A modified finite element method for solving the incompressible Navier-Stokes equations
Abstract
Beginning with the Galerkin finite element method and the simplest appropriate isoparametric element for modeling the Navier-Stokes equations, the spatial approximation is modified in two ways in the interest of cost-effectiveness: the mass matrix is 'lumped' and all coefficient matrices are generated via 1-point 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 advection-dominated 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 time-dependent Benard convection in three dimensions.
- Publication:
-
Large-Scale Computations in Fluid Mechanics
- Pub Date:
- 1985
- Bibcode:
- 1985ams..conf..193G
- Keywords:
-
- Benard Cells;
- Computational Fluid Dynamics;
- Finite Element Method;
- Galerkin Method;
- Navier-Stokes Equation;
- Vortex Shedding;
- Advection;
- Boussinesq Approximation;
- Circular Cylinders;
- Incompressible Fluids;
- Poisson Equation;
- Power Spectra;
- Reynolds Number;
- Time Dependence;
- Fluid Mechanics and Heat Transfer