两种浸入式边界方法的比较

介绍两类不同的浸入式边界方法及其对它的改进. 然后采用均匀矩形交错网格和压力校正投影法,对不可压流场中的二维圆柱绕流进行了数值求解并对比了两类方法的精度.计算分析表明,连续显力法具有构造简单,适用性强的优点. 但离散隐力法在物面边界精度上要优于前者. 改进后,在二阶精度的离散格式下物面边界精度较低的显示力源法的精度有一定提高,同时发现,加密网格以提高数值精度的方法对于连续显力法并不总是有效.而同样格式下,离散隐力法具有更高精度,其中预测-校正离散隐力法可以在此基础上获得更小的计算误差和更快的收敛速度. 数值解与文献已有的数值和实验结果吻合得很好,表明边界算法及其程序是可靠和有效的.      

基于反馈力浸入边界法模拟复杂动边界流动

浸入边界法是模拟流固耦合的重要数值方法之一。本文采用反馈力浸入边界方法,对旋转圆柱和水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟。其中,固体边界采用一系列离散的点近似代替,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。固体对流场的作用通过构造适宜的反馈力函数实现。本文首先通过旋转圆柱绕流的计算结果同实验结果进行对比,吻合较好,验证了该计算方法的可靠性。然后针对水电站水力过渡过程中水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟,得到导叶动态绕流后的流场分布特性和涡结构的演化特性。     

二维细胞在剪切流中的运动特性

主要模拟二维细胞在剪切流中的运动特性.计算过程采用浸入边界法,将细胞模化成Navier-Stokes方程中的力源,而不是真实物体.假设细胞的初始形状为椭圆,细胞内外流体粘性相同,细胞膜的弹性力模型选用E-S模型.本文模拟四种不同真圆度情况下细胞的形变情况,观测到初始阶段细胞沿着长轴方向做拉伸和旋转运动,达到稳定状态后细胞作类坦克履带式运动;并且发现细胞达到稳定状态所需要的时间随真圆度的增加而增加,而细胞的稳态倾角随真圆度的增加而减少.     

自主泳动弹性绳的轨迹模拟

研究柔性结构与流体间耦合作用,可以促进软体机器人的发展.通过速度快、精度高的数值模拟方法模拟水下机器人的实时运动轨迹,可以为真实实验提供测试方向与理论牵引,增大实验成功的可能性.本文研究有自主运动趋势的弹性绳在二维流场中的运动轨迹.首先,对弹性绳离散化建模并同时考虑拉压与扭转弹性力,从能量角度建立动力学方程,此模型可以较为真实地反映弹性绳内力对其运动产生的作用.然后基于半拉格朗日法建立流体求解器. 最后,提出简化的基于动量方程的浸入边界法作为耦合算法,通过直接修正网格速度代替浸入边界力法中力源项的作用.使用这种算法求解耦合作用兼具简便性与快速性.对弹性绳模型、流体模型与简化耦合模型依次解算,模拟了正弦形式波动弹性绳在水中的运动轨迹.结果显示,弹性绳在弹性内力与流固相互作用力共同影响下,该种新的浸入边界法可以实现对水下弹性绳运动轨迹的模拟.数值实验显示弹性绳的自主运动参考模型的初相位改变时,其前进方向会发生改变.该仿真模拟算法与平台可以为细长形软体水生机器人的研发提供参考.      

自主泳动弹性绳的轨迹模拟

研究柔性结构与流体间耦合作用,可以促进软体机器人的发展.通过速度快、精度高的数值模拟方法模拟水下机器人的实时运动轨迹,可以为真实实验提供测试方向与理论牵引,增大实验成功的可能性.本文研究有自主运动趋势的弹性绳在二维流场中的运动轨迹.首先,对弹性绳离散化建模并同时考虑拉压与扭转弹性力,从能量角度建立动力学方程,此模型可以较为真实地反映弹性绳内力对其运动产生的作用.然后基于半拉格朗日法建立流体求解器.最后,提出简化的基于动量方程的浸入边界法作为耦合算法,通过直接修正网格速度代替浸入边界力法中力源项的作用.使用这种算法求解耦合作用兼具简便性与快速性.对弹性绳模型、流体模型与简化耦合模型依次解算,模拟了正弦形式波动弹性绳在水中的运动轨迹.结果显示,弹性绳在弹性内力与流固相互作用力共同影响下,该种新的浸入边界法可以实现对水下弹性绳运动轨迹的模拟.数值实验显示弹性绳的自主运动参考模型的初相位改变时,其前进方向会发生改变.该仿真模拟算法与平台可以为细长形软体水生机器人的研发提供参考.     

