高精度有限差分法模拟Kelvin-Helmholtz不稳定性

 WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

三维不可压N-S方程的多重网格求解

应用全近似存储(Full Approximation Storage,FAS)多重网格法和人工压缩性方法求解了三维不可压Navi-er-Stokes方程.在解粗网格差分方程时,对Neumann边界条件采用增量形式进行更新,离散方程用对角化形式的近似隐式因子分解格式求解,其中空间无粘项分别用MUSCL格式和对称TVD格式进行离散.对90°弯曲的方截面管道流动和4:1椭球体层流绕流的数值模拟表明,多重网格的计算时间比单重网格节省一半以上,且无限制函数的MUSCL格式比TVD格式对流动结构有更好的分辨能力.     

基于SNGR方法的后缘噪声数值模拟

采用随机噪声产生和传播(SNGR)方法对后缘噪声进行数值模拟.SNGR方法结合随机方法和计算流体力学,耗费较少的计算资源就可以预测噪声水平.数值模拟时采用有限体积法求解雷诺平均Navier-Stokes(RANS)方程;采用有限差分法求解声学扰动方程,数值格式采用色散关系保持(DRP)格式,远场边界条件采用无反射边界条件.以二维平板和NACA0012翼型为例,编制程序,与参考结果对比表明,程序可以预测后缘噪声.     

边界条件对对流扩散方程数值稳定性的影响

本文利用数值计算方法对采用均分网格的一维线性无源的对流－扩散方程在各种边界条件下的稳定性进行了分析,燕求出了不同边界条件下一维问题的中心差分和ＱＵＩＣＫ格式的临界网格Ｐｅｃｌｅｔ数。指出按现有方法得出的临界网格Ｐｅｃｌｅｔ数是判别差分格式对流数值稳定性的最苛刻的要求。对中心差分和ＱＵＩＣＫ格式,除两点边值问题以外的其它边界条件下的稳定性范围均不小于或远远大于两点边值问题的稳定性范围。通过计算还得出了格式的数值稳定性主要取决于计算区域下游侧的边界条件类型而与计算区域上游侧的边界条件类型无关的结论。     

气相爆轰高阶中心差分-WENO组合格式自适应网格方法

研究一种高阶中心差分-WENO组合格式,并采用自适应网格方法进行二维和三维气相爆轰波的数值模拟.采用ZND爆轰模型的控制方程为包含化学反应源项的Euler方程组.组合格式在大梯度区采用WENO格式捕捉间断,在光滑区采用高阶中心差分格式提高计算效率.采用一种基于流场结构特征的自适应网格.计算结果,表明这种方法同时具有高精度、高分辨率和高效率的特点.     

QUICK格式在湍流旋流流动数值模拟中的应用

为研究不同精度的离散格式对湍流旋流流动数值模拟结果的影响,同时应用QUICK格式和混合格式对同轴射流旋流燃烧室内的湍流流动进行了数值模拟.在采用k-ε湍流模型的条件下,QUICK格式计算得到的燃烧室内气体轴向与切向速度及轴向脉动速度均方根值分布与实验数据符合较好,而混合格式给出的数值模拟结果则与实验有一定的偏差.     

柱坐标下Euler方程数值边界条件的一种处理方法

给出了柱坐标下Euler方程数值边界条件的一种处理方法.径向第一个网格点设在距离中心半点位置上.根据相应物理量的特性,在中心附近进行边界延拓,使得内点的高精度差分格式可以同样应用在网格中心附近,从而无需单侧差分格式,保持了一致的高阶精度.对于周向边界,也建立了一种周期延拓方法,使得在周向所有节点处都能够采用同样的高精度格式离散,并进行了数值试验.     

基于非结构网格CE/SE算法圆柱绕流气动声场模拟

本文采用时空守恒(CE/SE)格式求解Navier-Stoks方程与Euler方程,数值模拟了绕圆柱流动引发的气动噪声源及传播问题.对近声场与远声场采用了不同的控制方程和边界条件,分别得到了流场与声场解.将其与采用大涡模拟和FW-H方程得到的结果进行了对比,表明本文的数值方法能够很好地反映流场与声场的形态,能较好地模拟声场指向性及流场中的拟声现象,相比LES/FW-H方法能更精确地反映流场与声场的相互关系.     

