Chapman–Enskog analysis for finite-volume formulation of lattice Boltzmann equation

[1]  S. Chapman,et al.  On the Law of Distribution of Molecular Velocities, and on the Theory of Viscosity and Thermal Conduction, in a Non-Uniform Simple Monatomic Gas , 1916 .

[2]  David Enskog,et al.  Kinetische theorie der Vorgänge in Mässig verdünnten Gasen , 1917 .

[3]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[4]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[5]  C. Cercignani The Boltzmann equation and its applications , 1988 .

[6]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

[7]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[8]  S. Succi,et al.  The lattice Boltzmann equation on irregular lattices , 1992 .

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

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

[11]  Li-Shi Luo,et al.  Lattice-gas automata and lattice Boltzmann equations for two-dimensional hydrodynamics , 1993 .

[12]  Shiyi Chen,et al.  Simulation of Cavity Flow by the Lattice Boltzmann Method , 1994, comp-gas/9401003.

[13]  L. Luo,et al.  Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation , 1997 .

[14]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

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

[16]  So-Hsiang Chou,et al.  FINITE VOLUME SCHEME FOR THE LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES , 1999 .

[17]  Axel Klar,et al.  Discretizations for the Incompressible Navier-Stokes Equations Based on the Lattice Boltzmann Method , 2000, SIAM J. Sci. Comput..

[18]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  O. Filippova,et al.  A Novel Lattice BGK Approach for Low Mach Number Combustion , 2000 .

[20]  P. Dellar Bulk and shear viscosities in lattice Boltzmann equations. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  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.

[22]  P. Lallemand,et al.  Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Dominique d'Humières,et al.  Multireflection boundary conditions for lattice Boltzmann models. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  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.

[25]  S. Succi,et al.  Lattice Boltzmann method on unstructured grids: further developments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Pierre Lallemand,et al.  Theory of the lattice Boltzmann method: three-dimensional model for linear viscoelastic fluids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Victor Sofonea,et al.  Viscosity of finite difference lattice Boltzmann models , 2003 .

[28]  Sauro Succi,et al.  Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model , 2004 .

[29]  S. Succi,et al.  Unstructured lattice Boltzmann method in three dimensions , 2005 .

[30]  John Abraham,et al.  Multiple-relaxation-time lattice-Boltzmann model for multiphase flow , 2005 .

[31]  Henning Struchtrup,et al.  Macroscopic transport equation for rarefied gas flows : approximation methods in kinetic theory , 2005 .

[32]  Sauro Succi,et al.  Recent advances of Lattice Boltzmann techniques on unstructured grids , 2005 .

[33]  M. Junk,et al.  Asymptotic analysis of the lattice Boltzmann equation , 2005 .

[34]  Manfred Krafczyk,et al.  An upwind discretization scheme for the finite volume lattice Boltzmann method , 2006 .

[35]  Ulf D. Schiller,et al.  Statistical mechanics of the fluctuating lattice Boltzmann equation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  P. Dellar Two routes from the Boltzmann equation to compressible flow of polyatomic gases , 2008 .

[37]  Pietro Asinari,et al.  Asymptotic analysis of multiple-relaxation-time lattice Boltzmann schemes for mixture modeling , 2008, Comput. Math. Appl..

[38]  Guangwu Yan,et al.  A lattice Boltzmann model for the compressible Euler equations with second‐order accuracy , 2009 .

[39]  Alfonso Caiazzo,et al.  Comparison of analysis techniques for the lattice Boltzmann method , 2009, Comput. Math. Appl..

[40]  Dhiraj V. Patil,et al.  Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh , 2009, J. Comput. Phys..

[41]  Dhiraj V. Patil,et al.  Two‐dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation , 2012 .