- Author
-
Rehm, R. G.
|
Baum, H. R.
|
Barnett, P. D.
|
Corley, D. M.
- Title
- Finite Difference Calculations of Buoyant Convection in an Enclosure. Part 2: Verification of the Nonlinear Algorithm. Final Report.
- Coporate
- National Bureau of Standards, Gaithersburg, MD
- Report
-
NBSIR 84-2932,
September 1984,
35 p.
- Distribution
- AVAILABLE FROM National Technical Information Service (NTIS), Technology Administration, U.S. Department of Commerce, Springfield, VA 22161. Telephone: 1-800-553-6847 or 703-605-6000; Fax: 703-605-6900; Rush Service (Telephone Orders Only) 800-553-6847; Website: http://www.ntis.gov
- Keywords
-
equations
|
finite difference theory
|
fluid dynamics
|
stability
- Abstract
- Earlier, a novel mathematical model of buoyant convection in an enclosure was developed. The nonlinear equations constituting this model have recently been solved by finite difference methods in two dimensions. In this paper two solutions, obtained in special cases, to the model equations are presented. For both cases the solutions to the partial differential equations and to the finite difference equations used to approximate the differential equations are obtained by combinations of analytical and numerical techniques. Agreement between the exact solutions to the difference equations described in this paper and independently obtained numberical solutions was found nearly to the accuracy specified (usually 10-6) for an iterative procedure used in the computational scheme. The first solution is for a time-dependent irrotational, incompressible flow in an enclosure driven by sources and sinks of fluid as specified by the heat source. This problem arises from the full nonlinear equations with boundary conditions, in continuous or discrete form, by requiring that the velocity field be irrotational and the density remain constant. The second set of solutions arises when several other simplifications are made to the equations. The density is taken to be constant, the heating is assumed to be zero, the velocity field is taken to be twon dimensional and derivable from a stream function only, the vorticity is taken to be a constant, and the flow is independent of time. These solutions are used to determine the accuracy with which the code described in Reference 2 solves the nonlinear finite difference equations in special cases.