非正交网格上的九点格式在热传导问题中的改进

对文献[1]在二维Lagrange流体力学网格上构造的扩散方程九点差分格式做了进一步的讨论和改进,给出了一般形式边界条件的计算格式。数值试验的结果表明,这些改进提高了原格式数值结果的精度。     

统一坐标系下二维气动方程组的Runge-Kutta间断Galerkin有限元方法

构造了统一坐标系下二维可压缩气动方程组的Runge-Kutta 间断Galerkin(RKDG)有限元格式. 文中将流体力学方程组和几何守恒律统一求解, 所有计算都在固定的网格上进行, 在计算过程中不需要网格节点的速度信息. 文中对几个数值算例进行了数值模拟, 得到了较好的数值模拟结果.     

四阶紧致差分格式对静力模式中垂直网格计算频散性的影响

为了说明四阶紧致差分格式在大气和海洋数值模式中的潜在价值,提出一种通用方法,推导静力线性斜压适应方程组在微分和差分情况下的频散关系,水平尺度分100 km,10 km和1 km三种情况,从频率、水平群速和垂直群速方面,对采用二阶中央差和四阶紧致差分格式情况下,非跳点网格(N网格)、Lorenz网格(L网格)、Charney-Phillips网格(CP网格)、Lorenz时间跳点网格(LTS网格)和Charney-Phillips时间跳点网格(CPTS网格)的计算特性进行比较,发现采用高精度的四阶紧致差分格式总体上可以明显减少上述三种水平尺度波动在N网格、CP网格、L网格和CPTS网格上的频率、水平群速和垂直群速误差,但对LTS网格,采用四阶紧致差分格式,会使得计算水平群速和垂直群速误差变大.     

一种非结构/结构多层混合网格方法及其应用

对于粘性绕流的数值模拟,在自适应直角网格基础上,结合三角形非结构网格和结构化网格,利用其各自的优势和特点,提出一种生成混合杂交网格的思路和方法.在物面附近生成适合粘性流计算的大长宽比结构化网格,在远场分布自适应直角网格,快速离散计算空间.对于复杂的多体问题,采用三角形网格来连接各体网格,并运用网格合并的方法,保证各网格之间的光滑过渡与连接,提高网格质量.针对一些二维、三维外形的绕流问题,在上述网格基础上,采用B-L代数湍流模型和中心有限体积法,完成Navier-Stokes和Euler方程数值模拟的对比计算,结果表明网格生成和流场计算是正确的.     

黏性激波管的有限体积WENO格式数值模拟

本文采用OpenFOAM软件下实现的一种可实现任意阶数,可应用于非结构网格的有限体积WENO格式对黏性激波管问题进行模拟。模拟中对流项离散采用3阶精度、4阶精度该类WENO格式,网格形式采用结构网格和三角形非结构网格。结果表明,采用该类格式,三角形非结构网格的算精度、效率优于结构网格,3阶精度格式计算效率优于4阶精度。该工作表明OpenFOAM下采用3阶精度该类格式及非结构网格对叶轮机械内部流动等复杂流场的模拟更具优势与应用潜力.     

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.     

Deforming composite grids for solving fluid structure problems

We describe a mixed Eulerian–Lagrangian approach for solving fluid–structure interaction (FSI) problems. The technique, which uses deforming composite grids (DCG), is applied to FSI problems that couple high speed compressible flow with elastic solids. The fluid and solid domains are discretized with composite overlapping grids. Curvilinear grids are aligned with each interface and these grids deform as the interface evolves. The majority of grid points in the fluid domain generally belong to background Cartesian grids which do not move during a simulation. The FSI-DCG approach allows large displacements of the interfaces while retaining high quality grids. Efficiency is obtained through the use of structured grids and Cartesian grids. The governing equations in the fluid and solid domains are evolved in a partitioned approach. We solve the compressible Euler equations in the fluid domains using a high-order Godunov finite-volume scheme. We solve the linear elastodynamic equations in the solid domains using a second-order upwind scheme. We develop interface approximations based on the solution of a fluid–solid Riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids. The FSI-DCG approach is verified for three problems with known solutions, an elastic-piston problem, the superseismic shock problem and a deforming diffuser. In addition, a self convergence study is performed for an elastic shock hitting a fluid filled cavity. The overall FSI-DCG scheme is shown to be second-order accurate in the max-norm for smooth solutions, and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters.     

