Multistep lattice Boltzmann methods: Theory and applications
Sign Up to like & getrecommendations! Published in 2019 at "International Journal for Numerical Methods in Fluids"
DOI: 10.1002/fld.4716
Abstract: 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… read more here.
Keywords: multistep methods; order; lattice boltzmann; multistep lattice ... See more keywords
Exact optimal values of step-size coefficients for boundedness of linear multistep methods
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DOI: 10.1007/s11075-017-0354-5
Abstract: Linear multistep methods (LMMs) applied to approximate the solution of initial value problems—typically arising from method-of-lines semidiscretizations of partial differential equations—are often required to have certain monotonicity or boundedness properties (e.g., strong-stability-preserving, total-variation-diminishing or total-variation-boundedness… read more here.
Keywords: optimal values; linear multistep; size; step size ... See more keywords
Numerical Integration Schemes Based on Composition of Adjoint Multistep Methods
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DOI: 10.3390/a15120463
Abstract: A composition is a powerful tool for obtaining new numerical methods for solving differential equations. Composition ODE solvers are usually based on single-step basic methods applied with a certain set of step coefficients. However, multistep… read more here.
Keywords: multistep methods; composition adjoint; composition; based composition ... See more keywords