首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 109 毫秒
1.
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   

2.
提出了一种基于AH(Associated Hermite)正交基函数求解对流扩散方程的无条件稳定算法。该算法将方程的时间项通过Hermite多项式作为正交基函数进行展开,利用Galerkin方法消除时间变量项,从而导出有限维AH域隐式差分方程,突破了传统显式差分格式稳定性条件的限制,最后通过对AH域展开系数的求解得到该对流扩散方程的数值解。在数值算例中,将该算法与传统显示差分法和交替方向隐式差分法进行对比分析,数值计算结果表明,算法无条件稳定且其计算精度与时间步长无关,对于具有精细结构的对流换热问题,该算法具有明显的效率优势,且保持了较高的精度。  相似文献   

3.
对流扩散方程的摄动有限体积(PFV)方法及讨论   总被引:10,自引:2,他引:8  
高智  柏威 《力学学报》2004,36(1):88-93
在有限体积(FV)方法的重构近似中,引入数值摄动处理,即把界面数值通量摄动展开成网格间距的幂级数,并利用积分方程自身的性质求出幂级数的系数,同时获得高精度迎风和中心型摄动有限体积(PFV)格式.对标量输运方程给出积分近似为二阶、重构近似为二、三和四阶迎风和中心型PFV格式,这些PFV格式的结构形式及使用基点数与一阶迎风格式完全一致,迎风PFV格式满足对流有界准则;二阶和四阶中心PFV格式对网格Peclet数的任意值均为正型格式,比常用的二阶中心格式优越.用一维标量输运和方腔流动算例说明PFV格式的优良性能,并把PFV方法与性质相近的摄动有限差分(PFD)方法及相关的高精度方法作了对比分析.  相似文献   

4.
同位网格摄动有限体积格式求解浮力驱动方腔流   总被引:2,自引:1,他引:1  
代民果  高智 《力学学报》2006,38(6):733-740
利用对流扩散方程的摄动有限体积格式,在Rayleigh数从10$^{3}$ 到10$^{8}$的范围内对浮力驱动方腔流动问题作了数值模拟. 对流扩散方程的摄动 有限体积格式具有一阶迎风格式的简洁形式,使用相同的基点,重构近似精度高,特别是两 相邻控制体中心到公共界面的距离相等或不相等,PFV格式公式相同等优点. 在数值模拟中, 无论均匀网格还是非均匀网格均获得与DSC方法、自适应有限元法、多重网格法等Benchmark 解相符较好的数值结果,证明UPFV格式对高Rayleigh数对流传热问题的适用性和有效性.  相似文献   

5.
提出了求解多维对流-扩散方程的四阶半离散中心迎风格式。该格式以中心加权基本无振荡(CWENO)重构为基础,同时考虑到在Riemann扇内波传播的局部速度,从而更加准确地估计出了局部Riemann扇的宽度,最终既回避了网格的交错,又降低了格式的数值粘性,建立了介于迎风格式和中心格式之间的半离散中心迎风格式。本文还将该四阶半离散中心迎风格式与涡度-流函数方法相结合,有效地求解了二维不可压Euler方程组和Navier-Stokes方程组。  相似文献   

6.
方柱绕流的数值模拟   总被引:6,自引:0,他引:6  
童兵  祝兵  周本宽 《力学季刊》2002,23(1):77-81
采用有限差分法,对雷诺数为2.2×10~4的方柱绕流进行了大涡模拟(简称LES)。运用时间分裂控制(Split-Operator)法,将N-S方程分为对流步、扩散步和传播步。对Smagorinsky假设在近壁区的发散问题用两层模型进行处理。对流项用迎风—中心差分格式模拟,压力方程用SOR法迭代求解。计算得到的沿对称线的时均顺流向速度与文献上的实验结果进行了比较,结果吻合较好,同时还对绕方柱流的流场结构进行了分析研究。  相似文献   

7.
摄动有限差分方法研究进展   总被引:17,自引:1,他引:16  
高智 《力学进展》2000,30(2):200-215
振动有限差分(PFD)方法,既离散徽商项也离散非微商项(包括微商系数),在微商用直接差分近似的前提下提高差分格式的精度和分辨率.PFD方法包括局部线化微分方程的摄动精确数值解(PENS)方法和摄动数值解(PNS)方法以及考虑非线性近似的摄动高精度差分(PHD)方法。论述了这些方法的基本思想、具体技巧、若干方程(对流扩散方程、对流扩散反应方程、双曲方程、抛物方程和KdV方程)的PENS、PNS和PHD格式,它们的性质及数值实验.并与有关的数值方法作了必要的比较.最后提出值得进一步研究的一些课题.  相似文献   

