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1.

Three ways to lattice Boltzmann: a unified time-marching picture.

Ubertini S, Asinari P, Succi S.

Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jan;81(1 Pt 2):016311. Epub 2010 Jan 15.

PMID:
20365464
2.

Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow.

Guo Z, Zheng C, Shi B.

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 2):036707. Epub 2008 Mar 21.

PMID:
18517557
3.

Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability

Lallemand P, Luo LS.

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jun;61(6 Pt A):6546-62.

PMID:
11088335
4.

Semi-implicit-linearized multiple-relaxation-time formulation of lattice Boltzmann schemes for mixture modeling.

Asinari P.

Phys Rev E Stat Nonlin Soft Matter Phys. 2006 May;73(5 Pt 2):056705. Epub 2006 May 22.

PMID:
16803072
5.

Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions.

Lallemand P, Luo LS.

Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036706. Epub 2003 Sep 23.

PMID:
14524925
6.

Solving the Fokker-Planck kinetic equation on a lattice.

Moroni D, Rotenberg B, Hansen JP, Succi S, Melchionna S.

Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jun;73(6 Pt 2):066707. Epub 2006 Jun 22.

PMID:
16907023
7.

Lattice Boltzmann model for the one-dimensional nonlinear Dirac equation.

Shi B, Guo Z.

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 2):066704. Epub 2009 Jun 5.

PMID:
19658622
8.

Theory of the lattice Boltzmann equation: Lattice Boltzmann model for axisymmetric flows.

Guo Z, Han H, Shi B, Zheng C.

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Apr;79(4 Pt 2):046708. Epub 2009 Apr 20.

PMID:
19518381
9.

Taylor-series expansion and least-squares-based lattice Boltzmann method: Two-dimensional formulation and its applications.

Shu C, Niu XD, Chew YT.

Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2B):036708. Epub 2002 Mar 6.

PMID:
11909308
10.

Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows.

Guo Z, Shi B, Zhao TS, Zheng C.

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Nov;76(5 Pt 2):056704. Epub 2007 Nov 15.

PMID:
18233787
11.

Bulk and shear viscosities in lattice Boltzmann equations.

Dellar PJ.

Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 1):031203. Epub 2001 Aug 27.

PMID:
11580323
12.

Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme.

Palpacelli S, Succi S, Spigler R.

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Sep;76(3 Pt 2):036712. Epub 2007 Sep 28.

PMID:
17930366
13.

Kinetic lattice Boltzmann method for microscale gas flows: issues on boundary condition, relaxation time, and regularization.

Niu XD, Hyodo SA, Munekata T, Suga K.

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Sep;76(3 Pt 2):036711. Epub 2007 Sep 27.

PMID:
17930365
14.

Lattice Boltzmann schemes for the nonlinear Schrödinger equation.

Zhong L, Feng S, Dong P, Gao S.

Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 2):036704. Epub 2006 Sep 25.

PMID:
17025783
15.

Theory of the lattice Boltzmann method: three-dimensional model for linear viscoelastic fluids.

Lallemand P, D'Humières D, Luo LS, Rubinstein R.

Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 1):021203. Epub 2003 Feb 19.

PMID:
12636662
16.

Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation.

Reis T, Phillips TN.

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026702. Epub 2008 Feb 8.

PMID:
18352143
17.

Lattice Boltzmann equation for microscale gas flows of binary mixtures.

Guo Z, Asinari P, Zheng C.

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Feb;79(2 Pt 2):026702. Epub 2009 Feb 9.

PMID:
19391869
18.

Theoretical and numerical study of axisymmetric lattice Boltzmann models.

Huang H, Lu XY.

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 2):016701. Epub 2009 Jul 8.

PMID:
19658832
19.

Force imbalance in lattice Boltzmann equation for two-phase flows.

Guo Z, Zheng C, Shi B.

Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Mar;83(3 Pt 2):036707. Epub 2011 Mar 28.

PMID:
21517625
20.

Straight velocity boundaries in the lattice Boltzmann method.

Latt J, Chopard B, Malaspinas O, Deville M, Michler A.

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056703. Epub 2008 May 13.

PMID:
18643191
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