An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load

Most existing research on the vulnerability of power grids based on complex networks ignores the electrical characteristics and the capacity of generators and load. In this paper, the electrical betweenness is defined by considering the maximal demand of load and the capacity of generators in power grids. The loss of load, which reflects the ability of power grids to provide sufficient power to customers, is introduced to measure the vulnerability together with the size of the largest cluster. The simulation results of the IEEE-118 bus system and the Central China Power Grid show that the cumulative distributions of node electrical betweenness follow a power-law and that the nodes with high electrical betweenness play critical roles in both topological structure and power transmission of power grids. The results prove that the model proposed in this paper is effective for analyzing the vulnerability of power grids.     

Local rectangular refinement with application to axisymmetric laminar flames

Within realistic combustion devices, physical quantities may change by an order of magnitude over an extremely thin flamefront, while remaining nearly unchanged throughout large areas nearby. Such behaviour dictates the use of adaptive numerical methods. The recently developed local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes novel multiple-scale finite-difference discretizations, and incorporates a damped modified Newton's method for simultaneously solving systems of governing elliptic PDEs. Here, the LRR method is applied to two axisymmetric laminar flames: a premixed Bunsen flame with one-step chemistry and a diffusion flame employing various complex chemical mechanisms. The Bunsen flame's position is highly dependent upon grid spacing, especially on coarse grids; it stabilizes only with adequate refinement. The diffusion flame results show excellent agreement with experimental data for flame structure, temperature and major species. For both flames, the LRR results on intermediate grids are comparable to those obtained on equivalently refined conventional grids. Solution accuracy on the final LRR grids could not be achieved using conventional grids because the latter exceeded the available computer memory. In general, the LRR method required about half the grid points, half the memory and half the computation time of the solution process on conventional grids.     

三维非结构粘性网格生成方法

描述了一套适合粘性流动计算的三维非结构网格自动生成方法.在物面附近的粘性作用区域,采用推进层方法生成各向异性的"扁平"四面体网格,并通过一定的网格伸长控制参数,实现整个流场区域网格高度的平滑过渡.当粘性网格的推进高度达到预定要求时,推进层方法自动停止,转而采用阵面推进方法生成常规意义的尽量接近正四面体的各向同性网格.同时给出了利用该方法生成的M6机翼非结构粘性网格来求解机翼粘性绕流的简单算例.     

Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids

The present paper deals with an efficient and accurate limiting strategy for the multi-dimensional hyperbolic conservation laws on unstructured grids. The multi-dimensional limiting process (MLP) which has been successfully proposed on structured grids is extended to unstructured grids. The basic idea of the proposed limiting strategy is to control the distribution of both cell-centered and cell-vertex physical properties to mimic multi-dimensional nature of flow physics, which can be formulated to satisfy so called the MLP condition. The MLP condition can guarantee high-order spatial accuracy and improved convergence without yielding spurious oscillations. Starting from the MUSCL-type reconstruction on unstructured grids followed by the efficient implementation of the MLP condition, MLP slope limiters on unstructured meshes are obtained.Thanks to its superior limiting strategy and maximum principle satisfying characteristics, the newly developed MLP on unstructured grids is quite effective in controlling numerical oscillations as well as accurate in capturing multi-dimensional flow features. Numerous test cases are presented to validate the basic features of the proposed approach.     

二维自适应结构网格的变分生成方法

提出-一种二维结构网格的自适应生成方法,即采用变分方程控制网格的疏密程度以及光滑性、正交性和正规性,并且所有的控制方程具有-致的量纲.几个数值算例表明,给出的网格自适应生成方法能够较好地收敛到方程的唯-解,同时产生性质良好的二维自适应结构网格.