A Compressible Thermal Lattice Boltzmann Model with Factorization Symmetry

REFERENCES

• Y. H. Qian , D. D'Humires , and P. Lallemand , Lattice BGK Models for Navier-Stokes Equation , Europhys. Lett. , vol. 17 , pp. 479 – 484 , 1992 .
   Google Scholar
• Y. H. Qian , Smulating Thermohydrodynamics with Lattice BGK Models , J. Sci. Comput. , vol. 8 , pp. 231 – 242 , 1993 .
   Google Scholar
• S. Y. Chen and G. D. Doolen , Lattice Boltzmann Method for Fluid Flows , Annu. Rev. Fluid Mech. , vol. 30 , pp. 329 – 364 , 1998 .
   Web of Science ®Google Scholar
• S. Succi , The Lattice Boltzamnn Equation: For Fluid Dynamics and beyond , Numerical Mathematics and Scientific Computation , Clarendon Press , Oxford , UK , 2001 .
   Google Scholar
• L. Jahanshaloo , E. Pouryazdanpanah , S. Che , and A. Nor , Review on the Application of the Lattice Boltzmann Method for Turbulent Flow Simulation , Numeri. Heat Transfer A , vol. 64 , pp. 938 – 958 , 2013 .
   Web of Science ®Google Scholar
• P. Lopez and Y. Bayazitoglu , High Knudsen Number Thermal Flows with the D2Q13 Lattice Boltzmann Model , Numer. Heat Transfer A , vol. 64 , pp. 93 – 106 , 2013 .
   Web of Science ®Google Scholar
• P. Lallemand and L. S. Luo , Hybrid Finite-Difference Thermal Lattice Boltzmann Equation , Int. J. Mod. Phys. B , vol. 17 , pp. 41 – 47 , 2003 .
   Web of Science ®Google Scholar
• F. J. Alexander , H. Chen , S. Chen , and G. D. Doolen , Lattice Boltzmann Model for Compressible Fluids, Phys. Rev. A , vol. 46, pp. 1967–1970, 1992.
   PubMed Web of Science ®Google Scholar
• Y. Chen , H. Ohashi , and M. Akiyama , Thermal Lattice Bhatnagar-Gross-Krook Model without Nonlinear Deviations in Macrodynamic Equations , Phys. Rev. E , vol. 50 , pp. 2776 – 2783 , 1994 .
   PubMed Web of Science ®Google Scholar
• N. I. Prasianakis , S. S. Chikatamarla , I. V. Karlin , S. Ansumali , and K. Boulouchos , Entropic Lattice Boltzmann Method for Simulation of Thermal Flows , Math. Comput. Simulation , vol. 72 , pp. 179 – 183 , 2006 .
   Web of Science ®Google Scholar
• N. I. Prasianakis and I. V. Karlin , Lattice Boltzmann Method for Thermal Flow Simulation on Standard Lattices , Phys. Rev. E , vol. 76 , 016702 , 2007 .
   PubMed Web of Science ®Google Scholar
• N. I. Prasianakis and I. V. Karlin , Lattice Boltzmann Method for Simulation of Compressible Flows on Standard Lattices , Phys. Rev. E , vol. 78 , 016704 , 2008 .
   PubMed Web of Science ®Google Scholar
• X. Y. He , S. Y. Chen , and G. D. Doolen , A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , J. Comput. Phys. , vol. 146 , pp. 282 – 300 , 1998 .
   Web of Science ®Google Scholar
• Z. L. Guo , C. G. Zheng , B. C. Shi , and T. S. Zhao , Thermal Lattice Boltzmann Equation for Low Mach Number Flows: Decoupling Model , Phys. Rev. E , vol. 75 , 036704 , 2007 .
   Web of Science ®Google Scholar
• P. Lallemand and L. S. Luo , Theory of the Lattice Boltzmann Method: Acoustic and Thermal Properties in Two and Three Dimensions , Phys. Rev. E , vol. 68 , 036706 , 2003 .
   PubMed Web of Science ®Google Scholar
• V. Sofonea and R. F. Sekerka , Diffuse-Reflection Boundary Conditions for a Thermal Lattice Boltzmann Model in Two Dimensions: Evidence of Temperature Jump and Slip Velocity in Microchannels , Phys. Rev. E , vol. 71 , 066709 , 2005 .
