Finite Analytic Numerical Method for Unsteady TwoDimensional NavierStokes Equations
Abstract
The main purpose of this paper is to develop a finite analytic (FA) numerical solution for unsteady twodimensional NavierStokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. In this study the combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds numbers of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block ( H × H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, reststreamlines are given to illustrate the vortex motion downstream of the block.
 Publication:

Journal of Computational Physics
 Pub Date:
 February 1984
 DOI:
 10.1016/00219991(84)90038X
 Bibcode:
 1984JCoPh..53..209C
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 NavierStokes Equation;
 Two Dimensional Flow;
 Unsteady Flow;
 Vortex Shedding;
 Cavity Flow;
 Partial Differential Equations;
 Stream Functions (Fluids);
 Fluid Mechanics and Heat Transfer