A finite-element study of the Benard problem using parameter-stepping and bifurcation search
Abstract
The problem of fluid motion in a cavity with rigid sidewalls that is heated uniformly from below is studied by the finite-element method. The techniques of parameter-stepping and monitoring the determinant of the Jacobian matrix to find bifurcations are used. Results are presented for width-to-height ratios in the range 1 to 4, and for three different boundary conditions on the horizontal surfaces, namely both rigid, both free, and rigid bottom with free top. The nonlinear branches above the critical Rayleigh number are examined. Extension to non-Boussinesq flow are trivial.
- Publication:
-
International Journal for Numerical Methods in Fluids
- Pub Date:
- February 1984
- DOI:
- 10.1002/fld.1650040203
- Bibcode:
- 1984IJNMF...4..127J
- Keywords:
-
- Benard Cells;
- Branching (Mathematics);
- Computational Fluid Dynamics;
- Finite Element Method;
- Rayleigh-Benard Convection;
- Boussinesq Approximation;
- Buoyancy;
- Cavities;
- Fluid Boundaries;
- Parameterization;
- Rayleigh Number;
- Fluid Mechanics and Heat Transfer