   PubMed Web of Science ®Google Scholar
• Y. H. Zhang , X. J. Gu , R. W. Barber , and D. R. Emerson , Capturing Knudsen Layer Phenomena Using a Lattice Boltzmann Model , Phys. Rev. E , vol. 74 , 046704 , 2006 .
   Web of Science ®Google Scholar
• M. Koji , Numerical Simulation for Gas Microflows Using Boltzmann Equation , Comput. Fluids , vol. 35 , pp. 978 – 985 , 2006 .
   Web of Science ®Google Scholar
• S. H. Kim , H. Pitsch , and I. D. Boyd , Accuracy of Higher-Order Lattice Boltzmann Methods for Microscale Flows with Finite Knudsen Numbers , J. Comput. Phys. , vol. 227 , pp. 8655 – 8671 , 2008 .
   Web of Science ®Google Scholar
• S. Ansumali , I. V. Karlin , S. Arcidiacono , A. Abbas , and N. I. Prasianakis , Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy , Phys. Rev. Lett. , vol. 98 , 124502 , 2007 .
   PubMed Web of Science ®Google Scholar
• G. H. Tang , Y. H. Zhang , and D. R. Emerson , Lattice Boltzmann Models for Nonequilibrium Gas Flows , Phys. Rev. E , vol. 77 , 046701 , 2008 .
   Web of Science ®Google Scholar
• J. P. Meng , Y. H. Zhang , and X. W. Shan , Multiscale Lattice Boltzmann Approach to Modeling Gas Flows , Phys. Rev. E , vol. 83 , 046701 , 2011 .
   Web of Science ®Google Scholar
• Q. Li , Y. He , G. Tang , and W. Tao , Lattice Boltzmann Modeling of Microchannel Flows in the Transition Flow Regime , Microfluid. Nanofluid. , vol. 10 , pp. 607 – 618 , 2011 .
   Web of Science ®Google Scholar
• X. W. Shan , X. F. Yuan , and H. D. Chen , Kinetic Theory Representation of Hydrodynamics: A Way beyond the Navier-Stokes Equation , J. Fluid Mech. , vol. 550 , pp. 413 – 441 , 2006 .
   Web of Science ®Google Scholar
• K. Qu , C. Shu , and Y. T. Chew , Alternative Method to Construct Equilibrium Distribution Functions in Lattice-Boltzmann Method Simulation of Inviscid Compressible Flows at High Mach Number , Phys. Rev. E , vol. 75 , 036706 , 2007 .
   Web of Science ®Google Scholar
• I. V. Karlin , A. N. Gorban , S. Succi , and V. Boffi , Maximum Entropy Principle for Lattice Kinetic Equations , Phys. Rev. Lett. , vol. 81 , pp. 6 – 9 , 1998 .
   Web of Science ®Google Scholar
• I. Karlin and P. Asinari , Factorization Symmetry in the Lattice Boltzmann Method , Physica A—Stat. Mech. Appl. , vol. 389 , pp. 1530 – 1548 , 2010 .
   Web of Science ®Google Scholar
• S. S. Chikatamarla and I. V. Karlin , Lattices for the Lattice Boltzmann Method , Phys. Rev. E , vol. 79 , 046701 , 2009 .
   PubMed Web of Science ®Google Scholar
• Q. Li , Y. L. He , Y. Wang , and W. Q. Tao , Coupled Double-Distribution-Function Lattice Boltzmann Method for the Compressible Navier-Stokes Equations , Phys. Rev. E , vol. 76 , 056705 , 2007 .
   Web of Science ®Google Scholar
• Y. Wang , Y. He , Q. Li , G. Tang , and W. Tao , Lattice Boltzmann Model for Simulating Viscous Compressible Flows, Int. J. Mod. Phys. C , vol. 21, pp. 383–407, 2010.
   Web of Science ®Google Scholar
• P. Woodward and P. Colella , The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks , J. Comput. Phys. , vol. 54 , pp. 115 – 173 , 1984 .
   Web of Science ®Google Scholar