局部热壁面多孔介质方腔内自然对流的数值研究

本文对上下壁面绝热、左侧壁面长度为b的嵌装加热器部分维持恒定温度T_h而剩余部分绝热,且右侧壁面维持恒定温度T_c的多孔介质方腔内的自然对流换热进行了数值研究.在热壁面无量纲长度B=0.5(B=b/L)的条件下,综合研究了左侧壁面受热部分中心距上壁面的无量纲长度D(D=d/L)、Da数、Ra数和孔隙率对腔体内自然对流换热的影响.数值计算结果表明,左侧壁面受热部分位置的不同对腔体内自然对流换热有很大的影响,D在0.6附近取值时,Na数最大.Da数、Ra数对腔体的自然对流换热影响较大,而孔隙率对换热的影响较小.     

自然对流的LB方法模拟及其非线性特性

采用LB方法和QUICK差分方法模拟了方腔内竖直平板自然对流和底部加热方腔内自然对流换热问题.实现了LB方法对具有孤立体的封闭空间内耦合的流动和传热问题的数值模拟,所得数值结果与QUICK差分方法的数值结果及已有的烟可视化实验结果一致;两种方法对底部加热方腔内自然对流问题的预测结果均出现了静态分岔和动态分岔;根据底部加热方腔内自然对流换热数值结果给出的极限环型速度相图和功率谱表明,两种方法得到的数值结果的非线性特性一致.     

基于SIMPLE求解对流-扩散方程的一种新方法

针对SIMPLE系列算法,通过分别求解控制容积界面和节点两个位置的对流-扩散方程来提高数值计算精度,提出了一种流动与传热数值模拟的新方法。采用新的数值方法对顶盖驱动流与正方腔自然对流进行了数值模拟。数值模拟结果表明,在相同网格划分时,新的数值方法相对迎风格式、乘方格式、QUICK格式SIMLE算法的计算精度高;而在计算精度基本相同时,新方法有较高的计算效率。     

三维方腔内竖直平板自然对流的数值模拟

三维方腔内竖直平板自然对流的数值模拟杨沫，李少华，徐志明，杨善让（东北电力学院动力系吉林１３２０１２）陶文铨（西安交通大学动力系西安７１００４９）关键词封闭腔；自然对流；数值模拟１引言三维封闭腔内孤立物体的自然对流换热在工程上具有广泛应用背景。例如；...     

深低温球内伪稳态自然对流换热研究

基于CFD仿真软件FLUENT,建立了封闭球形容腔内氦气关键物性参数随温度变化的深低温自然对流仿真模型。利用该模型对封闭球形容腔内20～100 K温度下不同瑞利数(10~8Ra10~(11))伪稳态自然对流换热进行了数值模拟,得到了速度场分布、温度场分布和努塞尔数(Nu).开展了液氢温区球形封闭容腔内氦气伪稳态自然对流换热试验。通过与试验数据的对比分析,验证了本文所提出的深低温自然对流模型的有效性。利用最小二乘法,获得了深低温球形容腔内氦气自然对流换热准则数方程。     

周期性边界条件下多孔介质方腔内自然对流换热数值研究

对充满多孔介质的倾斜方腔,在其上下壁面绝热、右侧壁面维持恒温To及左侧壁面温度基于To随时间按正弦规律变化的情况下,采用Brinkman扩展达西模型和SIMPLER算法对方腔内的自然对流与换热进行了非稳态数值模拟,方腔倾角α的范围为0°～90°,Pr数为1,Ra数为106.计算研究不同的振荡频率和方腔倾角对方腔内对流换热的影响.数值模拟结果表明:振荡频率f为60π,方腔倾角为43°时,方腔内的换热最强.     

