Lattice Boltzmann algorithm for simulating thermal flow in compressible fluids

An algorithm has been developed for incorporating the effects of temperatur e into lattice Boltzmann simulations. Instead of modeling the internal ener gy 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 distribut ion. The energy is then coupled to the density and momentum via the partiti on between moving and nonmoving particles in a conventional two-speed model . The algorithm is tested against a number of systems for which analytic re sults are available. These include nonuniform conductivity between two plat es, entry length behavior for flow in a channel between two parallel plates , and critical Rayleigh number behavior in Rayleigh-Benard convection. Quan titative agreement is found in all cases. (C) 2000 Academic Press.