权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Development of Numerical Method for Mesoscopic Flow

细观流动数值方法的发展

基本信息

批准号：
09680474
负责人：
YABE Takashi
金额：
$ 1.98万
依托单位：
TOKYO INSTITUTE OF TECHNOLOGY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

For the research of microscopic phenomena, molecular dynamics model has been proposed and for macroscopic level various kinds of hydrodynamic solvers have been investigated for a long time. In this research, we search for a numerical method to treat mesoscopic level that means the intermediate scale between and microscopic and macroscopic levels . For this purpose, we have used the CIP method which has been proposed by the author and has been proved to be accurate even with coarse grid system. In this research, we have used the Boltzmann equation which is six dimensions in phase space. Thus time evolution is merely an advection through six dimensions. Since the CIP method has been proved to be quite effective in solving advection equation, we applied this method and for simplicity we repeated one-dimensional CIP method to extend it to hyper-dimensional space.In order to test the algorithm, we solved two and four dimensional Vlasov equation which is collisionless Boltzmann equation, and applied it to linear Landau damping and nonlinear two-stream instability coupled with electric fields.Comparison with conventional particle codes and spline method has been done and it has been proven that particle codes need 10-100 times more memory than the CIP method for obtaining the same results. For a sufficiently accurate form of velocity distribution function required by mesoscopic calculations, particle codes needed 100 times more memory than the CIP method. Distribution functions given by spline methods become negative and have large spikes. These comparisons show the effectiveness of the CIP method in this research.We have varied the velocity grids and found that even with velocity grids less than 10 the CIP can give quite an accurate result. Finally, six dimensional code has been constructed and run on personal computer. One Alpha-chip-based personal computer needed only 6.7 hours for the calculation of Landau damping with 16 X 16 X 16 X 8 X 8 X 8 grids.

对于微观现象的研究，人们提出了分子动力学模型，而对于宏观层次，人们研究了各种流体动力学求解方法。在这项研究中，我们寻求一种数值方法来处理介观水平，即介于微观和宏观水平之间的中间尺度。为此，我们使用了作者提出的CIP方法，该方法已被证明即使在粗网格系统下也是准确的。在本研究中，我们使用了相空间中的六维Boltzmann方程。因此，时间演化只是一场穿越六个维度的平流。由于CIP方法在求解对流方程方面已经被证明是非常有效的，我们应用了该方法，为了简单起见，我们将一维CIP方法推广到超维空间。为了验证算法的有效性，我们求解了二维和四维Vlasov方程，该方程是无碰撞的Boltzmann方程，并将其应用于线性Landau阻尼和非线性双流不稳定性与电场的耦合。与传统的粒子编码和Spline方法进行了比较，证明了粒子编码获得相同结果需要的内存是CIP方法的10-100倍。对于介观计算所需的足够精确的速度分布函数形式，粒子代码所需的内存是CIP方法的100倍。由样条法给出的分布函数变为负值并且有很大的尖峰。这些比较表明了CIP方法在本研究中的有效性。我们改变了速度网格，发现即使在速度网格小于10的情况下，CIP方法也可以给出相当准确的结果。最后，构造了六维码，并在个人计算机上运行。一台基于Alpha芯片的个人计算机仅需6.7小时即可计算16×16×16×8网格的朗道阻尼力。