Enhancement of the stability of lattice Boltzmann methods by dissipation control

A.N. Gorban1, D.J. Packwood2
1Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
2Mathematics Institute, University of Warwick, Coventry, UK

Tài liệu tham khảo

Benzi, 1992, The lattice Boltzmann equation: theory and applications, Phys. Rep., 222, 145, 10.1016/0370-1573(92)90090-M Chen, 1998, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Dyn., 30, 329, 10.1146/annurev.fluid.30.1.329 Succi, 2001 Higeura, 1989, Lattice gas dynamics with enhanced collsions, Europhys. Lett. EPL, 9, 345, 10.1209/0295-5075/9/4/008 Packwood, 2011, Time step expansions and the invariant manifold approach to lattice Boltzmann models, vol. 75, 169 Karlin, 2003, Irreversibility in the short memory approximation, Physica A, 327, 399, 10.1016/S0378-4371(03)00510-7 Bhatnagar, 1954, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94, 511, 10.1103/PhysRev.94.511 Lätt, 2006, Numerical analysis of the averaged flow field in a turbulent lattice Boltzmann simulation, Physica A, 362, 6, 10.1016/j.physa.2005.09.016 D. d’Humieres, Generalized lattice Boltzmann equations, in: Rarefied Gas Dynamics, Vancouver, 1994, pp. 450–458. d’Humieres, 2002, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 360, 437, 10.1098/rsta.2001.0955 Dellar, 2002, Non-hydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations, Phys. Rev. E, 65, 036309, 10.1103/PhysRevE.65.036309 Dellar, 2003, Incompressible limits of lattice Boltzmann equations using multiple relaxation times, J. Comput. Phys., 190, 351, 10.1016/S0021-9991(03)00279-1 Dellar, 2006, Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations, Physica A, 362, 132, 10.1016/j.physa.2005.09.012 Lallemand, 2000, Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, 61, 6546, 10.1103/PhysRevE.61.6546 Karlin, 1998, Maximum entropy principle for lattice kinetic equations, Phys. Rev. Lett., 81, 6, 10.1103/PhysRevLett.81.6 Karlin, 1999, Perfect entropy functions of the lattice Boltzmann method, Europhys. Lett., 47, 182, 10.1209/epl/i1999-00370-1 Brownlee, 2006, Stabilization of the lattice Boltzmann method using the Ehrenfests’ coarse-graining idea, Phys. Rev. E, 74, 037703, 10.1103/PhysRevE.74.037703 Brownlee, 2007, Stability and stabilization of the lattice Boltzmann method, Phys. Rev. E, 75, 036711, 10.1103/PhysRevE.75.036711 Brownlee, 2008, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A, 387, 385, 10.1016/j.physa.2007.09.031 Tosi, 2006, Numerical stability of entropic versus positivity-enforcing lattice Boltzmann schemes, Math. Comput. Simul., 72, 227, 10.1016/j.matcom.2006.05.007 Luo, 2011, Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations, Phys. Rev. E, 83, 056710, 10.1103/PhysRevE.83.056710 Wu, 2014, Oscillatory rarefied gas flow inside rectangular cavities, J. Fluid Mech., 748, 350, 10.1017/jfm.2014.183 Brownlee, 2013, Add-ons for lattice Boltzmann methods: regularization, filtering and limiters, Prog. Comput. Phys., 3, 31 Ansumali, 2003, Minimal entropic kinetic models for hydrodynamics, Europhys. Lett., 63, 798, 10.1209/epl/i2003-00496-6 Yong, 2005, Nonexistence of H-theorem for some lattice Boltzmann models, J. Stat. Phys., 121, 91, 10.1007/s10955-005-5958-9 Ansumali, 2000, Stabilization of the lattice Boltzmann method by the H theorem: a numerical test, Phys. Rev. E, 62, 7999, 10.1103/PhysRevE.62.7999 Gorban, 2012, Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions, Phys. Rev. E, 86, 025701(R), 10.1103/PhysRevE.86.025701 Ansumali, 2002, Kinetic boundary conditions in the lattice Boltzmann method, Phys. Rev. E, 66, 026311, 10.1103/PhysRevE.66.026311 Auteri, 2002, Numerical investigation on the stability of singular driven cavity flow, J. Comput. Phys., 183, 1, 10.1006/jcph.2002.7145 Boghosian, 2004, Entropic lattice Boltzmann model for Burgers’s equation, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 362, 1691, 10.1098/rsta.2004.1410 Brezillon, 2010, A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics, Comput. Fluids, 39, 1226, 10.1016/j.compfluid.2010.03.006 Bruneau, 2006, The 2D lid-driven cavity problem revisited, Comput. & Fluids, 35, 326, 10.1016/j.compfluid.2004.12.004 Goodrich, 1990, Hopf bifurcation in the driven cavity, J. Comput. Phys., 90, 219, 10.1016/0021-9991(90)90204-E Gorban, 2010, Entropy: the Markov ordering approach, Entropy, 12, 1145, 10.3390/e12051145 Hou, 1995, Simulation of cavity flow by the lattice Boltzmann method, J. Comput. Phys., 118, 329, 10.1006/jcph.1995.1103 Karlin, 2011, Comment on “Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations”, Phys. Rev. E, 84, 068701, 10.1103/PhysRevE.84.068701 Packwood, 2009, Entropy balance and dispersive oscillations in lattice Boltzmann models, Phys. Rev. E, 80, 067701, 10.1103/PhysRevE.80.067701 Ricot, 2009, Lattice Boltzmann method with selective viscosity filter, J. Comput. Phys., 228, 4478, 10.1016/j.jcp.2009.03.030 Tadmor, 2006, Entropy stable approximations of Navier–Stokes equations with no artificial numerical viscosity, J. Hyperbolic Differ. Equ., 3, 529, 10.1142/S0219891606000896 Pan, 2000, A projection/wave-like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier–Stokes equations, Comput. Fluid Dyn. J., 9, 28 Peng, 2003, Transition in a 2-D lid-driven cavity flow, Comput. & Fluids, 32, 337, 10.1016/S0045-7930(01)00053-6 Abouhamza, 2003, A neutral stability curve for incompressible flows in a rectangular driven cavity, Math. Comput. Modelling, 38, 141, 10.1016/S0895-7177(03)90012-4 Shen, 1991, Hopf bifurcation of the unsteady regularized driven cavity flow, J. Comput. Phys., 95, 228, 10.1016/0021-9991(91)90261-I Tosi, 2008, An introduction to entropic lattice Boltzmann scheme, SIMAI e-Lect. Notes, 1 Tadmor, 2003, Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems, Acta Numer., 12, 451, 10.1017/S0962492902000156 Succi, 2002, Colloquium: role of the H theorem in lattice Boltzmann hydrodynamic simulations, Rev. Modern Phys., 74, 1203, 10.1103/RevModPhys.74.1203