The cumulant method for computational kinetic theory
The cumulant method for computational kinetic theory
复制标题
计算动力学理论的累积方法
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
H. Hoffmann
中科院分区：
文献类型：
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作者：
S. Seeger;H. Hoffmann
提出了一种基于运动论的气体动力学数值模拟新方法。该方法基于相空间密度的累积展开式，从而得到一组准线性双曲型偏微分方程。将该方法与格拉德矩量法进行了比较。这两种方法都同意低阶近似，但所提出的方法显示出额外的非线性项高阶近似。从相空间密度的条件出发，导出了理想反射边界面和理想粗糙边界面的累积量边界条件。本文采用Lax方法对二维BGK流体进行了数值分析，得到了一种易于在并行计算机上实现的算法。结果发现同意定性与矩理论的预测。
We propose a new method for numerical simulation of gas dynamics based on kinetic theory. The method is based on a cumulant-expansion-ansatz for the phase space density, which leads to a set of quasi-linear, hyperbolic partial differential equations. The method is compared to the moment method of Grad. Both methods agree for low-order approximations but the method proposed shows additional non-linear terms for high order approximations. Boundary conditions on the cumulants for an ideally reflecting and an ideally rough boundary surface are derived from conditions on the phase space density. A Lax-method is used for numerical analysis of a 2d-BGK fluid, which results in an easy-to-implement algorithm well suited for implementation on massivly parallel computers. The results are found to agree qualitatively with predictions from moment theories.