Optimal preconditioning of lattice Boltzmann methods

[1]  Lin,et al.  Lattice boltzmann method on composite grids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  P. Philippi,et al.  Lattice Boltzmann equation linear stability analysis: thermal and athermal models. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Norberto Fueyo,et al.  Preconditioned Navier-Stokes schemes from the generalised lattice Boltzmann equation , 2008 .

[4]  Sanjoy Banerjee,et al.  Steady state convergence acceleration of the generalized lattice Boltzmann equation with forcing term through preconditioning , 2008, J. Comput. Phys..

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

[6]  W. Shyy,et al.  A multi‐block lattice Boltzmann method for viscous fluid flows , 2002 .

[7]  H. Raszillier,et al.  Symbolic Computation as a Tool for High-Order Long-Wave Stability Analysis of Thin Film Flows with Coupled Transport Processes , 1999 .

[8]  C. L. Merkle,et al.  The application of preconditioning in viscous flows , 1993 .

[9]  Sauro Succi,et al.  Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions , 2004 .

[10]  I. Karlin,et al.  Entropy and Galilean invariance of lattice Boltzmann theories. , 2006, Physical review letters.

[11]  Bastien Chopard,et al.  Lattice Boltzmann method with regularized pre-collision distribution functions , 2006, Math. Comput. Simul..

[12]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  W. Shyy,et al.  Viscous flow computations with the method of lattice Boltzmann equation , 2003 .

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

[15]  Shiyi Chen,et al.  Stability Analysis of Lattice Boltzmann Methods , 1993, comp-gas/9306001.

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

[17]  C. Shu,et al.  A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows , 2007 .

[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]  Jean-Antoine Désidéri,et al.  Numerical methods for the Euler equations of fluid dynamics , 1985 .

[20]  E. Turkel,et al.  PRECONDITIONING TECHNIQUES IN COMPUTATIONAL FLUID DYNAMICS , 1999 .

[21]  K. Breuer,et al.  Gaseous slip flow in long microchannels , 1997 .

[22]  Peter M. A. Sloot,et al.  Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method , 1999 .

[23]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[24]  G. Karniadakis,et al.  Microflows and Nanoflows: Fundamentals and Simulation , 2001 .

[25]  Ernst Rank,et al.  A Multigrid-Solver for the Discrete Boltzmann Equation , 2002 .

[26]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

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

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

[29]  B. Armaly,et al.  Experimental and theoretical investigation of backward-facing step flow , 1983, Journal of Fluid Mechanics.

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

[31]  Alexander N Gorban,et al.  Stability and stabilization of the lattice Boltzmann method. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Chih-Ming Ho,et al.  MICRO-ELECTRO-MECHANICAL-SYSTEMS (MEMS) AND FLUID FLOWS , 1998 .

[33]  W. Shyy,et al.  Improved treatment of the open boundary in the method of Lattice Boltzmann equation , 2005 .

[34]  Zhaoli Guo,et al.  Preconditioned lattice-Boltzmann method for steady flows. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  D. d'Humières,et al.  Two-relaxation-time Lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions , 2008 .

[36]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[37]  O. Botella,et al.  BENCHMARK SPECTRAL RESULTS ON THE LID-DRIVEN CAVITY FLOW , 1998 .

[38]  O. Filippova,et al.  Acceleration of Lattice-BGK schemes with grid refinement , 2000 .

[39]  D. Wolf-Gladrow.  Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[40]  M. Krafczyk,et al.  An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations , 2006 .

[41]  Dimitri J. Mavriplis,et al.  Multigrid solution of the steady-state lattice Boltzmann equation , 2006 .

[42]  J. Korvink,et al.  Cascaded digital lattice Boltzmann automata for high Reynolds number flow. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  P. Lallemand,et al.  Momentum transfer of a Boltzmann-lattice fluid with boundaries , 2001 .

[44]  M. D. Deshpande,et al.  FLUID MECHANICS IN THE DRIVEN CAVITY , 2000 .

[45]  Taehun Lee,et al.  Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.