Marangoni效应下的液桥自由面

改进Ｏｓｈｅｒ的ＬｅｖｅｌＳｅｔ方法用来计算考虑Ｍａｒａｎｇｏｎｉ效应的液桥自由面及内部的涡流．提出以双调和函数来作为Ｌｅｖｅｌ函数,从而避免了它们的奇性．求出的自由面的波纹形状以及二次涡远比简化算法所得要小．     

不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

非正交网格控制容积法分析复杂形状池内的流动

介绍一种基于非正交网格控制容积法的数学模型，及其在圆形沉沙池流动研究中的应用．该模型求解轴对称流动的连续方程及时均Ｎ－Ｓ方程，并采用标准ｋ－ε紊流模型，模拟圆形池内的流动．由于采用非正交网格，此计算模型可精确模拟几何形状较复杂的沉沙池内的流动，利用上述模型对某实际沉沙池进行了流场计算，计算所得流场与模型试验实测值符合良好．     

非正交网格控制容积法分析复杂形状池内的流动

介绍一种基于非正交网格控制容积法的数学模型，及其在圆形沉沙池流动研究中的应用．该模型求解轴对称流动的连续方程及时均Ｎ－Ｓ方程，并采用标准ｋ－ε紊流模型，模拟圆形池内的流动．由于采用非正交网格，此计算模型可精确模拟几何形状较复杂的沉沙池内的流动，利用上述模型对某实际沉沙池进行了流场计算，计算所得流场与模型试验实测值符合良好．     

带有襟翼偏转的三维机翼绕流的N—S方法解

给出了带襟翼偏转的三维机翼绕流的一种求解Ｎ－Ｓ方程的计算方法,采用区域求解算法和对接分区网络技术相结合的方法,有效地求解了绕此外形的复杂流动,区域求解算法中提出了一种满足通量守恒的内边界耦合条件,流场求解时采用中心差分的限体积方法对空间通量顶进行离散,采用显式推进方法进行时间方向的积分,数值算例表明本方法是求解带襟翼偏转的机翼绕流的有效方法。     

不可压粘流N－S方程的边界积分解法

对原变量的Ｎ－Ｓ方程进行一阶时间离散，采用共轭梯度法解除压强－速度的耦合．对所得的一系列Ｌａｐｌａｃｅ方程、Ｐｏｓｓｉｏｎ方程和Ｈｅｌｍｈｏｔｚ方程均进行边界积分法求解，首次得到了粘性Ｎ－Ｓ方程的边界积分表示式．圆柱的定常、非定常尾迹计算结果表明了本文方法的有效性．     

不可压粘流N－S方程的边界积分解法

对原变量的Ｎ－Ｓ方程进行一阶时间离散，采用共轭梯度法解除压强－速度的耦合．对所得的一系列Ｌａｐｌａｃｅ方程、Ｐｏｓｓｉｏｎ方程和Ｈｅｌｍｈｏｔｚ方程均进行边界积分法求解，首次得到了粘性Ｎ－Ｓ方程的边界积分表示式．圆柱的定常、非定常尾迹计算结果表明了本文方法的有效性．     

线性船舶兴波阻力边界元新方法

采用常数边界元对船舶与流体界面进行离散，求解船舶兴波势及船舶兴波阻力。这种方法可避免在船舶与流体自由面交线上安置节点，因而避免了这些节点建立补充方程。因为满足自由面条件的Ｈａｖｅｌｏｃｋ源函数的源点和场点不能同时在自由面上，使得自由面上的节点无法用Ｈａｖｅｌｏｃｋ源函数的建立方程。如对自由面交线上的节点建立补充方程，则要对线性自由面条件中包含的未知势函数的二阶导数用差分形式表达，引入较大误差。     

有限厚度流体层界面运动Rayleigh-Taylor不稳定性的数值模拟

采用二阶ＴＶＤ格式及ＬｅｖｅｌＳｅｔ方法计算了二维可压缩有限厚度流体层Ｒａｙｌｅｉｇｈ Ｔａｙｌｏｒ流体不稳定性。计算结果与Ｔａｙｌｏｒ的线性解和Ｏｔ的薄层非线性解析解符合很好。     

