Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger's equation

Velivelli, Aditya C.; Bryden, Kenneth M.

doi:10.1016/j.physa.2005.09.031

Cited by 50 publications

(15 citation statements)

References 7 publications

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“…[4]。目前，LBM 已经广泛应用于多相流 [5]、多组分流 [6]、多孔介质流 [7]、悬浮流 [8]等复杂问题。此外， LBM 可以求解 Burgers 方程 [9] [10]、KdV 方程 [11]，Lorenz 方程 [12]，Schrödinger 方程 [13] …”

Section: 引言近 30 年来，格子 Boltmzann 方法(Lbm)已经发展成为一种有效的计算流体动力学(cfd)方法[1]unclassified

A Lattice Boltzmann Model for the Steady State Compressible Flows

闫¹

2017

IJFD

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Section: 引言近 30 年来，格子 Boltmzann 方法(Lbm)已经发展成为一种有效的计算流体动力学(cfd)方法[1]unclassified

A Lattice Boltzmann Model for the Steady State Compressible Flows

闫¹

2017

IJFD

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“…粒子流 [5]，磁流体 [6]，多孔介质流 [7]以及反应扩散系统 [8]等。此外，LBM在求解非线性物理方程领域也有出色的表现，如波动方程 [9]、KDV方程 [10]、Burgers方程 [11] [12]、非线性Schrödinger方程 [13] [14] [15] 和 Poisson 方程 [16] …”

Section: 模拟方法[2] [3] [4]。目前，lbm已广泛用于模拟单组分水动力学问题[2]，多相和多组分流动，包括悬浮unclassified

A Lattice Runge-Kutta-Boltzmann Model for the Reaction Diffusion Equation

闫铂¹,

王建朝²,

闫广武³

2017

AAM

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A lattice Runge-Kutta-Boltzmann model for the reaction diffusion equations is constructed in this paper. By using the classical Runge-Kutta formula, we obtain four-order accuracy of truncation error. The Chapman-Enskog expansion and multi-scale technique are employed in order to obtain a series of equations in different time scales and modify partial differential equations of the reaction diffusion equations. Numerical tests show that the scheme can be used to simulate the reaction diffusion equations.

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“…It means that it represents a valuable tool of analysis for microfluids. Moreover, the explicit time marching scheme, based on an advection and a collision step, makes it much more efficient when dealing with unsteady problems with respect to the classical CFD solvers that have to solve algebraic systems resulting from the discretization of the NS equations (see [8]). On the other hand, the method has a weakly-compressible nature and so it is more computationally expensive for almost steady fluid problems.…”

Section: Introductionmentioning

confidence: 99%