An extended spectral analysis of the lattice Boltzmann method: modal interactions and stability issues

[1]  J. Neumann,et al.  Uber merkwürdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen , 1929 .

[2]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[3]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases : an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases , 1954 .

[4]  L. Kovasznay Turbulence in Supersonic Flow , 1953 .

[5]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[6]  L. Kovasznay,et al.  Non-linear interactions in a viscous heat-conducting compressible gas , 1958, Journal of Fluid Mechanics.

[7]  L. Boltzmann Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen , 1970 .

[8]  C. D. Mote,et al.  Comments on curve veering in eigenvalue problems , 1986 .

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

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

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

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

[13]  B. Shizgal,et al.  Generalized Lattice-Boltzmann Equations , 1994 .

[14]  Harris,et al.  Hydrodynamic behavior of lattice Boltzmann and lattice Bhatnagar-Gross-Krook models. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[16]  R. Worthing,et al.  Stability of lattice Boltzmann methods in hydrodynamic regimes , 1997 .

[17]  Y. Qian Fractional Propagation and the Elimination of Staggered Invariants in Lattice-BGK Models , 1997 .

[18]  Dominique d'Humières,et al.  A lattice Boltzmann model for Jeffreys viscoelastic fluid , 1998 .

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

[20]  Shiyi Chen,et al.  A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , 1998 .

[21]  Li-Shi Luo,et al.  Unified Theory of Lattice Boltzmann Models for Nonideal Gases , 1998 .

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

[23]  M. Y. Hussaini,et al.  An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems , 1999 .

[24]  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.

[25]  F. Durst,et al.  Numerical analysis of the pressure drop in porous media flow with lattice Boltzmann (BGK) automata , 2000 .

[26]  Hudong Chen,et al.  H-theorem and origins of instability in thermal lattice Boltzmann models , 2000 .

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

[28]  P. Dellar Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Mengping Zhang,et al.  AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS , 2003 .

[30]  Richard Shock,et al.  Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method , 2004, Journal of Fluid Mechanics.

[31]  J. Chomaz,et al.  GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity , 2005 .

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

[33]  Raoyang Zhang,et al.  Extended volumetric scheme for lattice Boltzmann models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  P. Philippi,et al.  From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  X. Yuan,et al.  Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation , 2006, Journal of Fluid Mechanics.

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

[37]  P. Sagaut,et al.  Homogeneous Turbulence Dynamics , 2008 .

[38]  X. Shan,et al.  Galilean invariance of lattice Boltzmann models , 2008, 0801.2924.

[39]  François Dubois,et al.  Equivalent partial differential equations of a lattice Boltzmann scheme , 2008, Comput. Math. Appl..

[40]  R. Adhikari,et al.  Duality in matrix lattice Boltzmann models. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Hudong Chen,et al.  A Lattice-Boltzmann / Finite-Difference Hybrid Simulation of Transonic Flow , 2009 .

[42]  Pierre Sagaut,et al.  Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics , 2009, J. Comput. Phys..

[43]  D. d'Humières,et al.  Optimal Stability of Advection-Diffusion Lattice Boltzmann Models with Two Relaxation Times for Positive/Negative Equilibrium , 2010 .

[44]  Pierre Sagaut,et al.  Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics , 2011, J. Comput. Phys..

[45]  Gaël Varoquaux,et al.  The NumPy Array: A Structure for Efficient Numerical Computation , 2011, Computing in Science & Engineering.

[46]  Nicholas A J Lieven,et al.  On the Quantification of Eigenvalue Curve Veering: A Veering Index , 2011 .

[47]  Zhaoli Guo,et al.  Discrete unified gas kinetic scheme for all Knudsen number flows: low-speed isothermal case. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Emmanuel Lévêque,et al.  Direct and large-eddy simulation of turbulent flows on composite multi-resolution grids by the lattice Boltzmann method , 2014, J. Comput. Phys..

[49]  I. Karlin,et al.  Gibbs' principle for the lattice-kinetic theory of fluid dynamics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  O. Malaspinas Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization , 2015, 1505.06900.

[51]  P. Philippi,et al.  Investigation of an entropic stabilizer for the lattice-Boltzmann method. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  I. Karlin,et al.  Entropic lattice Boltzmann model for compressible flows. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  J. Boussuge,et al.  Simulations of LAGOON landing-gear noise using Lattice Boltzmann Solver , 2015 .

[54]  Ulrich Rüde,et al.  Massively Parallel Algorithms for the Lattice Boltzmann Method on NonUniform Grids , 2015, SIAM J. Sci. Comput..

[55]  D. Casalino,et al.  Turbofan Broadband Noise Prediction Using the Lattice Boltzmann Method , 2016 .

[56]  Jean-François Boussuge,et al.  Revisiting the spectral analysis for high-order spectral discontinuous methods , 2017, J. Comput. Phys..

[57]  P. Philippi,et al.  High-order regularization in lattice-Boltzmann equations , 2017 .

[58]  G. Wissocq,et al.  Recursive regularization step for high-order lattice Boltzmann methods. , 2017, Physical review. E.

[59]  P. Sagaut,et al.  A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for Lattice Boltzmann method-based large eddy simulation , 2018, Journal of Turbulence.

[60]  Jizu Huang,et al.  A lattice Boltzmann model for multiphase flows with moving contact line and variable density , 2018, J. Comput. Phys..