Optimization Strategies for the Entropic Lattice Boltzmann Method

The entropic formulation of the lattice Boltzmann method (LBM) features enhanced numerical stability due to its compliance with the Boltzmann H-theorem. This stability comes at the price of some computational overhead, associated with the need of adjusting the local relaxation time of the standard LBM in such a way as to secure compliance with the H-theorem. In this paper, we discuss a number of possible optimization strategies to reduce the computational overhead of entropic LBMs.

[1]  Xiaoyi He,et al.  Lattice Boltzmann simulation of electrochemical systems , 2000 .

[2]  Sauro Succi,et al.  Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations , 2002 .

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

[4]  X. He,et al.  Discretization of the Velocity Space in the Solution of the Boltzmann Equation , 1997, comp-gas/9712001.

[5]  Alexander N Gorban,et al.  Maximum Entropy Principle for Lattice Kinetic Equations , 1998 .

[6]  I. Karlin,et al.  Stabilization of the lattice boltzmann method by the H theorem: A numerical test , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  I. Karlin,et al.  Kinetic boundary conditions in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[9]  K. Ebihara,et al.  Numerical simulation of coalescence and breakup of rising droplets , 2003 .

[10]  S. Orszag,et al.  Extended Boltzmann Kinetic Equation for Turbulent Flows , 2003, Science.

[11]  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.

[12]  Akio Tomiyama,et al.  Simulation of Bubble Motion under Gravity by Lattice Boltzmann Method , 2001 .

[13]  Bruce M. Boghosian,et al.  On the dependence of the Navier–Stokes equations on the distribution of molecular velocities , 2004 .

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

[15]  Matthaeus,et al.  Lattice Boltzmann model for simulation of magnetohydrodynamics. , 1991, Physical review letters.

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

[17]  M. Markus,et al.  On-off intermittency and intermingledlike basins in a granular medium. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[19]  H. C. Ottinger,et al.  Minimal entropic kinetic models for hydrodynamics , 2002, cond-mat/0205510.

[20]  Shiyi Chen,et al.  Simulation of Cavity Flow by the Lattice Boltzmann Method , 1994, comp-gas/9401003.

[21]  Iliya V. Karlin,et al.  Entropy Function Approach to the Lattice Boltzmann Method , 2002 .

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

[23]  P. Coveney,et al.  Entropic lattice Boltzmann methods , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

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

[25]  Bruce M. Boghosian,et al.  Quaternionic Madelung Transformation and Non-Abelian Fluid Dynamics , 2004 .

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

[27]  S. Zaleski,et al.  Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow , 1994 .

[28]  E. Erturk,et al.  Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers , 2004, ArXiv.

[29]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[30]  Santosh Ansumali,et al.  Single relaxation time model for entropic lattice Boltzmann methods. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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