Numerical parametric analysis of nonlinear phenomena in the confined Benard problem

Conference · Wed Jan 01 04:00:00 EST 1986 · Trans. Am. Nucl. Soc.; (United States)

OSTI ID:6727785

Azmy, Y Y

The nonlinearity of the fluids equations permits the existence of multiple solutions for many fluids problems of practical interest. It is of great importance to investigate the existence of multiple solutions and their dependence on the relevant parameters in fluids problems. In a parametric study, these parameters are varied and the problem is solved to obtain the equilibrium solution(s) at each point in the region of parameter space under investigation. For most nontrivial, realistic problems the equilibrium solution is obtained numerically, and to cover a reasonable portion of the parameter space a large number of calculations is required. Highly accurate and computationally efficient numerical methods, such as the nodal integral method (NIM), are therefore necessary to conduct parametric studies of nonlinear problems. A NIM has been developed recently for the numerical solution of natural thermal convection problems in the Boussinesq approximation. The high accuracy and computational efficiency of this method have been established by comparing coarse-mesh NIM solutions to the benchmark solution of the double-glazing problem, obtained via h/sup 2/ extrapolation of fine-mesh finite-difference results. The authors used this NIM to carry out a numerical parametric study of the equilibrium solution surface for the confined Benard problem. Because of the high accuracy of the NIM, they were able to analyze the bifurcations and catastrophes present in the solution surface of this problem using a rather coarse, 6 x 6, mesh.

• Research Organization: Univ. of Virginia, Charlottesville
• OSTI ID: 6727785
• Report Number(s): CONF-861102-
• Conference Information: Journal Name: Trans. Am. Nucl. Soc.; (United States) Journal Volume: 53
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
CONVECTION
ENERGY TRANSFER
FLUID FLOW
HEAT TRANSFER
MASS TRANSFER
NATURAL CONVECTION
NONLINEAR PROBLEMS
PARAMETRIC ANALYSIS
TWO-DIMENSIONAL CALCULATIONS