三角翼大迎角不可压粘流的数值模拟

研究了人工压缩法拟压缩性系数β的选取，采用函数形式的β有效地加速了收敛过程．采用求解不可压Ｎ－Ｓ方程，对三角翼大迎角绕流进行了数值模拟，得到了与实验吻合很好的结果．分析和讨论了大迎角旋涡流动的复杂物理现象     

Simulation of the two-fluid model on incompressible flow with Fractional Step method for both resolved and unresolved scale interfaces

In the present paper, the Fractional Step method usually used in single fluid flow is here extended and applied for the two-fluid model resolution using the finite volume discretization. The use of a projection method resolution instead of the usual pressure-correction method for multi-fluid flow, successfully avoids iteration processes. On the other hand, the main weakness of the two fluid model used for simulations of free surface flows, which is the numerical diffusion of the interface, is also solved by means of the conservative Level Set method (interface sharpening) (Strubelj et al., 2009). Moreover, the use of the algorithm proposed has allowed presenting different free-surface cases with or without Level Set implementation even under coarse meshes under a wide range of density ratios. Thus, the numerical results presented, numerically verified, experimentally validated and converged under high density ratios, shows the capability and reliability of this resolution method for both mixed and unmixed flows.     

水动力作用下低速射流碎化的数值模拟

为研究射流在水动力作用下的碎化特性,采用有限体积法对轴对称坐标下Navier-Stokes方程进行了求解,考虑重力和表面张力的影响,并通过Volume-of-Fluid法与Level-Set法成功捕捉到界面的不稳定发展、变形及射流碎化过程,分析了流场内部速度场和压力场分布,结果表明,射流碎化长度随Re/We“5数呈指数型增加,最后探讨了射流速度、直径及周围流体密度、粘性等参量对射流的碎化过程的影响规律.     

基于四阶半离散中心迎风格式的虚拟流方法的应用

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,因此再将新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。     

Numerical simulation of 3D free surface flows,with multiple incompressible immiscible phases. Applications to impulse waves

A numerical method for the solution to the density‐dependent incompressible Navier–Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid phases together with an additional vacuum phase separated with a free surface. It is based on a volume‐of‐fluid approach involving N indicator functions (one per phase, identified by its density) that guarantees mass conservation within each phase. An additional indicator function for the whole liquid domain allows to treat boundary conditions at the interface between the liquid domain and a vacuum. The system of partial differential equations is solved by implicit operator splitting at each time step: first, transport equations are solved by a forward characteristics method on a fine Cartesian grid to predict the new location of each liquid phase; second, a generalized Stokes problem with a density‐dependent viscosity is solved with a FEM on a coarser mesh of the liquid domain. A novel algorithm ensuring the maximum principle and limiting the numerical diffusion for the transport of the N phases is validated on benchmark flows. Then, we focus on a novel application and compare the numerical and physical simulations of impulse waves, that is, waves generated at the free surface of a water basin initially at rest after the impact of a denser phase. A particularly useful application in hydraulic engineering is to predict the effects of a landslide‐generated impulse wave in a reservoir. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical study of breaking waves by a two‐phase flow model

A two‐phase flow model, which solves the flow in the air and water simultaneously, is presented for modelling breaking waves in deep and shallow water, including wave pre‐breaking, overturning and post‐breaking processes. The model is based on the Reynolds‐averaged Navier–Stokes equations with the k ?ε turbulence model. The governing equations are solved by the finite volume method in a Cartesian staggered grid and the partial cell treatment is implemented to deal with complex geometries. The SIMPLE algorithm is utilised for the pressure‐velocity coupling and the air‐water interface is modelled by the interface capturing method via a high resolution volume of fluid scheme. The numerical model is validated by simulating overturning waves on a sloping beach and over a reef, and deep‐water breaking waves in a periodic domain, in which good agreement between numerical results and available experimental measurements for the water surface profiles during wave overturning is obtained. The overturning jet, air entrainment and splash‐up during wave breaking have been captured by the two‐phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems.Copyright © 2011 John Wiley & Sons, Ltd.     

