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A novel thermal model for the lattice Boltzmann method in incompressible limit. (English) Zbl 0919.76068
Summary: A novel lattice Boltzmann thermal model is proposed for studying thermohydrodynamics in incompressible limit. The new model introduces an internal energy density distribution function to simulate the temperature field. The macroscopic density and velocity fields are still simulated using the density distribution function. Compared with the multispeed thermal lattice Boltzmann models, the current scheme is numerically more stable. In addition, the new model can incorporate viscous heat dissipation and compression work done by the pressure, in contrast to the passive-scalar-based thermal lattice Boltzmann models. Numerical simulations of Couette flow with a temperature gradient and Rayleigh-Bénard convection agree well with analytical solutions and benchmark data.

MSC:
76M28Particle methods and lattice-gas methods (fluid mechanics)
76A02Foundations of fluid mechanics
80A20Heat and mass transfer, heat flow
82B20Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82-08Computational methods (statistical mechanics)