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

本研究发展了一种求解复杂条件下流体的数值方法--“变形单胞方法”，并将其应用于工程问题。复杂条件是指分析的范围不是直角的、具有复杂边界条件的移动边界和特殊的外力。该方法基于可随运动边界变形的单元中的积分型守恒定律，对各种边界条件进行统一处理。1.自由表面和密度界面波：对斜坡上两层流体中的自由表面和密度界面波进行了垂向分析。针对这一问题，研究了“开边界条件”和“微胞”。物体与流体的相互作用：假设了体内/体外流动或漂浮体的问题，但它们是不久的将来的主题，与下一项相关的磁场驱动的非磁性物体…更多的TiC流体。流体在特殊外力作用下：对“磁性流体中的波”进行了理论和数值研究。理论分析的结果如下：(1)自由表面或密度界面上的共振波在交变磁场作用下的稳定性可用Mathieu方程或其推广形式来研究；(2)保角变换方法很好地描述了强磁场作用下的强非线性多值自由表面形状。它们将为数值和实验研究提供指导。在数值分析中，用变形单胞方法成功地分析了交变磁场作用下的残余波，且结构变化不大。微重力下的流体是未来的主题。计算流体力学基础：建立了一个新的“广泛使用的流体三维分析系统”。该系统支持大量原创代码的广泛生成，减少了编程和管理数据的负担：(1)循环程序可以在代码的所有部分通用；(2)可以在代码的任何部分以统一的方式获取全球编号。这一系统被认为是积极和系统地积累稳定和准确的方法和诊断技术的基础。较少

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