带有障碍物溃坝流动问题的有限元数值模拟研究

针对下游带有障碍物的溃坝流动问题,本文基于两相流动模型,在有限元算法框架下对其进行数值模拟研究。依据水平集(Level Set)方法追踪运动界面,并引入了一个简单的修正技术,保证较好的质量守恒性。为了精确表示运动界面,采用稳定和有效的间断有限元方法求解双曲型Level Set及其重新初始化方程。对于两相统一Navier-Stokes方程,首先利用分裂格式对其解耦,然后通过SUPG (Streamline Upwind Petrov Galerkin)方法进行数值求解。模拟研究了下游带有障碍物的牛顿流体溃坝流动问题,得到的数值结果与文献已有模拟结果及实验结果均吻合较好。此外,还考虑了幂律型非牛顿流体,并分析了不同特性非牛顿流体对于溃坝流动过程和界面形态等的影响。     

A finite element analysis of a free surface drainage problem of two immiscible fluids

A sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two-dimensional model and solved numerically. This problem is a transient two-phase free or moving boundary problem, the slag surface and the slag–metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time-stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace is given.     

Interaction of a solitary wave and a front step simulated by level set method

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｖｅｌＳｅｔｍｅｔｈｏｄｈａｓｂｅｅｎｄｅｖｅｌｏｐｅｄｆｏｒｃｏｍｐｕｔｉｎｇｔｈｅｍｏｔｉｏｎｏｆｔｗｏ＿ｐｈａｓｅｆｌｏｗｂｙＯｓｈｅｒｅｔａｌ.[1,2 ].Ｉｎｔｈｉｓｗｏｒｋ ,ｔｈｅｉｎｃｏｍｐｒｅｓｓｉｂｌｅＮ＿Ｓｅｑｕａｔｉｏｎｓａｒｅｓｏｌｖｅｄｉｎｔｈｅｗｈｏｌｅｄｏｍａｉｎ ,ａｎｄｔｈｅｉｎｔｅｒｆａｃｅｉｓｔｒａｃｋｅｄｔｈｒｏｕｇｈａＬｅｖｅｌＳｅｔｆｕｎｃｔｉｏｎ .ＴｈｅＬｅｖｅｌＳｅｔｆｕｎｃｔｉｏｎｉｓｄｅｆｉｎｅｄａｓａｄｉｓｔａｎｃｅｆｕｎ…     

An implicit two‐dimensional non‐hydrostatic model for free‐surface flows

An implicit finite volume model in sigma coordinate system is developed to simulate two‐dimensional (2D) vertical free surface flows, deploying a non‐hydrostatic pressure distribution. The algorithm is based on a projection method which solves the complete 2D Navier–Stokes equations in two steps. First the pressure term in the momentum equations is excluded and the resultant advection–diffusion equations are solved. In the second step the continuity and the momentum equation with only the pressure terms are solved to give a block tri‐diagonal system of equation with pressure as the unknown. This system can be solved by a direct matrix solver without iteration. A new implicit treatment of non‐hydrostatic pressure, similar to the lower layers is applied to the top layer which makes the model free of any hydrostatic pressure assumption all through the water column. This treatment enables the model to evaluate both free surface elevation and wave celerity more accurately. A series of numerical tests including free‐surface flows with significant vertical accelerations and nonlinear behaviour in shoaling zone are performed. Comparison between numerical results, analytical solutions and experimental data demonstrates a satisfactory performance. Copyright © 2006 John Wiley & Sons, Ltd.     

An adaptive numerical scheme for solving incompressible 2‐phase and free‐surface flows

In this paper, we present a numerical scheme for solving 2‐phase or free‐surface flows. Here, the interface/free surface is modeled using the level‐set formulation, and the underlying mesh is adapted at each iteration of the flow solver. This adaptation allows us to obtain a precise approximation for the interface/free‐surface location. In addition, it enables us to solve the time‐discretized fluid equation only in the fluid domain in the case of free‐surface problems. Fluids here are considered incompressible. Therefore, their motion is described by the incompressible Navier‐Stokes equation, which is temporally discretized using the method of characteristics and is solved at each time iteration by a first‐order Lagrange‐Galerkin method. The level‐set function representing the interface/free surface satisfies an advection equation that is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level‐set function (redistancing) as well as the construction of a convenient flow for the level‐set advection equation. Numerical results are presented for both bifluid and free‐surface problems.