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

Co-operative Research on Numerical Solutions in Seience and Technology

科技数值解的合作研究

基本信息

批准号：
07304022
负责人：
TABATA Masahisa
金额：
$ 4.74万
依托单位：
HIROSHIMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07304022/
关键词：
finite element method drag and lift vortex method and vortex sheet leak boundary condition domain decomposition method parallel computation algorithm Navier-Stokes equations computation with guaranteed error bounds 並列計算自由境界問題差分微分方程式

项目摘要

1. When the problem is axisymmetric, we can transform original three-dimensional problems to two-dimensional ones by introducing cylidrincal coordinates. The amount of required computation is reduced drastically but a singularity appears on the axis of symmetry. We have introduced suitable finite element subdivisions and weighted function spaces adapted to the singularity and obtained convergence results and optimal error estimates for both mixed and stabilized finite element approximations to flow problems.2. We have developed a new method for getting much more precise force exerted from fluid to bodies in flows. Using a weak form we transform the surface integrals to body integrals for the computation of drag and lift forces. We have establish error analyzes and found more precise values of drag and lift coefficients of bodies of any shape.3. The vortex layr is one of main fundamental processes of the turbulence and it is important ot find out the mechanism. We have studied numerically the behavior of two-dimensional vortex leyers in shear flows. We have observed that the phenomena differ much depending on the signs of vortices of vortex layrs and shear layrs.4. Leak boundary conditions often appear in phenomena of engineering and environmental problems. We have formulated and analyzed the boundary condition. We have also developed a unmerical method.5. We have combined higher-order finite elements and a residual iteration method in order to estimate errors of numerical solutions of nonlinear elliptic problems in the maximum norm. We have improved drastically the verification accuracy of numerical solutions.6. We have proposed collocation type two-step Runge-Kutta methods. They preserve the orders and stability and are easily implemented on parallel computers. We have constructed higher-order two-step Runge-Kutta methods by a suitable setting of collocation points, implemented it in the prediction and correction type, and realized a high-performance computation.

1.当问题为轴对称时，通过引入圆柱坐标，可以将原来的三维问题转化为二维问题。所需的计算量大大减少，但奇异性出现在对称轴上。我们引入了适合于奇异性的有限元剖分和加权函数空间，得到了流动问题的混合有限元和稳定有限元的收敛结果和最优误差估计.我们发展了一种新的方法来获得更精确的力从流体施加到物体的流动。利用一个弱形式，我们将表面积分转化为体积分，用于计算阻力和升力。我们建立了误差分析，并找到了任何形状物体的阻力和升力系数的更精确的值.涡层是湍流的主要基本过程之一，对其机理的研究具有重要意义。本文用数值方法研究了剪切流中二维涡层的行为。我们观察到，不同的涡旋层和剪切层的涡旋符号，其现象有很大的不同.泄漏边界条件经常出现在工程和环境问题中。我们已经制定和分析的边界条件。我们还开发了一个unmerical方法。本文将高阶有限元和剩余迭代法相结合，给出了非线性椭圆问题数值解的最大模误差估计。我们大大提高了数值解的验证精度.我们提出了配置型两步Runge-Kutta方法。它们保持了顺序和稳定性，并且很容易在并行计算机上实现。通过适当设置配置点，构造了高阶两步Runge-Kutta方法，并将其实现为预测校正型，实现了高性能计算。