Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics
Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics
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DOI：
10.1016/j.jcp.2008.10.021
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发表时间：
2009-03-01
影响因子：
4.1
通讯作者：
Sagaut, Pierre
中科院分区：
文献类型：
--
作者：
Marie, Simon;Ricot, Denis;Sagaut, Pierre
计算气动声学（CAA）仿真需要精确的方案来捕捉声学波动的动力学，这是弱的相比，气动。本文研究和比较了两种格式：基于高阶格式的经典方法和格子Boltzmann方法。参考宏观方程是三维等温可压缩Navier-Stokes方程。对这些线性化方程进行了冯·诺依曼分析，以获得精确的平面波解。恢复了三个物理模式，并得到了相应的理论色散关系。然后对Navier-Stokes方程的空间离散和时间离散进行了同样的分析，以量化空间离散和时间离散对精确解的影响。不同的顺序被认为是离散化，有和没有一个统一的平均流量。三种不同的晶格玻尔兹曼模型，然后提出和研究与冯诺依曼分析。得到了这些模型的理论色散关系，并对模型的误差项进行了辨识和研究。结果表明，格子Boltzmann模型中的色散误差仅由空间和时间离散引起，连续离散速度Boltzmann方程与Navier-Stokes方程具有相同的精确色散。最后，对不同格式的色散和耗散误差进行了定量比较。结果表明，格子Boltzmann方法在空间上比高阶格式耗散小，在时间上比二阶格式和三步Range-Kutta格式色散小。然后比较了这两种方案在给定误差水平下的浮点运算次数。(C)2008年爱思唯尔公司All rights reserved.
Computational aeroacoustic (CAA) simulation requires accurate schemes to capture the dynamics of acoustic fluctuations, which are weak compared with aerodynamic ones. In this paper, two kinds of schemes are studied and compared: the classical approach based on high order schemes for Navier-Stokes-like equations and the lattice Boltzmann method. The reference macroscopic equations are the 3D isothermal and compressible Navier-Stokes equations. A Von Neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions. Three physical modes are recovered and the corresponding theoretical dispersion relations are obtained. Then the same analysis is made on the space and time discretization of the Navier-Stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions. Different orders of discretization are considered, with and without a uniform mean flow. Three different lattice Boltzmann models are then presented and studied with the Von Neumann analysis. The theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied. It is shown that the dispersion error in the lattice Boltzmann models is only due to the space and time discretization and that the continuous discrete velocity Boltzmann equation yield the same exact dispersion as the Navier-Stokes equations. Finally, dispersion and dissipation errors of the different kind of schemes are quantitatively compared. It is found that the lattice Boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3-step Range-Kutta scheme in time. The number of floating point operations at a given error level associated with these two kinds of schemes are then compared. (C) 2008 Elsevier Inc. All rights reserved.