A modified finite element method for solving the incompressible NavierStokes equations
Abstract
Beginning with the Galerkin finite element method and the simplest appropriate isoparametric element for modeling the NavierStokes equations, the spatial approximation is modified in two ways in the interest of costeffectiveness: the mass matrix is 'lumped' and all coefficient matrices are generated via 1point quadrature. After appending an 'hourglass' correction term to the diffusion matrices, the modified semidiscretized equations are integrated in time using the forward (explicit) Euler method in a special way to compensate for that portion of the time truncation error which is intolerable for advectiondominated flows. The scheme is completed by the introduction of a subcycling strategy that permits less frequent updates of the pressure field with little loss of accuracy. These techniques are described and analyzed, and the resulting code is demonstrated on two sample problems: flow past a circular cylinder at Re not greater than 400, and timedependent Benard convection in three dimensions.
 Publication:

LargeScale Computations in Fluid Mechanics
 Pub Date:
 1985
 Bibcode:
 1985ams..conf..193G
 Keywords:

 Benard Cells;
 Computational Fluid Dynamics;
 Finite Element Method;
 Galerkin Method;
 NavierStokes Equation;
 Vortex Shedding;
 Advection;
 Boussinesq Approximation;
 Circular Cylinders;
 Incompressible Fluids;
 Poisson Equation;
 Power Spectra;
 Reynolds Number;
 Time Dependence;
 Fluid Mechanics and Heat Transfer