Comparison of Galerkin and control volume finite element for advection–diffusion problems

The control volume finite element method (CVFEM) was developed to combine the local numerical conservation property of control volume methods with the unstructured grid and generality of finite element methods (FEMs). Most implementations of CVFEM include mass‐lumping and upwinding techniques typical of control volume schemes. In this work we compare, via numerical error analysis, CVFEM and FEM utilizing consistent and lumped mass implementations, and stabilized Petrov–Galerkin streamline upwind schemes in the context of advection–diffusion processes. For this type of problem, we find no apparent advantage to the local numerical conservation aspect of CVFEM as compared to FEM. The stabilized schemes improve accuracy and degree of positivity on coarse grids, and also reduce iteration counts for advection‐dominated problems. Published in 2005 by John Wiley & Sons, Ltd.     

蒸汽发生器干燥器三维流场数值模拟计算

针对压水堆核电厂蒸汽发生器波形板干燥器的结构特点,采用通用计算流体力学软件ANSYS-Fluent中的多孔介质模型对蒸汽发生器用波形板干燥器进行三维流场的数值模拟计算,得到干燥器区域的流场情况以及干燥器孔板入口处蒸汽的流速分布情况,确定在极限工况下干燥器孔板入口处蒸汽的最高流速．在设计蒸汽发生器干燥器时,应确保极限工况下干燥器入口蒸汽的最高流速低于通过试验确定的特定波形板片的临界速度,以确保干燥器的所有区域均工作在其允许的分离能力以内．     

纳米尺度绕流现象中流体分子运动行为研究

采用分子动力学模拟方法,研究纳米尺度低Re数(Re=20)条件下,氩流体流过铂(FCC(100))金属圆柱的绕流现象.从流线和速度矢量分布两方面刻画涡的周期性产生、发展和脱落过程.结果显示,一个涡脱落周期大约为0.3 ns,斯特劳哈尔数St约为0.2;时均对称涡的长度是圆柱直径的1.4倍,涡径与圆柱直径相当.从速度场和密度场的角度刻画回流区,并进一步研究典型区域(圆柱中心线附近区域及下游邻近区域)的速度分布特性.     

THE FINITE DIFFERENCE STREAMLINE DIFFUSION METHODS FOR TIME-DEPENDENT CONVECTION-DIFFUSION EQUATIONS

In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L~2-norm.     

LOCAL ERROR ESTIMATES FOR METHODS OF CHARACTERISTICS INCORPORATING STREAMLINE DIFFUSION

Allen and Liu (1995) introduced a new method for a time-dependent convec-tion dominated diffusion problem, which combines the modified method of characteristics and method of streamline diffusion. But they ignored the fact that the accuracy of time discretization decays at half an order when the characteristic line goes out of the domain. In present paper, the author shows that, as a remedy, a simple lumped scheme yields a full accuracy approximation. Forthermore, some local error bounds independent of the small viscosity are derived for this scheme outside the boundary layers.     

线性定常对流占优对流扩散问题的无网格解法

应用无网格Galerkin方法求解对流占优对流扩散问题时会出现非物理现象的数值伪振荡,本文将SUPG方法、GLS方法、SGS方法与无网格Galerkin方法相耦合,成功解决了对流扩散方程中对流项占优时的数值伪振荡问题。运用本文构造的方法,采用线性基和具有C2连续的权函数,应用移动最小二乘法可容易地构造高阶导数连续的形函数,从而避免了有限元方法中当采用线性元插值时,因忽略稳定项中二阶导数项而降低计算精度和稳定性的问题。数值实验表明:本文构造的方法具有计算精度高、稳定性好、计算算法实施简单、前后处理方便的优点,这些方法不仅能适用于对流项占优问题,而且也能很好地消除反应项占优时的数值伪振荡问题。     

A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.