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?Benard convection. Quantitative agreement is found in all cases.

[1]  Sauro Succi,et al.  THERMOHYDRODYNAMIC LATTICE BGK SCHEMES WITH NON-PERTURBATIVE EQUILIBRIA , 1998 .

[2]  Alejandro L. Garcia,et al.  Stabilization of thermal lattice Boltzmann models , 1995 .

[3]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[4]  Chen,et al.  Lattice Boltzmann thermohydrodynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[6]  Xiaowen Shan,et al.  SIMULATION OF RAYLEIGH-BENARD CONVECTION USING A LATTICE BOLTZMANN METHOD , 1997 .

[7]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[8]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[9]  K. Denbigh,et al.  The Principles of Chemical Equilibrium , 1956 .

[10]  Robert S. Bernard,et al.  Boundary conditions for the lattice Boltzmann method , 1996 .

[11]  Skordos,et al.  Initial and boundary conditions for the lattice Boltzmann method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  J. Whitelaw,et al.  Convective heat and mass transfer , 1966 .

[13]  B. Alder,et al.  Analysis of the lattice Boltzmann treatment of hydrodynamics , 1993 .

[14]  Pierre Lallemand,et al.  Lattice Gas Hydrodynamics in Two and Three Dimensions , 1987, Complex Syst..

[15]  S. Wolfram.  Cellular automaton fluids 1: Basic theory , 1986 .

[16]  Sauro Succi,et al.  Exponential Tails in Two-Dimensional Rayleigh-Bénard Convection , 1993 .

[17]  Matthaeus,et al.  Lattice Boltzmann model for simulation of magnetohydrodynamics. , 1991, Physical review letters.

[18]  Shiyi Chen,et al.  A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , 1998 .

[19]  Linda Vahala,et al.  Thermal Lattice Boltzmann Simulations of Variable Prandtl Number Turbulent Flows , 1998 .

[20]  Qisu Zou,et al.  N ov 1 99 6 On pressure and velocity flow boundary conditions and bounceback for the lattice Boltzmann BGK model , 2008 .

[21]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  James Buick,et al.  Lattice Boltzmann modeling of interfacial gravity waves , 1998 .