An efficient quasilinear finite element method for solving the incompressible NavierStokes equations at large Reynolds numbers
Abstract
A numerical method is described for solving the timedependent NavierStokes equations for incompressible viscous fluid flows. The method results from a three step implicit scheme for the time discretization and from a finite element approximation for the space discretization. The typical fractional step method leads to an uncoupling between the nonlinearity and incompressibility and the convective terms appear in a linearized semiimplicit form. The discretization avoids the use of Least Squares methods to treat the nonlinearity. Excellent convergence properties are obtained which improve as the Reynolds number increases. Conjugate gradients algorithms are developed for solving the resulting linear systems, including unsymmetrical matrices. For convection dominated flows, a balancing dissipation technique is introduced in order to stabilize the oscillatory nature of the solution.
 Publication:

Analysis of Laminar Flow over a Backward Facing Step
 Pub Date:
 1984
 Bibcode:
 1984alfb.proc..124B
 Keywords:

 Computational Fluid Dynamics;
 Conjugate Gradient Method;
 Finite Element Method;
 High Reynolds Number;
 Incompressible Flow;
 NavierStokes Equation;
 Computational Grids;
 Linear Equations;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer