Solution of 3D Velocity-Vorticity Formulation of the Navier-Stokes Equations by Boundary Element Method

摘要

A novel algorithm for the simulation of laminar viscous flows by solving of 3D velocity-vorticity formulation of the Navier-Stokes equations is presented. The algorithm employs a combination of a subdomain boundary element method (BEM) and single domain BEM. The subdomain BEM is used to solve the kinematics and vorticity transport equations. We use continuous quadratic interpolation of function and discontinuous linear interpolation of flux. The resulting over-determined system of linear equations is solved in a least squares manner. The single domain BEM is employed to calculate boundary vorticity values, which are used as Dirichlet boundary conditions for the vorticity transport equation. The versatility and accuracy of the proposed algorithm is proven by simulating 3D channel flow and 3D lid driven cavity flows up to Re = 103.