Thermodynamic consistency of liquid-gas lattice Boltzmann simulations.

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multiphase fluid systems. However, the underlying second-order analysis of the equation of motion has long been known to be insufficient to consistently derive the fourth-order terms that are necessary to represent an extended interface. These same terms are also responsible for thermodynamic consistency--i.e., to obtain a true equilibrium solution with both a constant chemical potential and a constant pressure. In this article we present an equilibrium analysis of nonideal lattice Boltzmann methods of sufficient order to identify those higher-order terms that lead to a lack of thermodynamic consistency. We then introduce a thermodynamically consistent forcing method.

[1]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Alexandros Kalarakis,et al.  Galilean-invariant lattice-Boltzmann simulation of liquid-vapor interface dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Hirotada Ohashi,et al.  LATTICE-BOLTZMANN SIMULATION OF TWO-PHASE FLUID FLOWS , 1998 .

[5]  A. Wagner,et al.  Spinodal Decomposition in Two-Dimensional Binary Fluids , 1998 .

[6]  H. Callen.  Thermodynamics and an Introduction to Thermostatistics , 1988 .

[7]  Xiaoyi He,et al.  Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows , 2002 .

[8]  G. Doolen,et al.  Discrete Boltzmann equation model for nonideal gases , 1998 .

[9]  Li-Shi Luo,et al.  Unified Theory of Lattice Boltzmann Models for Nonideal Gases , 1998 .

[10]  Dimitrios V. Rovas,et al.  An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models , 1998 .

[11]  Takaji Inamuro,et al.  A Galilean Invariant Model of the Lattice Boltzmann Method for Multiphase Fluid Flows Using Free-Energy Approach , 2000 .

[12]  Santosh Ansumali,et al.  Consistent lattice Boltzmann method. , 2005, Physical review letters.

[13]  Yeomans,et al.  Lattice Boltzmann simulations of liquid-gas and binary fluid systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  S. Zaleski,et al.  Lattice Boltzmann model of immiscible fluids. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[15]  A. Wagner,et al.  Investigation of Galilean invariance of multi-phase lattice Boltzmann methods , 2004, cond-mat/0410555.