Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales

The simulation of multiphase flows is an outstanding challenge, due to the inherent complexity of the underlying physical phenomena and to the fact that multiphase flows are very diverse in nature, and so are the laws governing their dynamics. In the last two decades, a new class of mesoscopic methods, based on minimal lattice formulation of Boltzmann kinetic equation, has gained significant interest as an efficient alternative to continuum methods based on the discretisation of the NS equations for non ideal fluids. In this paper, three different multiphase models based on the lattice Boltzmann method (LBM) are discussed, in order to assess the capability of the method to deal with multiphase flows on a wide spectrum of operating conditions and multiphase phenomena. In particular, the range of application of each method is highlighted and its effectiveness is qualitatively assessed through comparison with numerical and experimental literature data.

[1]  Daniel H. Rothman,et al.  Immiscible cellular-automaton fluids , 1988 .

[2]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[3]  J. Buick,et al.  Gravity in a lattice Boltzmann model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  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.

[5]  Taehun Lee,et al.  Wall boundary conditions in the lattice Boltzmann equation method for nonideal gases. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Peter V. Coveney,et al.  HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries , 2008, Comput. Phys. Commun..

[7]  Massimo Bernaschi,et al.  MUPHY: A parallel MUlti PHYsics/scale code for high performance bio-fluidic simulations , 2009, Comput. Phys. Commun..

[8]  Taehun Lee,et al.  Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids , 2009, Comput. Math. Appl..

[9]  S. Succi,et al.  Rupture of a ferrofluid droplet in external magnetic fields using a single-component lattice Boltzmann model for nonideal fluids. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  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.

[11]  P. Fischer,et al.  Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Ernst Rank,et al.  a Lb-Based Approach for Adaptive Flow Simulations , 2003 .

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

[14]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[15]  D. Jacqmin.  Regular Article: Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling , 1999 .

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

[17]  Zhaoxia Yang,et al.  A combined lattice BGK/level set method for immiscible two-phase flows , 2009, Comput. Math. Appl..

[18]  Ulrich Rüde,et al.  Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids , 2009 .

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

[20]  A. De Luca,et al.  Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape. , 2007, Physical review letters.

[21]  Sauro Succi,et al.  Applying the lattice Boltzmann equation to multiscale fluid problems , 2001, Comput. Sci. Eng..

[22]  Iliya V. Karlin,et al.  Perfect entropy functions of the Lattice Boltzmann method , 1999 .

[23]  Sauro Succi,et al.  Lattice Boltzmann simulations of capillary filling: Finite vapour density effects , 2008, 0801.4223.

[24]  B. Chopard,et al.  Theory and applications of an alternative lattice Boltzmann grid refinement algorithm. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  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.

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

[27]  Peter M. A. Sloot,et al.  Lattice-Boltzmann hydrodynamics on parallel systems , 1998 .

[28]  Sauro Succi,et al.  Massively Parallel Lattice-Boltzmann Simulation of Turbulent Channel Flow , 1997 .

[29]  U. Rüde,et al.  Lattice Boltzmann Model for Free Surface Flow for Modeling Foaming , 2005 .

[30]  A Lamura,et al.  Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Andrew W. Cook,et al.  Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae , 2006 .

[32]  S. Orszag,et al.  Extended Boltzmann Kinetic Equation for Turbulent Flows , 2003, Science.

[33]  Theo G. Theofanous,et al.  A pseudocompressibility method for the numerical simulation of incompressible multifluid flows , 2004 .

[34]  L. Luo,et al.  Theory of the lattice Boltzmann method: two-fluid model for binary mixtures. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[36]  Aiguo Xu,et al.  Phase separation of incompressible binary fluids with lattice Boltzmann methods , 2004 .

[37]  D. H. Rothman,et al.  Microscopic modeling of immiscible fluids in three dimensions by a lattice Boltzmann method , 1992 .

[38]  Ignacio Pagonabarraga,et al.  LUDWIG: A parallel Lattice-Boltzmann code for complex fluids , 2001 .

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

[40]  Interface width and bulk stability: requirements for the simulation of deeply quenched liquid-gas systems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Sauro Succi,et al.  Lattice Boltzmann simulations of phase-separating flows at large density ratios: the case of doubly-attractive pseudo-potentials , 2010 .

[42]  Julia M. Yeomans,et al.  A Lattice Boltzmann Model of Binary Fluid Mixture , 1995, comp-gas/9511001.

[43]  G. Gonnella,et al.  Lattice Boltzmann simulations of lamellar and droplet phases , 1998 .

[44]  C. Béguin,et al.  Maximal deformation of an impacting drop , 2004, Journal of Fluid Mechanics.

[45]  S. Di Francesco,et al.  CFD modelling approach for dam break flow studies , 2009 .

[46]  A. Lamura,et al.  A lattice Boltzmann model of ternary fluid mixtures , 1995 .

[47]  Sauro Succi,et al.  Lattice Boltzmann Models with Mid-Range Interactions , 2007 .

[48]  S Succi,et al.  Lattice Boltzmann models for nonideal fluids with arrested phase-separation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  J. Eggers.  Nonlinear dynamics and breakup of free-surface flows , 1997 .

[50]  M. Sbragaglia,et al.  Continuum free-energy formulation for a class of lattice Boltzmann multiphase models , 2009, 0901.4799.

[51]  Raoyang Zhang,et al.  A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh-Taylor Instability , 1998 .

[52]  Sauro Succi,et al.  Lattice Boltzmann spray-like fluids , 2008 .

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

[54]  Ching-Long Lin,et al.  A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio , 2005 .

[55]  Gretar Tryggvason,et al.  Computational Methods for Multiphase Flow: Frontmatter , 2007 .

[56]  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.