Finite element models for viscous incompressible flow
Abstract
A classification of the different finite element models for viscous incompressible flow is carried out in a consistent manner on the basis of the weighted residual methods, in particular, the Galerkin technique. The simplest formulation is the solenoidal approximation in terms of velocities that satisfy the continuity equation as dependent variables. For nonsinusoidal velocity field, the incompressibility condition has to be introduced into the functional, giving the primitive variables formulation. Substituting an energy rate function into the functional gives the mixed formulations, with velocities, pressure, and viscous stresses as variables. Further still, one can define different variables over different parts of the body, and produce a more general statement, from which the hybrid principles and all the previous ones can be deduced.
 Publication:

In: International Symposium on Innovative Numerical Analysis in Applied Engineering Science
 Pub Date:
 1977
 Bibcode:
 1977inaa.symp....7B
 Keywords:

 Finite Element Method;
 Galerkin Method;
 Incompressible Flow;
 Viscous Flow;
 Continuity Equation;
 Dependent Variables;
 NavierStokes Equation;
 Velocity Distribution;
 Weighting Functions;
 Fluid Mechanics and Heat Transfer