Basic of Numerical Analysis for a Variety of Fluids under Complex Conditions and its Application to Engineering Problems

本研究提出了复杂条件下流体的“变形单元法”数值计算方法，并将其应用于工程问题。复杂条件是指非反角分析域、具有复杂边界条件的运动边界和特殊外力。该方法基于随移动边界而变形的单元格的积分型守恒定律，统一处理各种边界条件。本研究确定的主题是：1。自由表面波和密度界面波：对斜坡上两层流体中的自由表面波和密度界面波进行了垂直分析。针对这一问题，研究了“开边界条件”和“微胞”。相互作用的体与流体：体内/体外流动或浮体的问题是假定的，但它们与与下一项相关的“磁场驱动的非磁性体……更多的流体”一起是近期的主题。特殊外力作用下的流体：对“磁流体中的波动”进行了理论和数值研究。理论分析的结果如下：(1)交变磁场作用下共振波在自由表面或密度界面上的稳定性可以用Mathieu方程或其推广来研究；(2)保角映射法很好地描述了强磁场作用下的强非线性多值自由曲面形状。它们将为数值和实验研究提供指导。在数值分析中，采用变形单元法对交变磁场引起的谐振波进行了成功的分析，而其框架只发生了很小的变化。小重力下的流体是今后研究的主题。以计算流体力学为基础，新建立了一个“广泛应用的流体三维分析系统”。该系统支持大量原始部分的计算机代码的广泛创建，并通过以下方式减少了编程和管理数据的负担：(1)循环过程可以在代码的所有部分中普遍使用；(2)在码的任何部分都可以统一获取全局号码。该系统是积极、系统地储备稳定、准确的方法和诊断技术的基础。少

This reasearch has developed a numerical method called "deformable-cell method" for fluids under complex conditions, and applied it to engineering problems. Complex conditions mean the domain of analysis not reactangular, moving boundaries with complex boundary conditions, and special external forces. The method is based on integral-type laws of conservation in cells which is deformable in accordance with moving boundaries, and various boundary conditions are treated in a unified manner there. The themes specified in this research are :1. Free surface and density interface waves : Vertical analysis on free surface and desity interface waves in a two-layred fluid on a slope was performed. In connection with this problem, "open boundary condition" and "tiny cell" were investigated.2. Interacting bodies and fluid : Problems on flows in vivo/in vitro or floating bodies was supposed, but they are the themes in the near future together with "nonmagnetic body driven by magnetic field in magne … More tic fluid" related with the next item.3. Fluid under special external force : "Waves in magnetic fluid" have been investigated both theoretically and numerically. The following are the results of theretical analysis : (1) Stability of the resonant waves on the free surface or on the density interface by alternating magnetic fields can be investigated by the Mathieu equation or its extension ; (2) The method of conformal mapping describes well the strongly-nonlinear multivalued free surface shapes under strong magnetic field. They will give guides for numerical and experimental researches. In numerical analysis, resnant waves caused by alternating magnetic fields were analyzed by the deformable-cell method successfully with only a small change of its framework. The fluid under smal gravity is the theme in the future.4. Basis on computational fluid dynamics : A "system for three-dimensional analysis of fluids for wide uses" has been newly constructed. This system supoprts extensively creating computer codes with a large original part, and diminished the loads of programming and managing data by : (1) The loop procedures can be used commonly in all parts of the code ; (2) Global numbers can be acquired in a unified manner at any part of the code. This system is considered as the basis for stocking positively and systematically the knowhow on stable and accurate methods and diagnoses. Less