In collaboration with Dr. Ming-Chih
Lai and
Michael Cross and with support from the Department of
Energy, we are developing a suite of computer codes for
simulating the three-dimensional Boussinesq equations in
large aspect ratios and for long times, so that we can make
quantitative comparisons with prior experiments, test
various theoretical ideas, and make predictions for further
experiments.
The codes are presently based on second-order accurate finite difference discretizations of equations and boundary conditions and there will be a separate codes for box, cylindrical, and periodic boundary conditions. Iterative methods (presently preconditioned conjugate gradient and eventually multigrid) are used to solve the Poisson and Helmholtz equations associated with updating the momentum equation at each time step.
Example of problems of interest are understanding: the supercritical transition to spatiotemporal chaos near onset in rotating cells; the transition to spiral defect chaos as a function of aspect ratio and Prandtl number; the dynamics of a convecting fluid at small Prandtl number; and spoke convection for moderate to high Prandtl number fluids at higher Rayleigh numbers.