majority of numerical methods when dealing with velocity-vorticity formulation. Since the application of BEM results in fully populated system matrices, also the flow kinematics computation is done by combining BEM and FEM, the latter for computation of internal velocities, keeping the CPU time and computer storage requirements at the level close to Finite Element Method. To speed up the computation process and to distribute storage of integrals over several processors the algebraic parallelization of kinematics was performed. Lid driven flow in a cubic cavity was computed to show the robustness and versatility of the proposed numerical formulation. Results for Reynolds number value Re=100 and Re=1000 show good agreement with benchmark results.