Finite element solution theory for threedimensional boundary flows
Abstract
A finite element algorithm is derived for the numerical solution of a threedimensional flow field described by a system of initialvalued, elliptic boundary value partial differential equations. The familiar threedimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 November 1974
 DOI:
 10.1016/00457825(74)900127
 Bibcode:
 1974CMAME...4..367B
 Keywords:

 Boundary Layer Equations;
 Finite Element Method;
 Flow Distribution;
 Laminar Boundary Layer;
 Three Dimensional Boundary Layer;
 Turbulent Boundary Layer;
 Algorithms;
 Boundary Conditions;
 Computer Techniques;
 Convergence;
 Elliptic Differential Equations;
 Error Analysis;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer