Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Bénard convection in a box
A semi-implicit finite-difference algorithm for integrating the Boussinesq equations in two- and three-dimensional boxes, with sidewalls that are periodic, thermally insulated, or thermally conducting is presented. The approach is useful for simple geometries such as a box, cylinder, torus, and annulus, with boundary conditions such that various linear operators are separable so that fast direct methods can be applied. The resulting algorithm is sufficiently efficient that aspect ratios up to Γ≈20 can be studied on a single-processor workstation over several days.
Chiam, KH; Lai, MC; Greenside, HS
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