基于弱可压与不可压光滑粒子动力学方法的封闭方腔自然对流数值模拟及算法对比

为了对比研究弱可压光滑粒子动力学(WCSPH)方法和不可压光滑粒子动 力学(ISPH)方法在模拟封闭方腔自然对流问题时的特性, 采用粒子位移技术有效地解决了高瑞利数条件下, 拉格朗日型SPH方法模拟封闭方腔自然对流时流体域内的粒子聚集和空穴问题, 将拉格朗日型SPH 方法求解封闭方腔自然对流问题的最高瑞利数提高到了10⁶; 进而通过对比瑞利数分别为10⁴, 10⁵, 10⁶的条件下, 采用拉格朗日型WCSPH、 拉格朗日型ISPH、欧拉型ISPH三种SPH方法模拟得到的封闭方腔速度分布云图、 温度分布云图、壁面努赛尔特数分布曲线和平均努塞尔特数, 分析了三种SPH方法在模拟封闭方腔自然对流时的精度、稳定性和计算效率. 结果表明: 在低瑞利数条件下, 以上三种SPH方法都可以较好地模拟此问题, 在高瑞利数条件下, 欧拉型ISPH方法的模拟结果最为精确; 拉格朗日型WCSPH方法模拟所得结果比拉格朗日型ISPH方法模拟所得结果稍好些. 关键词： 光滑粒子动力学 不可压光滑粒子动力学 粒子位移技术 自然对流     

复杂多孔介质腔体内自然对流换热的数值研究

采用曲线坐标系下压力与速度耦合的SIMPLEC算法,数值研究复杂多孔介质腔体内的自然对流换热问题.腔体的曲面温度分别保持恒定,上下表面绝热.在曲线坐标系中用有限容积法离散方程,并采用Brinkman扩展达西模型及局部非热平衡模型求解,综合研究Rayleigh数,Darcy数、孔隙率等参数对腔体内自然对流换热的影响.计算结果表明:Rayleigh数和Darcy数的影响最大而孔隙率的影响很小,同时存在使得腔体内换热达到最强的最佳纵横比.     

二维方腔非稳态自然对流数值模拟研究

本文针对二维方腔中非稳态自然对流过程进行了数值研究,方腔一侧被等温冷却,另一侧受到三块热板脉动加热,热板温度满足两种不同规律,脉动周期0.01 s<τ<500 s,脉动大小0<α<0.40,所研究的自然对流问题取Ra=106,工质为空气(Pr=0.70)。研究结果表明:方腔中冷板瞬时对流换热量与相应稳态时有很大差异;在一定条件下,热板温度脉动周期和脉动量对冷板的换热量均有很大的影响。     

自然对流换热的高精度非结构网格有限体积法

用非结构网格有限体积法求解自然对流换热时,传统的对流项离散格式难以兼顾数值精度与计算效率,我们发展了一种耦合高精度格式的延迟修正方法,用于对流项的离散.高Re数下方腔驱动流数值计算验证了该方法具有较高的计算精度和较好的稳定性.Boussinesq流体的自然对流换热数值模拟,表明该方法能有效克服高Ra数时数值计算发散,可准确捕捉自然对流换热问题中不同偏心率下的等温线和流线分布特征.     

基于SIMPLE的紧致方法

通过泰勒展式系数匹配的方法发展了基于非等距网格的有限容积紧致格式,采用延迟修正的方法建立了基于SIMPLE的紧致方法,,该方法能够得到高精度的数值解,增加迭代求解代数方程组的稳定性。对底部加热的方腔内自然对流换热问题进行数值模拟,结果表明,紧致方法比二阶中心差分方法具有更高的精度。     

A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave equation

The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-point sixth-order compact scheme. The first-order derivative terms in the first step are approximated by a sixth-order dispersion-relation-preserving scheme that preserves the physically inherent dispersive nature. The compact Helmholtz solver, on the other hand, allows us to use relatively few nodal points in a stencil, while achieving a higher-order accuracy. The midpoint rule is a symplectic time integrator for Hamiltonian systems, which may be a preferable method to solve the spatially discretized evolution equation. To give an assessment of the dispersion-preserving scheme, we provide a detailed analysis of the dispersive and dissipative errors of this algorithm. Via a variety of examples, we illustrate the efficiency and accuracy of the proposed scheme by examining the errors in different norms and providing the rates of convergence of the method. In addition, we provide several examples to demonstrate that the conserved quantities of the equation are well preserved by the implicit midpoint time integrator. Finally, we compare the accuracy, elapsed computing time, and spatial and temporal rates of convergence among the proposed method, a complete integrable particle method, and the local discontinuous Galerkin method.     