8.
从迎风紧致逼近^[1]出发,提出数值求解可压Navier-Stokes方程的一种高精度的数值方法。利用Steger-Warming的通量分裂技术^[2]将守恒型方程中的流通向量分裂成两部分,在此基础上据风向构造逼近于无粘项的三阶迎风紧致有限差分格式。对方程中的粘性部分采用通常的二阶差分逼近。所建立的差分格式被用来数值求解了三维粘性绕流问题。  相似文献   

9.
二维对流扩散方程的欧拉—拉格朗日分裂格式   总被引:2,自引:0,他引:2  
忻孝康  唐登海 《力学学报》1989,21(4):403-411
本文在[1]基础上发展了一种有效的处理大P_e(R_e)数、非定常二维对流扩散方程的欧拉-拉格朗日(E-L)分裂格式,由于方法本质上与区域形状无关,且不需再分网格,因此是一种无网格的E-L方法,特别对于定常流动,E.-L.分裂格式可以导致比一阶迎风格式更精确的单调、无振荡格式,文中对于常系数、变系数和非线性的二维非定常和定常对流扩散方程的(初)边值问题进行了数值计算,数值结果与精确解的比较表明,本方法具有很好的精度,解是单调无振荡的,比通常一阶迎风格式具有较少的数值扩散,最大计算网格P-e(R-e)数可达100—500。  相似文献   

10.
高智 《力学学报》2012,44(3):505-512
利用数值摄动算法, 通过扩散格式数值摄动重构把对流扩散方程的2阶中心差分格式(2-CDS)重构为高精度高分辨率格式, 解析分析和模型方程计算证实了新格式的高精度不振荡性质. 新格式是把物理黏性使流动光滑化的扩散运动规律引入2-CDS 中的结果. 该法显然与构建高级离散格式的常见方法不同. 证实: 数值摄动重构中引入扩散运动规律的结果格式与引入对流运动规律(下游不影响上游的规律)的结果格式一致, 说明对离散方程的数值摄动运算, 在维持原格式结构形式不动的条件下, 不仅能提高格式精度和稳健性, 且可揭示对流离散运动规律与扩散离散运动规律之间的内在关联;同时证实, 文中提出和使用的上、下游分裂方法是构建高精度不振荡离散格式的一个有效方法.  相似文献   

11.
This paper considers a finite difference scheme for modelling the convection/diffusion equation in strongly convective flow regimes including circumstances in which significant source terms are present. The main objective is to provide an alternative approach to central and/or upwind difference methods which for various reasons are unsatisfactory. To illustrate the main features of the scheme, an assessment of its accuracy is made by means of a Taylor expansion analysis and a study of its performance in two model problems. As a demonstration of its generality for use in large-scale practical problems, some numerical results are presented for the prediction of the temperature distribution in a flow through a partially blocked heated rod bundle. The main conclusions are that in almost all practical circumstances results obtained using the scheme are not susceptible to false diffusion or spatial oscillations, which are, respectively, the inherent weaknesses in many upwind and central difference scheme formulations, and in general its use results in improved overall accuracy.  相似文献   

12.
For a class of nonlinear convection–diffusion equation in multiple space dimensions, a kind of upwind finite‐volume element (UFVE) scheme is put forward. Some techniques, such as calculus of variations, commutating operators and prior estimates, are adopted. It is proved that the UFVE scheme is unconditionally stable and satisfies maximum principle. Optimal‐order estimates in H1‐norm are derived to determine the error in the approximate solution. Numerical results are presented to observe the performance of the scheme. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

