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3.13.4 Numerical stability criteria and other considerations

For a heat flux of 800 Wm$ ^2$ and a rotation rate of $ 10^{-4}$ s$ ^{-1}$ the plume-scale can be expected to be a few hundred meters guiding our choice of grid resolution. This in turn restricts the timestep we can take. It is also desirable to minimise the level of diffusion and viscosity we apply.

For this class of problem it is generally the advective time-scale which restricts the timestep.

For an extreme maximum flow speed of $ \vert \vec{u} \vert = 1 ms^{-1}$, at a resolution of 50 m, the implied maximum timestep for stability, $ \delta t_u$ is



The choice of $ \delta t = 10$ s is a safe 20 percent of this maximum.

Interpreted in terms of a mixing-length hypothesis, a magnitude of Laplacian diffusion coefficient $ \kappa_h (= \kappa_v) = 0.1$ m$ ^2$s$ ^{-1}$ is consistent with an eddy velocity of 2 mm s$ ^{-1}$ correlated over 50 m.

next up previous contents
Next: 3.13.5 Experiment configuration Up: 3.13 Surface Driven Convection Previous: 3.13.3 Discrete numerical configuration   Contents
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