f Research In Rayleigh-Benard convection simulation

Simulation of Three-Dimensional Convecting Flows

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.

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