The imposition of incompressibility constraints via variational adjustment of velocity fields
Abstract
In the study of the dynamics of an incompressible fluid situations occur in which the velocity field specified on a set of discrete nodes is deficient in some measure of satisfying the incompressibility constraint, i.e., the solenoidal vector field constraint. In each of a number of considered situations it would be desirable to modify a given velocity field, in as small a way as possible, so that the adjusted field would satisfy the incompressibility condition in the matter desired. Using the finite element method, variational adjustment techniques for the considered situations have been developed. The three techniques developed are similar in that each employs the method of Lagrange multipliers to minimize the velocity adjustment in a weighted least squares sense subject to the imposed constraint of incompressibility. The techniques differ, however, in their formulation and implementation.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1978
 Bibcode:
 1978nmlt.proc..983S
 Keywords:

 Finite Element Method;
 Flow Velocity;
 Incompressibility;
 Laminar Flow;
 Variational Principles;
 Velocity Distribution;
 Wind Profiles;
 Air Land Interactions;
 Compressibility Effects;
 Ducted Flow;
 Lagrange Multipliers;
 NavierStokes Equation;
 Fluid Mechanics and Heat Transfer