Solution of the Time-Dependent Incompressible Navier-Stokes and Boussinesq Equations Using the Galerkin Finite Element Method

摘要

This research was directed toward the generation of a time-dependent, three-dimensional model of the atmospheric boundary layer using the Galerkin finite element method (GFEM). Along the way, capabilities were developed for solving the two-dimensional Navier-Stokes and Boussinesq equations, both steady and time-dependent. These innovative techniques for time-dependent flows are described and illustrated. The GFEM is applied to the primitive variable (u,P,T) equations, thus generating, in the conventional manner, a coupled system of ordinary differential equations in time. A time integration method which gives very accurate, and reasonably efficient solutions to these time-dependent problems is discussed. It is stable for any grid spacing and Reynolds number, is non-dissipative, and incorporates an automatic time stem selection strategy. The techniques are then demonstrated by means of two numerical examples - both starting with a motionless sytem: (1) a thermally driven square cavity which goes to a steady-state and (2) isothermal flow around a circular cylinder which leads to periodic vortex shedding. (ERA citation 05:001656)