改进的奇异边界法模拟三维位势问题

奇异边界法是与基本解法相对应的一种边界型无网格数值离散方法. 该方法提出了源点强度因子的概念, 克服了传统基本解方法中最复杂最头疼的虚拟边界问题.基于边界元法中处理奇异积分的数值处理技术, 导出了源点强度因子的解析表达式, 提出了改进的无网格奇异边界法, 并进一步将该方法应用于三维位势问题. 该方法消除了传统方法中样本点的选取, 在不增加计算量的前提下, 极大地提高了奇异边界法的计算精度与稳定性.      

基于2D网格的轴对称浸没边界法

浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.      

M_p图与(M)_1图选用不同基本结构的力法分析1)

在传统的结构力学力法教学中,无论是力法基本方程的建立还是方程中系数和自由项的求解,都要求在同一基本结构上进行.本文通过实例计算和比较,采用公式叠加原理分析了当M_p图与M_1图分别选自不同的基本结构时,力法基本方程的物理意义以及计算过程的科学意义.结果显示在力法计算中,基于不同的基本结构求解超静定问题,可简化力法的计算过程.用本文方法开展教学,有利于学生对力法的深入理解和掌握.     

流固偶合运动的边界元法

本文给出了流固偶合运动(包括物体散射辐射及偶合运动)的边界元法理论和应用.对于散射问题,求出了物体引起的散射势及入射波作用于物体的载荷.对于辐射问题,求出了辐射势及物体在流体中运动的附加质量和附加阻尼.偶合问题包括求其中包含的散射势和辐射势以及作用于物体之上的散射力、物体的附加质量、附加阻尼、物体在入射波作用下的运动.在偶合运动问题中,本文采取了边界积分方程与物体在流体中的运动方程联立求解的方法,并将其运用到边界元法的数值过程中.所编制的程序有较高的精度.最后给出了数值计算结果与理论解的比较.     

平头物体三维带空泡入水的数值模拟

本文用时间步进法和边界积分方程方法数值求解平头物体的垂直及斜向入水过程,这是一个在非线性自由面条件下,物体与流体有耦合作用,三维、非定常、理想不可压流体的运动问题,自由面用Lagrangian参数描述,物面用固结在物体上的Eulerian坐标描述,数值计算上提出了物面动力学条件(流-固耦合运动方程)和自由面动力学条件的二阶精度的时间差分隐格式,最后给出若干入水情况的详细计算结果。     

An immersed boundary method for unstructured meshes in depth averaged shallow water models

The representation of geometries as buildings, flood barriers or dikes in free surface flow models implies tedious and time‐consuming operations in order to define accurately the shape of these objects when using a body fitted numerical mesh. The immersed boundary method is an alternative way to define solid bodies inside the computational domain without the need of fitting the mesh boundaries to the shape of the object. In the direct forcing immersed boundary method, a solid body is represented by a grid of Lagrangian markers, which define its shape and which are independent from the fluid Eulerian mesh. This paper presents a new implementation of the immersed boundary method in an unstructured finite volume solver for the 2D shallow water equations. Moving least‐squares is used to transmit information between the grid of Lagrangian markers and the fluid Eulerian mesh. The performance of the proposed implementation is analysed in three test cases involving different flow conditions: the flow around a spur dike, a dam break flow with an isolated obstacle and the flow around an array of obstacles. A very good agreement between the classic body fitted approach and the immersed boundary method was found. The differences between the results obtained with both methods are less relevant than the errors because of the intrinsic shallow water assumptions. Copyright © 2015 John Wiley & Sons, Ltd.     

A new modification of the immersed‐boundary method for simulating flows with complex moving boundaries

In this paper, a new immersed‐boundary method for simulating flows over complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. The present method is based on a finite‐difference approach on a staggered mesh together with a fractional‐step method. It must be noted that the immersed boundary is generally not coincident with the position of the solution variables on the grid, therefore, an appropriate strategy is needed to construct a relationship between the curved boundary and the grid points nearby. Furthermore, a momentum forcing is added on the body boundaries and also inside the body to satisfy the no‐slip boundary condition. The immersed boundary is represented by a series of interfacial markers, and the markers are also used as Lagrangian forcing points. A linear interpolation is then used to scale the Lagrangian forcing from the interfacial markers to the corresponding grid points nearby. This treatment of the immersed‐boundary is used to simulate several problems, which have been validated with previous experimental results in the open literature, verifying the accuracy of the present method. Copyright © 2006 John Wiley & Sons, Ltd.     

