共查询到20条相似文献，搜索用时 0 毫秒
1.
Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel proce- dures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analvsis. 相似文献
2.
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method. 相似文献
3.
周哲玮 《应用数学和力学(英文版)》1988,9(1):77-86
This paper presents a kind of distortion of Hagen-Poiseuille velocity profile in pipe Poiseuille flow. This distortion can be regarded as a general expression of the influence on the mean flow by nonlinear interaction of various components of axisymmetric perturbations. Through the investigation of the stability behaviour of this velocity profile, this paper obtains unstable result induced by axisymmetric perturbations for the first time, and thus presents a new possible approach which leads to instability of Hagen-Poiseuille flow. 相似文献
4.
A. MARUOKA M. MARIN M. KAWAHARA 《International Journal of Computational Fluid Dynamics》2013,27(3-4):313-322
This paper presents a formulation for optimal control of a forced convection flow. The state equation that governs the forced convection flow can be expressed as the incompressible Navier-Stokes equations and energy equation. The optimal control can be formulated as finding a control force to minimize a performance function that is defined to evaluate a control object. The stabilized finite element method is used for the spatial discretization, while the Crank-Nicolson scheme is used for the temporal discretization. The Sakawa-Shindo method, which is an iterative procedure, is applied for minimizing the performance function. 相似文献
5.
Yueqiang Shang ;Hongtao Ran 《Discrete and continuous dynamical systems》2023,28(7):4087-4107
We present and study a parallel subgrid stabilized algorithm for simulating the incompressible Navier-Stokes equations with nonlinear slip boundary conditions. The algorithm uses finite element discretizations and an approach of completely overlapping region division for the parallelization, where an elliptic projection operator is applied to define the stabilization term. It has the following appealing features: 1) each subproblem used to calculate a local solution in a subdomain is actually a global problem defined on a global mesh that is locally refined around the subdomain; 2) it can re-use existing sequential software in coding, where both parallelization and stabilization are easy to implement based on existing sequential codes without extensive effort; 3) it inherits the advantages of the subgrid stabilization method and the completely overlapping region division approach; 4) with suitable algorithmic parameters, it is able to yield an optimal convergence rate for the approximate solutions with a comparable accuracy to that of the solutions from the global subgrid stabilized method, with considerable reduction in computational time. With the help of a local a priori estimate, we estimate error bounds of the obtained solutions from the algorithm, and perform some numerical tests to validate the theoretical prediction and illustrate the applicability of the proposed algorithm. 相似文献
6.
ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｃｏｎｔａｉｎｉｎｇｚｅｒｏｐｏｉｎｔｂｅａｓｉｍｐｌｙ＿ｃｏｎｎｅｃｔｅｄｂｏｕｎｄｅｄｏｐｅｎｓｅｔｏｆＲ2 ｗｉｔｈｓｍｏｏｔｈｂｏｕｎｄａｒｙΓａｎｄｌｅｔΩ′ｄｅｎｏｔｅｔｈｅｃｏｍｐｌｅｍｅｎｔｏｆΩ ∪Γ .ＴｈｅｅｘｔｅｒｉｏｒｎｏｎｓｔａｔｉｏｎａｒｙＮａｖｉｅｒ＿ＳｔｏｋｅｓｐｒｏｂｌｅｍｆｏｒａｆｌｕｉｄｏｃｃｕｐｙｉｎｇΩ′ｃｏｎｓｉｓｔｓｉｎｆｉｎｄｉｎｇｔｈｅｖｅｌｏｃｉｔｙ ｕ(ｘ,ｔ)ｏｆｔｈｅｆｌｕｉｄａｎｄｉｔｓｐｒｅｓｓｕｒｅ ｐ(ｘ ,… 相似文献
7.
ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｃｏｎｓｉｄｅｒｔｗｏ＿ｇｒｉｄｍｅｔｈｏｄｆｏｒｔｈｅｓｔｒｅａｍｆｕｎｃｔｉｏｎｆｏｒｍｏｆｔｈｅｓｔａｔｉｏｎａｒｙＮａｖｉｅｒ＿Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓ.Ｔｈｅａｄｖａｎｔａｇｅｓｏｆｔｈｅｓｔｒｅａｍｆｕｎｃｔｉｏｎｆｏｒｍａｒｅｔｈａｔｔｈｅｉｎｃｏｍｐｒｅｓｓｉｂｉｌｉｔｙｃｏｎｄｉｔｉｏｎｉｓｓａｔｉｓｆｉｅｄａｕｔｏｍａｔｉｃａｌｌｙａｎｄｔｈｅｐｒｅｓｓｕｒｅｉｓｎｏｔｐｒｅｓｅｎｔｉｎｔｈｅｗｅａｋｆｏｒｍ .Ｔｈｅｍｅｔｈｏｄｉｓｂａｓｅｄ… 相似文献
8.
In this paper the perturbation method about two parameters is applied to the problem of large deflection of a cricular plate with exponentially varying thickness under uniform pressure. An asymptotic solution up to the third-order is derived. In comparison with the exact solutions in special cases, the asymptotic solution shows a precise accuracy. 相似文献
9.
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms. 相似文献
10.