基于紧致差分的Grad-Shafranov方程快速解法

在等离子体平衡重建迭代计算过程中,需要快速求解Grad-Shafranov方程(G-S方程)。构造了具有四阶精度紧致差分格式的离散方程,采用离散正弦变换技术对其进行快速求解并采用CUDATM实现GPU并行加速,将其应用到EAST等离子体平衡重建PEFIT代码中,实现基于紧致差分格式的快速G-S方程求解。结果表明,在65×65的网格下,给定方程右端项电流分布的前提下,使用GPU求解G-S方程所需时间为大约34μs。     

Numerical comparisons of time–space iterative method and spatial iterative methods for the stationary Navier–Stokes equations

This paper makes some numerical comparisons of time–space iterative method and spatial iterative methods for solving the stationary Navier–Stokes equations. The time–space iterative method consists in solving the nonstationary Stokes equations based on the time–space discretization by the Euler implicit/explicit scheme under a weak uniqueness condition (A2). The spatial iterative methods consist in solving the stationary Stokes scheme, Newton scheme, Oseen scheme based on the spatial discretization under some strong uniqueness assumptions. We compare the stability and convergence conditions of the time–space iterative method and the spatial iterative methods. Moreover, the numerical tests show that the time–space iterative method is the more simple than the spatial iterative methods for solving the stationary Navier–Stokes problem. Furthermore, the time–space iterative method can solve the stationary Navier–Stokes equations with some small viscosity and the spatial iterative methods can only solve the stationary Navier–Stokes equations with some large viscosities.     

求解Navier-Stokes方程组的组合紧致迎风格式

给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.     

三维对流扩散方程非等距网格上的四阶紧致格式及其多重网格方法

提出了数值求解三维变系数对流扩散方程非等距网格上的四阶精度19点紧致差分格式,为了提高求解效率,采用多重网格方法求解高精度格式所形成的大型代数方程组。数值实验结果表明本文方法对于不同的网格雷诺数问题,在精确性、稳定性和减少计算工作量方面均明显优于7点中心差分格式。     

非结构网格下非定常流场双时间步长的加权ENO-强紧致杂交高分辨率格式

针对三维非定常、可压缩流场的Navier-Stokes方程组,本文提出一种新的双时间步长高精度快速迭代格式。该格式在时间上具有二阶精度,在空间离散上不低于三阶。在对流项与粘性项的处理上,本格式分别采用了加权ENO-强紧致格式与紧致四阶精度格式的思想。几个典型算例的实践表明:计算结果与相关实验数据比较吻合,初步表明了该算法可以在非结构网格下具有高效率与高分辨率的特征。     

Dark and kink soliton solutions of the generalized ZK–BBM equation by iterative scheme

The generalized ZK–BBM equation is solved using iterative scheme of the Adomian decomposition method (ADM) and variational iteration method (VIM). A dark and a kink soliton solutions of the generalized ZK–BBM equation are obtained under initial conditions. The convergence analysis of the ADM and VIM solution shows that these solutions are convergent. The comparison of the ADM and VIM solutions with the exact solution shows that the solutions of the generalized ZK–BBM equation by the iterative methods are almost exact. The absolute errors show that the accuracy and efficiency of the ADM and VIM depend on the problem and its domain. It is found that the iterative scheme of Adomian decomposition method and variational iteration method are quite efficient for the soliton solution of the generalized ZK–BBM equation.     

An Acceleration Method for Stationary Iterative Solution to Linear System of Equations

An acceleration scheme based on stationary iterative methods is presented for solving linear system of equations. Unlike Chebyshev semi-iterative method which requires accurate estimation of the bounds for iterative matrix eigenvalues, we use a wide range of Chebyshev-like polynomials for the accelerating process without estimating the bounds of the iterative matrix. A detailed error analysis is presented and convergence rates are obtained. Numerical experiments are carried out and comparisons with classical Jacobi and Chebyshev semi-iterative methods are provided.     

Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D poisson equation

A fourth-order compact difference discretization scheme with unequal meshsizes in different coordinate directions is employed to solve a three-dimensional (3D) Poisson equation on a cubic domain. Two multgrid methods are developed to solve the resulting sparse linear systems. One is to use the full-coarsening multigrid method with plane Gauss–Seidel relaxation, which uses line Gauss–Seidel relaxation to compute each planewise solution. The other is to construct a partial semi-coarsening multigrid method with the traditional point or plane Gauss–Seidel relaxations. Numerical experiments are conducted to test the computed accuracy of the fourth-order compact difference scheme and the computational efficiency of the multigrid methods with the fourth-order compact difference scheme.