Temperature equation

IncompressibleNavierStokes.jl supports adding a temperature equation, which is coupled back to the momentum equation through a gravity term [4].

To enable the temperature equation, you need to add boundary conditions for temp in setup:

setup = Setup(;
    kwargs...,
    boundary_conditions = (; 
        u = (bc...),
        temp = (bc...),
    ),
)

In solve_unsteady, add force! = boussinesq! and the following params:

solve_unsteady(;
    kwargs...,
    start = (; u, temp), # Initial vector field `u` and scalar field `temp`
    force! = boussinesq!,
    params = (;
        viscosity = 1e-3, # for diffusion of velocity
        conductivity = 1e-3, # for diffusion of temperature
        gravity = 1.0, # Gravity constant in momentum equation
        gdir = 2, # Direction of gravity
        dodissipation = true, # Redirect velocity dissipation to temperature
    ),
)