Buoyant term in the vorticity transport equation is described as (Pr * Ra * dt/dx)

Discretizing this buoyant term,

Pr * Ra * [T(i, j) - T(i-1, j)]/dx .

In the simulation of the natural convection with bottom heating(T=1: bottom boundary, T=0: upper boundary), when we set the initial condition as isothermal T=0, then "T(i, j) - T(i-1, j)" is always zero, and convection does not begin for a long.

How to treat this buoyant term and equations ?

(Though I am not good at English, I will try to write as well as possible.)

Junomian,

From the very start of your simulation, the dT/dx will not be zero close to the bottom boundary, because at the bottom boundary T=1 and the initial guess elsewhere is T=0. Therefore the convection effects, depending on the thermodynamic properties of the fluid and Ra value, should be clearly visible in your simulation.

regards

DML