在Navier-Stokes方程和k-ω湍流模型的基础上,利用流线迎风有限元方法结合ALE动网格技术对亚临界雷诺数下的圆柱受迫振动问题开展了数值模拟研究。本文的数值模型成功模拟了Re=5000条件下,圆柱发生受迫振动时尾迹区内的2S,2P和P+S尾流模式;对Re=10000情况下,无量纲振幅分别为0.3,0.4,0.5的圆柱受迫振动问题开展了数值模拟,分析了给定振幅条件下圆柱受力随振动频率的变化关系以及受迫振动的锁定区间。以上数值计算结果与Gopalkrishnan (1993)的实验结果基本符合。研究结果表明,二维数值模型能够基本正确地反映出圆柱发生受迫振动时的涡激振动特性以及有关的受力变化趋势,为今后进一步开展三维数值分析工作奠定了基础。 相似文献
11.
Fan Chen;Ming Cui ;Chenguang Zhou 《Discrete and continuous dynamical systems》2023,28(4):2768-2788
In this paper, we investigate a two-grid finite element method (FEM) for two-dimensional nonlinear unsaturated soil water flow problems. The application of two-grid methods can transform the solution of nonlinear problems on the fine grid to the solution of nonlinear problems on the coarse grid and the solution of linear problems on the fine grid. Based on the error results of standard FEM, we derive the continuous and discrete time error estimates in the energy norm for the two-grid method. Numerical experiments are carried out with the linear element as an example to illustrate that the two-grid method can achieve the similar optimal accuracy as standard FEM with less time as long as the two mesh sizes satisfy $ H = O(sqrt{h}) $. 相似文献
12.
In this paper the problem of a circular beam subjected to radial impact by a rigid mass at its tip in its own plane is investigated on the basis of rigid-perfectly plastic assumption. The analytical solution of the particle velocities is obtained as the function of travelling plastic hinge location. By analysing the solution, some special properties of circular beam problem are found. 相似文献
13.
首先导出了广义Stokes方程Petrov—Galerkin有限元数值解的当地事后误差估算公式;以非连续二阶鼓包（bump）函数空间为速度、压强误差的近似空间,该估算基于求解当地单元上的广义Stokes问题。然后,证明了误差估算值与精确误差之间的等价性。最后,将误差估算方法应用于Navier—Stokes环境,以进行不可压粘流计算中的网格自适应处理。数值实验中成功地捕获了多强度物理现象,验证了本文所发展的方法。 相似文献
14.
本文介绍了作者在西安交通大学ELXSI-6400并行机调试的大型结构有限元分析程序—PARNFAP。该程序利用子结构方法实现有限元计算的并行化,计算结果表明其具有良好的并行性能。 相似文献
15.
16.
提出一种Fourier-Legendre谱元方法用于求解极坐标系下的Navier-Stokes方程,其中极点所在单元的径向采用Gauss-Radau积分点,避免了r=0处的1/r坐标奇异性。时间离散采用时间分裂法,引入数值同位素模型跟踪同位素的输运过程验证数值模拟的精度,分别利用谱元法和有限差分法的迎风差分格式求解匀速和加速坩埚旋转流动中的同位素方程。计算结果表明,有限差分法中的一阶迎风差分格式存在严重的数值假扩散,二阶迎风差分格式的数值结果较精确,增加节点可以有效地缓解数值扩散。然而,谱元法具有以较少节点得到高精度解的优势。 相似文献
17.
This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier- Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well. 相似文献
18.
A parallel computer implementation of a vorticity formulation for the analysis of incompressible viscous fluid flow problems is presented. The vorticity formulation involves a three‐step process, two kinematic steps followed by a kinetic step. The first kinematic step determines vortex sheet strengths along the boundary of the domain from a Galerkin implementation of the generalized Helmholtz decomposition. The vortex sheet strengths are related to the vorticity flux boundary conditions. The second kinematic step determines the interior velocity field from the regular form of the generalized Helmholtz decomposition. The third kinetic step solves the vorticity equation using a Galerkin finite element method with boundary conditions determined in the first step and velocities determined in the second step. The accuracy of the numerical algorithm is demonstrated through the driven‐cavity problem and the 2‐D cylinder in a free‐stream problem, which represent both internal and external flows. Each of the three steps requires a unique parallelization effort, which are evaluated in terms of parallel efficiency. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
P. J. Reuderink F. N. van de Vosse A. A. van Steenhoven M. E. H. van Dongen J. D. Janssen 《国际流体数值方法杂志》1993,16(7):597-612
The fluid flow in distensible tubes is analysed by a finite element method based on an uncoupled solution of the equations of wall motion and fluid flow. Special attention is paid to the choice of proper boundary conditions. Computations were made for sinusoidal flow in a distensible uniform tube with the Womersley parameter α = 5, and a ratio between tube radius and wavelenth from 0·0001 to 0·5. The agreement between the numerical results and Womersley's analytic solution depends on the speed ratio between fluid and wave velocity, and is fair for speed ratios up to 0·05. The analysis of the flow field in a distensible tube with a local inhomogeneity revealed a marked influence of wave phenomena and wall motion on the velocity profiles. 相似文献
20.
The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method. 相似文献