The current versions of the Nonisothermal Flow, LES interfaces only support incompressible flow. When gravity is active in the model, buoyancy effects may be taken into account using The Boussinesq Approximation. For large eddy simulations (LES) of nonisothermal flow, the temperature field is divided up into resolved and unresolved scales, in the same way as is done for the velocity and pressure fields (see Theory for the Large Eddy Simulation Interfaces). For incompressible flow, the energy equation can be projected onto the resolved scales, w, producing the following weak form equation,

where q is the inward heat flux on the boundary of the spatial domain . The unresolved temperature scales are modeled in terms of the residual to the energy equation and the intrinsic time-scale,

Here, C4 is a constant depending on the shape of the element and G is the covariant metric tensor.

For further details, see Theory for the Large Eddy Simulation Interfaces.

When automatic wall treatment is applied in an LES model, a flux condition is imposed for the temperature equation. The heat flux between the fluid with temperature Tf and a wall with temperature Tw, is,

where ρ is the fluid density, Cp is the fluid heat capacity, is the friction velocity and T+ is the dimensionless temperature, given by,

E and κ are the L-VEL parameters used in the automatic wall treatment expressions (see Automatic Wall Treatment).