Development of Finite Element Analysis System for Unsteady, Incompressible Viscous Fluid Flows

本研究的目的是发展一个求解非定常不可压Navier-Stokes方程的数值方法，并将其实现为一个适用于各种非定常流动问题的程序系统。(1)有限元求解方法的发展：利用研究者提出的一种独特的直接时间积分方法，通过对连续性条件和边界条件的特殊处理，从原始变量形式的有限元方程出发，导出了一组非线性递推方程，它表示了不可压缩约束下速度和压力的演化。在本推导中没有引入过多的人工技术。在每个积分步骤中，对非线性对流项进行迭代处理。(2)执行 ...更多信息 由于推导的非线性递推方程组的系统系数矩阵是非对称的，且可能具有带状轮廓，因此采用了Skyline存储的LDU分解方法作为方程求解器。只要时间积分间隔是固定的，仅需要执行一次因式分解，并且在此之后，仅需要重复因式分解阵列的前向归约/后向替换。准备了几种类型的后处理器，以便以图形方式表达速度、压力、流线、涡量、流体力等的空间分布或时间历史。(3)验证本分析系统的性能：比较的数值结果，包括涡脱落问题，需要解决大型系统矩阵方程，与实验观察和测量表明，时间相关的解决方案同意相当好的实验可视化流场，和流体力作用在障碍物上可以预测。少

The aim of the present research is to develop a numerical procedure for solving the time-dependent, incompressible Navier-Stokes equations, and to implement the procedure as a program system which is applicable to various unsteady flow problems.The followings are the summary of the promotion and the results of the present project.(1) Development of finite element solution procedure: A set of non-linear recurrence equations, which represent evolution of the velocities and the pressures under the incompressibility constraint, are derived from the finite element equations of the primitive variable formulation, by using a unique direct time integration method developed by the investigators and particular processes regarding the continuity conditions and the boundary conditions. Excessively artificial techniques have not been introduced into the present derivation. An iteration process with respect to the non-linear convection terms is performed in every integration step.(2) Implementation … More of finite element program system: Since the system coefficient matrix of the derived non-linear recurrence equations is non-symmetric and may possess a band-profile, the LDU decomposition method using skyline storage is adopted as the equation solver. As far as the time integration interval is fixed, only one factorization need be performed and, after that, only the forward reduction/back substitution of the factorized array need be repeated. Several types of post-processors are prepared in order to express graphically the spatial distribution or the time history of velocity, pressure, streamlines, vorticity, fluid forces, or so on.(3) Verification of the performance of the present analysis system: Comparisons of the numerical results, including vortex shedding problems which require solving large system matrix equations, with experimental observation and measurements show that, the time-dependent solutions agree fairly well with the experimentally visualized flow field, and the fluid forces acting on the obstacles can be predicted. Less