A finite element implementation of the dual variable method for the NavierStokes equations
Abstract
The numerical solution of twodimensional, transient, incompressible NavierStokes problems on rather arbitrary bounded regions is considered. A finite element implementation of the method is presented, using quadrilateral piecewise bilinear velocity/constant pressure elements. The primary tool employed is combinatoric graph theory. A class of finite element decompositions is described, and the pertinent properties of such decompositions are discussed. Decompositions consisting of rectangular or square elements are considered as a special subclass, as are decompositions of flow regions which are not simply connected. Algorithms for the determination of a basis for N(A) and a particular solution are presented and discussed with examples.
 Publication:

Ph.D. Thesis
 Pub Date:
 1983
 Bibcode:
 1983PhDT........61S
 Keywords:

 Computer Techniques;
 Finite Element Method;
 Incompressible Flow;
 Linear Systems;
 NavierStokes Equation;
 Computation;
 Computer Programming;
 Computer Programs;
 Data Correlation;
 Independent Variables;
 Fluid Mechanics and Heat Transfer