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Multistep lattice Boltzmann methods: Theory and applications
Author(s) -
Wilde Dominik,
Krämer Andreas,
Küllmer Knut,
Foysi Holger,
Reith Dirk
Publication year - 2019
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4716
Subject(s) - lattice boltzmann methods , discretization , hpp model , lattice gas automaton , linear multistep method , mathematics , boltzmann equation , statistical physics , bhatnagar–gross–krook operator , lattice (music) , stability (learning theory) , boltzmann constant , mathematical analysis , algorithm , physics , computer science , mechanics , ordinary differential equation , differential equation , thermodynamics , differential algebraic equation , stochastic cellular automaton , cellular automaton , machine learning , reynolds number , acoustics , turbulence
Summary This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second‐order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third‐order accurate Adams‐Moulton method and the second‐order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.