Integral representation of field variables for the finite element solution of viscous flow problems
Abstract
The kinematics aspects of compressible and incompressible viscous flow problems are recasted into an integral representation for the velocity vector. For the incompressible flow problem, the kinetics aspect is similarly recasted into an integral representation. The result is a system of integral equations ideally suited for the finite element method. The integral representations are shown to permit the confinement of the computation field to the region of nonnegligible vorticity and dilatation which, for the incompressible flow, is identified with the viscous region. This drastic reduction in computation field results in a superior solution speed which is further improved by the use of a flowfield segmentation technique. The new approach is further shown to remove the difficulties associated with previous methods in specifying the far field and extraneous boundary conditions.
 Publication:

In: Finite element methods in engineering; Proceedings of the International Conference
 Pub Date:
 1974
 Bibcode:
 1974feme.proc..827W
 Keywords:

 Compressible Flow;
 Finite Element Method;
 Incompressible Flow;
 Integral Equations;
 Karman Vortex Street;
 Viscous Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Far Fields;
 Flow Distribution;
 NavierStokes Equation;
 Strouhal Number;
 Vorticity;
 Fluid Mechanics and Heat Transfer