Finite Element Simulation of Viscous Incompressible Flows

摘要

The Galerkin-finite element approximation to the Navier-Stokes equations is developed from the continuous conservation laws governing the time-dependent flow of a viscous incompressible fluid. A computer code implementing the approach is described and results from several example problems are discussed. Biquadratic Lagrangian isoparametric elements are used to discretize the velocities. Bilinear elements discretize the pressure unknown. The nonlinear problem that results from the convection term in the Navier-Stokes equations is solved using a Picard iteration for the correct velocity and pressure fields. The stiffness matrix is factored at each step of the iteration using a frontal solution technique. Results from both steady-state and time-dependent convection dominated flows are given. Extensive appendixes accompany the report including all the details necessary to develop a finite element code. (ERA citation 09:008734)