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New Numerical Methods for Flow Problems and their Numerical Simulation

流动问题的新数值方法及其数值模拟

基本信息

批准号：
10304007
负责人：
TABATA Masahisa
金额：
$ 12.03万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

(1) We have developed a numerical method for computing accurately drag and lift exerted by the fluid to a body immersed in the flow field. Transforming those values to equivalent integrals in the domain, we have succeeded in establishing error estimates. We have obtained accurate drag coefficients of a sphere by this method. The restults have been extended to evolutional problems and best possible error estimates have been obtained.(2) The system of Rayleigh-Benard equations with infinite Prandtl number is a mathematical model describing heat convection phenomena in slow flows such as the Earth's mantle convection.We have developed a finite element scheme for this system, established error estimates, made an effective parallel code for three-dimensional computation, and performed numerical simulation for the Earth's mantle convection.(3) We have developed mathematical theory and computation algorithms to find exact solutions of partial differential equations from numerical computation results. Those methods have been applied to the stationary Stokes equations, the Navier-Stokes equations, stationary bifurcation solution of heat convection problems.(4) We have applied Dirichlet-Neumann mapping to exterior problems and developed combined numerical methods with a charge simulation method for the harmonic equation and with a domain decomposition method for the Helmholtz equation.(5) We have constructed a mathematical model to analyze effect to ecological system caused by coastal oil pollution and performed the numerical simulation and the visualization. The obtained results are in good agreement with physical experimental results.(6) The interface of porous media flow takes various behavior depending on the initial state. Using finite difference method we have given a sufficient condition for the separation of the support of the solution and upper and lower estimates of the waiting time for the initial interface to keep invariant.

(1)本文发展了一种精确计算流体对浸没在流场中物体的阻力和升力的数值方法。将这些值转化为域中的等价积分，我们成功地建立了误差估计。我们用这种方法得到了球体的精确阻力系数。所得结果已推广到演化问题，并得到了最佳可能误差估计。(2)具有无穷Prandtl数的Rayleigh-Benard方程组是描述地幔对流等慢流热对流现象的数学模型，我们发展了该方程组的有限元格式，建立了误差估计，编制了有效的三维并行计算程序，并对地幔对流进行了数值模拟。(3)我们已经发展了数学理论和计算算法，从数值计算结果中找到偏微分方程的精确解。这些方法已应用于定常Stokes方程、Navier-Stokes方程、热对流问题的定常分歧解。(4)我们已经应用Dirichlet-Neumann映射到外部问题，并开发了相结合的数值方法与电荷模拟方法的谐波方程和区域分解方法的Helmholtz方程。(5)建立了海岸带石油污染对生态系统影响的数学模型，并进行了数值模拟和可视化。所得结果与物理实验结果吻合较好。(6)多孔介质渗流界面随初始状态的不同而呈现出不同的行为。利用有限差分方法，给出了解的支撑分离以及初始界面保持不变的等待时间的上下估计的充分条件。