Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

Details Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

2003-02-26

arxiv.org/abs/nlin/0302057v1

Nonlinear Sciences

Pattern Formation and Solitons

REVTeX, 30 pages, 5 figures

Scientific paper

10.1103/PhysRevE.68.026705

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.

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