13.
A non-adaptive method and a Lagrangian-Eulerian finite difference technique are used to analyse the dynamic response of liquid membrancs to imposed pressure variations. The non-adaptive method employs a fixed grid and upwind differences for the convection terms, whereas the Lagrangian-Eulerian technique uses operator splitting and decomposes the mixed convection-diffusion system of equations into a sequence of convection and diffusion operators. The convection operator is solved exactly by means of the method of characteristics, and its results are interpolated onto the fixed (Eulerian) grid used to solve the diffusion operator. It is shown that although the method of characteristics eliminates the numerical diffusion associated with upwinding the convection terms in a fixed Eulerian grid, the Lagrangian-Eulerian method may yield overshoots and undershoots near steep flow gradients or when rapid pressure gradients are imposed, owing to the interpolation of the results of the convection operator onto the fixed grid used to solve the diffusion operator. This interpolation should be monotonic and positivity-preserving and should satisfy conservation of mass and linear momentum. It is also shown that both the non-adaptive and Lagrangian-Eulerian finite difference methods produce almost identical (within 1%) results when liquid membranes are subjected to positive and negative step and ramp changes in the pressure coefficient. However, because of their non-adaptive character, these techniques require an estimate of the (unknown) length of the membrane and do not use all the grid points in the calculations. The liquid membrane dynamic response is also analysed as a function of the Froude number, convergence parameter and nozzle exit angle for positive and negative step and ramp changes in the pressure coefficient.  相似文献   

14.
二维对流扩散方程的高精度全隐式多重网格方法   总被引:6,自引:1,他引:5  
提出了数值求解二维非定常变系数对流扩散方程的一种时间二阶、空间四阶精度的三层全隐紧致差分格式。为了加快迭代求解隐格式时在每一个时间步上的收敛速度,采用多重网格加速技术,建立了适用于本文高精度金隐紧致格式的多重网格算法。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。  相似文献   

15.
Flux splitting is applied to the convective part of the steady Navier–Stokes equations for incompressible flow. Partial upwind differences are introduced in the split first-order part, while central differences are used in the second-order part. The discrete set of equations obtained is positive, so that it can be solved by collective variants of relaxation methods. The partial upwinding is optimized in the same way as for a scalar convection–diffusion equation, but involving several Peclet numbers. It is shown that with the optimum partial upwinding accurate results can be obtained. A full multigrid method in W-cycle form, using red–black successive under-relaxation, injection and bilinear interpolation, is described. The efficiency of this method is demonstrated.  相似文献   

16.
A fully implicit upwind finite difference numerical scheme has been proposed to investigate the characteristics of thermal entrance heat transfer in laminar pipe flows subject to a step change in ambient temperature. In order to demonstrate the results more clearly, a modified Nusselt number is introduced. The unsteady axial variations of modified Nusselt number, bulk fluid temperature, and wall temperature and the transient temperature profiles at certain axial locations are presented graphically for various outside heat transfer coefficients. The effects of the outside heat transfer coefficient on the heat transport processes in the flow are examined in detail. The results can be comprehensively explained by the interaction between the upstream convective heat transfer and the diffusion heat transfer in the radial direction. Steady state is reached when the axial convection balances the radial diffusion.  相似文献   

17.
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.  相似文献   

18.
The steady Navier–Stokes equations in primitive variables are discretized in conservative form by a vertex-centred finite volume method Flux difference splitting is applied to the convective part to obtain an upwind discretization. The diffusive part is discretized in the central way. In its first-order formulation, flux difference splitting leads to a discretization of so-called vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line Gauss–Seidel relaxation method is chosen here. This relaxation method is used as a smoother in a multigrid method. The components of this multigrid method are: full approximation scheme with F-cycles, bilinear prolongation, full weighting for residual restriction and injection of grid functions. Higher-order accuracy is achieved by the flux extrapolation method. In this approach the first-order convective fluxes are modified by adding second-order corrections involving flux limiting. Here the simple MinMod limiter is chosen. In the multigrid formulation the second-order discrete system is solved by defect correction. Computational results are shown for the well known GAMM backward-facing step problem and for a channel with a half-circular obstruction.  相似文献   

19.
This paper presents a detailed multi‐methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi‐discretizations of the scalar advection–diffusion equation. The errors are reported in terms of non‐dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid‐induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew‐symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov–Galerkin and its control‐volume finite element analogue, the streamline upwind control‐volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi‐discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super‐convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second‐order behaviour. In Part II of this paper, we consider two‐dimensional semi‐discretizations of the advection–diffusion equation and also assess the affects of grid‐induced anisotropy observed in the non‐dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi‐methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号