Finite solution of the Navier Stokes equations
Abstract
The solution of fluid mechanics problems defined by the NavierStokes equations presents such analytical difficulties that numerical methods using finite difference/finite elements appear to be the only reasonable means of solution within the foreseeable future. In this paper, a number of interesting fluid mechanics problems including the twodimensional NavierStokes equations governing the steady state, viscous, incompressible flow within a cavity are solved using the finite element program TWODEPEP with automatic usercontrolled mesh grading. The finite element used is the standard sixnode triangle with quadratic basis functions with one edge curved when adjacent to a curved boundary according to the isoparametric method. In addition, the main principles of software package design for a preprocessor program which reads the user input describing the problem in a problemoriented format designed to minimize the user effort is also described.
 Publication:

IN: Numerical methods in laminar and turbulent flow; Proceedings of the Fourth International Conference
 Pub Date:
 1985
 Bibcode:
 1985nmlt.proc..454E
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Finite Element Method;
 Flow Geometry;
 NavierStokes Equation;
 Two Dimensional Flow;
 Boundary Value Problems;
 Channel Flow;
 Ducted Flow;
 Incompressible Flow;
 Potential Flow;
 Preprocessing;
 Steady Flow;
 Fluid Mechanics and Heat Transfer