A second-order time accurate finite element method for quasi-incompressible viscous flows

摘要

A finite element method for quasi-incompressible viscous flows is presented. An equation for pressure is derived from a second-order time accurate Taylor-Galerkin procedure that combines the mass and the momentum conservation laws. At each time step, once the pressure has been determined, the velocity field is computed solving discretized equations obtained from another second-order time accurate scheme and a least-squares minimization of spatial momentum residuals. The terms that stabilize the finite element method (controlling wiggles and circumventing the Babuska-Brezzi condition) arise naturally from the process, rather than being introduced a priori in the variational formulation. A comparison between the present second-order accurate method and our previous first-order accurate formulation is shown. The method is also demonstrated in the computation of the leaky-lid driven cavity flow and in the simulation of a crossflow past a circular cylinder. In both cases, good agreement with previously published experimental and computational results has been obtained.