Large-Eddy Simulation of Thermal Flows based on Discrete-Velocity Models.

We derive a Godunov-type relaxation scheme for turbulent flows with heat transfer. The building block of this approach is a kinetic Boltzmann-type formulation for a model of turbulent thermal flows based on large-eddy simulation modeling. Discrete-velocity moments are taken in order to derive a relaxation system which is in turn solved by a relaxation scheme. High-order schemes are obtained by discretizing the relaxation system spatially with weighted essentially nonoscillatory reconstruction and temporally using an implicit-explicit discretization. In the limit of small Mach and small Knudsen numbers one obtains a high-order relaxation scheme for large-eddy simulation of turbulent thermal flows. The efficiency, accuracy, and high-resolution properties of the models are demonstrated in a variety of test examples