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Development of the numerical scheme and finite element analysis for thermo-electrically conducting fluids

热电导电流体数值方案和有限元分析的开发

基本信息

批准号：
05650176
负责人：
TANAHASHI Takahiko
金额：
$ 1.47万
依托单位：
KEIO University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05650176/
关键词：
MHD Thermal fluids FEM GSMAC method Hybrid method Natural convection Heat transfer Liquit metal BSMAC法熱伝達

项目摘要

The primitive variable methods have been proposed in the numerical scheme of magnetic field of thermo-electrically conducting fluids. The point to be emphasized in the above-mentioned scheme is to satisfy the conservation law of magnetic flux efficiently. In the present research, we have compared the two numerical schemes of magnetic field, namely the cross helicity method and the numerical residual method, concentrating on convergence of Poisson's equation of the velocity and magnetic fields. Moreover, the relationship between the periodicity of low prandtl number fluids and the convective inhibitation effect by Lorentz force has been clarified quantitatively. The frequency characteristics of kinetic energy, enstrophy, palinstrophy and hydromagnetic cross helicity are calculated by the maximum entropy method. Furthermore, we have presented a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method. In order to obtain an optimal shape function, we have introduced an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them interpolates accurately the functions appearing in convection-dominated flows, the other becomes a hybrid-streamlime-upwind weight function. And, we have defined a discrete del operator for the reduction of memory storage in the computer.As a result, we have achieved simplicity of formulation and high-speed calculation of the finite-element method.

本文提出了一种基于原始变量法的热导电流体磁场数值计算方法。上述方案的重点是有效地满足磁通守恒定律。在本研究中，我们比较了磁场的两种数值方法，即交叉螺旋度方法和数值剩余方法，集中在速度和磁场的泊松方程的收敛性。定量地阐明了低普朗特数流体的周期性与洛仑兹力对流湍流效应之间的关系。用最大熵方法计算了动能、涡度拟能、回文涡度和磁流体交叉螺旋度的频率特征。此外，我们还提出了一种新的混合流线迎风有限元方法，它是基于有限差分法领域中发展的有限分析方法。为了得到最优形函数，我们在定常对流扩散方程的微分算子上引入了一个伴随微分算子。满足这些微分算子的形函数是相互对偶的。其中一个精确地插值函数出现在对流占主导地位的流动，另一个成为一个混合的streamlime迎风权函数。为了减少计算机内存，我们定义了一个离散del算子，从而使有限元法的计算公式简单，计算速度快。