Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.

[1]  S Succi,et al.  Mesoscopic modeling of a two-phase flow in the presence of boundaries: The contact angle. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Ming Jia,et al.  Evaluation of force implementation in pseudopotential-based multiphase lattice Boltzmann models , 2012 .

[3]  Sauro Succi,et al.  Improved lattice boltzmann without parasitic currents for Rayleigh-Taylor instability , 2009 .

[4]  S Succi,et al.  Generalized lattice Boltzmann method with multirange pseudopotential. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  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.

[6]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[7]  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.

[8]  X. Shan.  Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M. Sbragaglia,et al.  Consistent pseudopotential interactions in lattice Boltzmann models. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Michael C. Sukop,et al.  Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers , 2005 .

[11]  Manfred Krafczyk,et al.  Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[13]  A. Xu,et al.  Lattice Boltzmann study on Kelvin-Helmholtz instability: roles of velocity and density gradients. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Liang-Shih Fan,et al.  Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Laura Schaefer,et al.  Equations of state in a lattice Boltzmann model , 2006 .

[16]  Yong Wang,et al.  Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Changfeng Ma,et al.  The lattice Boltzmann model for the second-order Benjamin–Ono equations , 2010 .

[18]  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.

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

[20]  Changfeng Ma,et al.  Lattice Boltzmann model for generalized nonlinear wave equations. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Yeomans,et al.  Lattice Boltzmann simulation of nonideal fluids. , 1995, Physical review letters.

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

[23]  D. A. Medvedev,et al.  On equations of state in a lattice Boltzmann method , 2009, Comput. Math. Appl..

[24]  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.

[25]  Shiyi Chen,et al.  A lattice Boltzmann model for multiphase fluid flows , 1993, comp-gas/9303001.

[26]  A. Xu,et al.  Lattice Boltzmann study of thermal phase separation: Effects of heat conduction, viscosity and Prandtl number , 2012 .

[27]  Fuzhi Tian,et al.  A bottom-up approach to non-ideal fluids in the lattice Boltzmann method , 2008 .

[28]  M. Ishii,et al.  Thermo-Fluid Dynamics of Two-Phase Flow , 2007 .

[29]  Y L He,et al.  Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[31]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .

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

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

[34]  Xiaowen Shan,et al.  Pressure tensor calculation in a class of nonideal gas lattice Boltzmann models. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  A. Xu,et al.  FFT-LB modeling of thermal liquid-vapor systems , 2010, 1011.3582.

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