Solving the incompressible NavierStokes equations using consistent mass and a pressure Poisson equation
Abstract
We derive and demonstrate a new technique for solving the time dependent incompressible NavierStokes equations using loworder (bilinear) finite elements. The scheme is based on using the consistent mass matrix for the physical processes of advection and diffusion, and the lumped mass approximation for the pressure gradient term. The implementation uses a simple semiimplicit projection method based on the original method of Chorin. It is shown that the new scheme is costeffective, relative to those using either lumped or consistent mass everywhere, especially for simulations in which accuracy of the advective (convective) transport process is particularly important. Steady results obtained from the scheme, which are slightly less accurate, are also addressed.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1988
 Bibcode:
 1988STIN...8915355G
 Keywords:

 Incompressible Flow;
 Mass;
 NavierStokes Equation;
 Poisson Equation;
 Pressure Gradients;
 Algorithms;
 Computational Fluid Dynamics;
 Time Dependence;
 Fluid Mechanics and Heat Transfer