Numerical determination of bifurcation points and catastrophe phenomena in thermal convection problems

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

OSTI ID:6668203

Azmy, Y Y; Dorning, J J

The nodal integral approach has been developed for the accurate numerical solution of linear and nonlinear problems. Recently, the basic ideas have been extended to develop a nodal integral method (NIM) for nonlinear natural thermal convection problems treated in the Boussinesq approximation, and used to obtain numerical solutions for natural convection in a closed cavity with insulated top and bottom and one hot and one cold side. Comparison of the solutions with reference solutions extrapolated from fine-mesh, finite difference solutions were used to establish the very high accuracy of the NIM, even on coarse meshes. The authors have now extended the NIM for nonisothermal problems to include a Euler-Newton continuation procedure in both the cavity tilt angle, theta, and the Rayleigh number, Ra. This has made it possible to study the very interesting two-parameter family of problems, which has as a special case the classic Benard convection problem a closed square cavity with insulated sides, a hot bottom, and cold top. In particular, it has enabled study of numerically the unfolding of the first bifurcation in the Benard problem into a structurally stable cusp catastrophe and the preservation of the second as a structurally unstable pitchfork bifurcation as the cavity tilt angle is varied from its Benard problem value theta = 0. Bifurcation of solutions in natural thermal convection problems has become increasingly important in reactor technology with the advent of inherently safe, innovative, advanced liquid-metal reactor designs, such as SAFR and PRISM.

• Research Organization: Univ. of Virginia, Charlottesville
• OSTI ID: 6668203
• Report Number(s): CONF-860610-
• Conference Information: Journal Name: Trans. Am. Nucl. Soc.; (United States) Journal Volume: 52
• Country of Publication: United States
• Language: English

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