Temperature equation

IncompressibleNavierStokes.jl supports adding a temperature equation, which is coupled back to the momentum equation through a gravity term [11].

To enable the temperature equation, you need to set the temperature keyword in setup:

setup = Setup(
    args...;
    kwargs...,
    temperature = temperature_equation(; kwargs...),
)

where temperature_equation can be configured as follows:

IncompressibleNavierStokes.temperature_equation — Function

temperature_equation(; 
    Pr,
    Ra,
    Ge,
    dodissipation = true,
    boundary_conditions,
    gdir = 2,
)

Temperature equation setup.

The equation is parameterized by three dimensionless numbers (Prandtl number, Rayleigh number, and Gebhart number), and requires separate boundary conditions for the temperature field. The gdir keyword specifies the direction gravity, while non_dim_type specifies the type of non-dimensionalization.

source

Some operators are available for the temperature equation:

IncompressibleNavierStokes.gravity! — Function

gravity!(F, temp, setup)

Compute gravity term (add to existing F).

source

IncompressibleNavierStokes.convection_diffusion_temp! — Function

convection_diffusion_temp!(c, u, temp, setup)

Compute convection-diffusion term for the temperature equation. Add result to c.

source

IncompressibleNavierStokes.dissipation! — Function

dissipation!(diss, diff, u, setup)

Compute dissipation term for the temperature equation. Add result to diss.

source