The research on homogenization, elasitic problems and the algorithms for numerical simulations of flows of liquids and development

均匀化、弹性问题及液体流动数值模拟算法的研究与发展

• 批准号: 11640098
• 负责人: KAIZU Satoshi
• 金额: $ 2.18万
• 依托单位: IBARAKI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640098/
• 关键词: two-layers problem; the density-dependent Stokes problem; generalized boundary problems; the adjoint method; energy fecay of the Rayleigh surface waves; numeric construction of free boundaries; superosition of plane waves in the half-space; converg

(1) Algorithm for numeric scheme on liquids flows : First, a theorem on errors of between the exact boundaries and numeric construction of boundaries are proposed by colleague and examined by numerically. Second, convergent finite element scheme for multi-flows miscible among different liquids, are proposed and proved. The governed equations are the Navier-Stokes equation for the first topic and the Stokes equation for the second one.(2) The Laplace equation is considered as the corresponding scalar equation to the Navier-Stokes equation, in order to treat in a unified way under the notion of the generalized boundary value probleml for elliptic partial differential equations by using the variational calculus. The approach is verified by numerical examples.(3) Among elastic waves, the Rayleigh surface waave is researched. In particular, the propagation of the Rayleigh surface wave is interested by us, and some estimates on decay of the local energy of the Rayleigh waves are obtained in many types of regions.(4) Generally in the total space, it is well known that waves are represented as superposition of plane waves. In this research, it is showd that, in the half-space region, a concrete form of superposition to elastic waves are obtained. This expression is expected to be applied to the construction of the Fourier transformation in the half-space.

(1)流体流动数值格式的算法：首先，同事提出了精确边界与数值边界构造之间的误差定理，并进行了数值验证。其次，提出并证明了不同液体混相多流的收敛有限元格式。控制方程是第一个题目的Navier-Stokes方程第二个题目的Stokes方程。(2)将拉普拉斯方程视为Navier-Stokes方程对应的标量方程，以便用变分微积分在椭圆型偏微分方程的广义边值问题的概念下统一处理。数值算例验证了该方法的有效性。(3)在弹性波中，对瑞利面波进行了研究。我们对瑞利面波的传播特别感兴趣，并在许多类型的区域中得到了瑞利面波局部能量衰减的一些估计。(4)一般在总空间中，波被表示为平面波的叠加。研究表明，在半空间区域，得到了弹性波叠加的具体形式。这个表达式可以应用到半空间中的傅里叶变换的构造中。

项目成果

Y.Ohura, K.Kobayashi and K.Onishi: "Numerical solution of an under-determined problem of the Laplace equation"J.of Applied Mechanics, JSCE. 2. 185-189 (1999)

Y.Ohura、K.Kobayashi 和 K.Onishi：“拉普拉斯方程欠定问题的数值解”J.of Applied Mechanics，JSCE。

王青川,大浦洋子,代田健二,大西和栄: "不足決定系2次元Laplace方程式の境界要素解"BTEC論文集. 第9巻. 57-61 (1999)

王庆川、大浦洋子、代田贤二、大西一惠：“欠定二维拉普拉斯方程的边界元解” BTEC Proceedings Vol. 9. 57-61 (1999)

藤間昌一: "A domain-decomposition finite-element scheme for flow problems"京都大学数理解析研究所講究録,「計算力学の新解法と領域分割法」. 1129. 9-22 (2000)

Shoichi Fujima：“流动问题的域分解有限元方案”京都大学数学科学研究所Kokyuroku，“计算力学的新求解方法和域分解方法”。1129. 9-22 (2000)。

藤間昌一: "A domain decomposition finite element scheme for flow problems- Choice of elements"数理解析研究所講究録. 1129. 9-22 (2000)

Shoichi Fujima：“流动问题的域分解有限元方案 - 元素的选择”数学科学研究所 Kokyuroku。1129. 9-22 (2000)。

M.Kawashita and G.Nakamura: "The poles of the resolvent for the exterior Neumann problem fo anisotropic elasticity"SIAM J.of Math.Anal,. 31. 701-725 (2000)

M.Kawashita 和 G.Nakamura：“各向异性弹性的外部诺依曼问题解决方案的极点”SIAM J.of Math.Anal，。