Analysis of the Unsteady NavierStokes Equations Based on Green’s Function Approach
Abstract
A computational method for the solutions of the timedependent NavierStokes equations in their stream function and vorticity formulation, is developed. Integral representations of stream function and vorticity and an integral equation for the timedependent boundary vorticity, are obtained by use of Green’s functions. A twodimensional flow in a rectangular cavity is considered, assuming that the fluid is at rest initially and the upper wall is set in motion at t{=}0. The discretization procedure is applied to solving the integral equations. Numerical solutions of transient state reaching the steady one are presented for Reynolds numbers R of 0, 100 and 200.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 May 1984
 DOI:
 10.1143/JPSJ.53.1702
 Bibcode:
 1984JPSJ...53.1702F
 Keywords:

 Computational Fluid Dynamics;
 Flow Equations;
 Green'S Functions;
 NavierStokes Equation;
 Unsteady Flow;
 Stream Functions (Fluids);
 Time Dependence;
 Two Dimensional Flow;
 Vorticity;
 Fluid Mechanics and Heat Transfer