Lattice Boltzmann Algorithm for Simulating Thermal Flow in Compressible Fluids

An algorithm has been developed for incorporating the effects of temperature into lattice Boltzmann simulations. Instead of modeling the internal energy as a moment of the distribution describing the flow of mass and momentum, the internal energy is modeled as a scalar field using a second distribution. The energy is then coupled to the density and momentum via the partition between moving and nonmoving particles in a conventional two-speed model. The algorithm is tested against a number of systems for which analytic results are available. These include nonuniform conductivity between two plates, entry length behavior for flow in a channel between two parallel plates, and critical Rayleigh number behavior in Rayleigh–Bénard convection. Quantitative agreement is found in all cases.