Navier－Stokes方程的非线性Galerkin有限元方法

Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的非线性Ｇａｌｅｒｋｉｎ有限元方法何银年，李开泰，向一敏（西安交通大学）ＮＯＮＬＩＮＥＡＲＧＡＬＥＲＫＩＮＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳ￥ＨｅＹｉｎ－ｎｉａｎ；Ｌｉ...     

一类针对Navier－Stokes方程的链状区域分裂法

一类针对Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的链状区域分裂法武云海（中山大学计算机系）ＡＫＩＮＤＯＦＬＩＮＫＤＯＭＡＩＮＤＥＣＯＭＰＯＳＩＴＩＯＮＭＥＴＨＯＤＦＯＲＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳ￥ＷｕＹｕｎ－ｈａｉ（ＤｅｐａｒｔｍｅｎｔｏｆＣ...     

Navier－Stokes方程模拟湍流非对称脱体涡流动

Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程模拟湍流非对称脱体涡流动蔡晋生，罗时钧（西北工业大学）ＮＡＶＩＥＲ－ＳＴＯＫＥＳＳＯＬＵＴＩＯＮＳＦＯＲＡＳＹＭＭＥＴＲＩＣＴＵＲＢＵＬＥＮＴＶＯＲＴＩＣＡＬＦＬＯＷＳ￥ＣａｉＪｉｎｓｈｅｎｇ；ＬｕｏＳｈｉｊｕｎ（Ｎｏｒ...     

基于SIMPLE算法求解Navier—Stokes方程

介绍求解Navier-Stokes65数值解法。针对不可压缩流体的的数值解法有涡量一流函数方法@SIMPLE57法．对基于同位网格的65SIMPLE法作详细讨论,给出该算法的推导过程,最终得出求解SIMPLE算法的求解步骤。应用该求解步骤对具体实例求解,得出结论。     

简化Navier一Stokes方程组推进解法的数值分析

我们在[1]中对简化 Navier-Stokes方程组(以下称 N-S方程组)的数学性质作了定性研究,指出:在 u相似文献   

非线性动力学方程的李级数解法及其应用

分别从推广的微分方程幂级数解的理论和线性算子半群理论等不同的角度研究了非线性动力学方程的求解问题,得到了所谓的李级数解法．并进一步讨论了算法的具体实施过程,它可以用于构造非线性动力学方程任意高阶的显式积分格式．最后,把李级数解法应用于求解广义Hamilton系统,它能保持广义Hamilton系统真解的典则性．数值算例显示该方法是有效的。     

Least-Squares Spectral Collocation for the Navier–Stokes Equations

A least-squares spectral collocation formulation for the Navier–Stokes problem is presented. By this new approach the well known Babuska–Brezzi condition can be avoided. Here we are able to employ polynomials of the same degree both for the velocity components and for the pressure. The collocation conditions and the boundary conditions lead to a overdetermined system which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear systems. The numerical simulations confirm the usual exponential rate of convergence for the spectral scheme.     

Stokes方程的结构稳定性研究

本文主要对一类Stokes流进行结构稳定性研究,通过证明,我们得到解对系数d是连续依赖以及收敛的．     

On the Numerical Controllability of the Two-Dimensional Heat,Stokes and Navier–Stokes Equations

The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the Navier–Stokes equations with Dirichlet boundary conditions. The main idea is to adapt the Fursikov–Imanuvilov formulation, see Fursikov and Imanuvilov (Controllability of Evolutions Equations, Lectures Notes Series, vol 34, Seoul National University, 1996); this approach has been followed recently for the one-dimensional heat equation by the first two authors. More precisely, we minimize over the class of admissible null controls a functional that involves weighted integrals of the state and the control, with weights that blow up near the final time. The associated optimality conditions can be viewed as a differential system in the three variables \(x_1\), \(x_2\) and t that is second-order in time and fourth-order in space, completed with appropriate boundary conditions. We present several mixed formulations of the problems and, then, associated mixed finite element Lagrangian approximations that are relatively easy to handle. Finally, we exhibit some numerical experiments.     

A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations

Recently, Douglas et al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component of the velocity in the stationary Stokes and Navier–Stokes equations, along with a piecewise-constant element for the pressure. We obtain a stable element in both cases for which optimal error estimates for the approximation of both the velocity and pressure in L ² can be established, as well as one in a broken H ¹-norm for the velocity. Received: January 1999 / Accepted: April 1999     

Stokes方程的一种预处理方法

本文研究了Stokes方程基于混合有限元离散的预处理方法.基于三角形剖分上速度场的连续P_2元以及压力场的P_0元,我们采用局部子区域逆矩阵建立了预处理子.通过分析预处理矩阵的特征值分布,我们证明了该预处理子大大改善原问题系数矩阵的条件数.本文给出了相应的数值结果.     

Spectral Method for Navier–Stokes Equations with Slip Boundary Conditions

In this paper, we propose a spectral method for the $n$ -dimensional Navier–Stokes equations with slip boundary conditions by using divergence-free base functions. The numerical solutions fulfill the incompressibility and the physical boundary conditions automatically. Therefore, we need neither the artificial compressibility method nor the projection method. Moreover, we only have to evaluate the unknown coefficients of expansions of $n-1$ components of the velocity. These facts simplify actual computation and numerical analysis essentially, and also save computational time. As the mathematical foundation of this new approach, we establish some approximation results, with which we prove the spectral accuracy in space of the proposed algorithm. Numerical results demonstrate its high efficiency and coincide the analysis very well. The main idea, the approximation results and the techniques developed in this paper are also applicable to numerical simulations of other problems with divergence-free solutions, such as certain partial differential equations describing electro-magnetic fields.     

Numerical solution of unsteady Navier–Stokes equations on curvilinear meshes

The objective of the present work is to extend our FDS-based third-order upwind compact schemes by Shah et al. (2009) [8] to numerical solutions of the unsteady incompressible Navier–Stokes equations in curvilinear coordinates, which will save much computing time and memory allocation by clustering grids in regions of high velocity gradients. The dual-time stepping approach is used for obtaining a divergence-free flow field at each physical time step. We have focused on addressing the crucial issue of implementing upwind compact schemes for the convective terms and a central compact scheme for the viscous terms on curvilinear structured grids. The method is evaluated in solving several two-dimensional unsteady benchmark flow problems.