A finite‐element study of the bénard problem using parameter‐stepping and bifurcation search
- 1 February 1984
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Fluids
- Vol. 4 (2) , 127-145
- https://doi.org/10.1002/fld.1650040203
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 non‐linear branches above the critical Rayleigh number are examined. Extensions to non‐Boussinesq flow are trivial.Keywords
This publication has 6 references indexed in Scilit:
- Mixed interpolation in primitive variable finite element formulations for incompressible flowInternational Journal for Numerical Methods in Engineering, 1981
- The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2International Journal for Numerical Methods in Fluids, 1981
- On the Onset of Free Convection in a Rectangular ChannelJournal of Non-Equilibrium Thermodynamics, 1981
- The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier‐Stokes equations: Part 1International Journal for Numerical Methods in Fluids, 1981
- Solution of the Boussinesq equations by means of the finite element methodComputers & Fluids, 1978
- The smooth transition to a convective régime in a two-dimensional boxProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978