A comparative study of direct‐forcing immersed boundary‐lattice Boltzmann methods for stationary complex boundaries

In this study, we assess several interface schemes for stationary complex boundary flows under the direct‐forcing immersed boundary‐lattice Boltzmann methods (IB‐LBM) based on a split‐forcing lattice Boltzmann equation (LBE). Our strategy is to couple various interface schemes, which were adopted in the previous direct‐forcing immersed boundary methods (IBM), with the split‐forcing LBE, which enables us to directly use the direct‐forcing concept in the lattice Boltzmann calculation algorithm with a second‐order accuracy without involving the Navier–Stokes equation. In this study, we investigate not only common diffuse interface schemes but also a sharp interface scheme. For the diffuse interface scheme, we consider explicit and implicit interface schemes. In the calculation of velocity interpolation and force distribution, we use the 2‐ and 4‐point discrete delta functions, which give the second‐order approximation. For the sharp interface scheme, we deal with the exterior sharp interface scheme, where we impose the force density on exterior (solid) nodes nearest to the boundary. All tested schemes show a second‐order overall accuracy when the simulation results of the Taylor–Green decaying vortex are compared with the analytical solutions. It is also confirmed that for stationary complex boundary flows, the sharper the interface scheme, the more accurate the results are. In the simulation of flows past a circular cylinder, the results from each interface scheme are comparable to those from other corresponding numerical schemes. Copyright © 2010 John Wiley & Sons, Ltd.     

Immersed boundary methods for fluid-structure interaction: A review

In this review, we introduce immersed boundary (IB) methods for fluid-structure interactions (FSIs) of rigid and elastic bodies. IB methods impose momentum forcing on an Eulerian mesh to satisfy boundary conditions on the interface between fluid and structure, which enables us to use a non-body conforming grid system for complex-shaped moving bodies. Imposition of the momentum forcing is performed directly through discrete delta function or indirectly through velocity reconstruction, by which IB methods have their own strengths and weaknesses to FSI problems of rigid and elastic bodies. To deal with FSI, IB methods using monolithic and partitioned (strong and weak coupling) approaches with different stability and cost have been suggested. Nevertheless, two important problems in FSI, cases of low density ratio of solid to fluid and high Reynolds number, have not been completely overcome by current IB methods in terms of the stability, accuracy and cost. These aspects are examined in this review.     

Improvement of mass source/sink for an immersed boundary method

An improved immersed boundary method using a mass source/sink as well as momentum forcing is developed for simulating flows over or inside complex geometries. The present method is based on the Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. A more accurate formulation of the mass source/sink is derived by considering mass conservation of the virtual cells in the fluid crossed by the immersed boundary. Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are used to validate the proposed formulation. The results indicate that the accuracy near the immersed boundary is improved by introducing the accurate mass source/sink. Copyright © 2006 John Wiley & Sons, Ltd.     

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical and numerical studies of the boundary slip in the immersed boundary‐thermal lattice Boltzmann method

We analytically and numerically investigate the boundary slip, including the velocity slip and the temperature jump, in immersed boundary‐thermal lattice Boltzmann methods (IB‐TLBMs) with the two‐relaxation‐time collision operator. We derive the theoretical equation for the relaxation parameters considering the effect of the advection velocity on the temperature jump of the IB‐TLBMs. The analytical and numerical solutions demonstrate that the proposed iterative correction methods without the computational cost of the sparse matrix solver reduce the boundary slip and boundary‐value deviation as effectively as the implicit correction method for any relaxation time. Because the commonly used multi‐direct forcing method does not consider the contributions of the body force to the momentum flux, it cannot completely eliminate the boundary slip because of the numerical instability for a long relaxation time. Both types of proposed iterative correction methods are more numerically stable than the implicit correction method. In simulations of flow past a circular cylinder and of natural convection, the present iterative correction methods yield adequate results without the errors of the velocity slip, the temperature jump, and the boundary‐value deviation for any relaxation time parameters and for any number of Lagrangian points per length. The combination of the present methods and the two‐relaxation‐time collision operator is suitable for simulating fluid flow with thermal convection in the multiblock method in which the relaxation time increases in inverse proportion to the grid size.     

Simulation of two‐phase flow–body interaction problems using direct forcing/fictitious domain–level set method

In the present paper, a direct forcing/fictitious domain (DF/FD)–level set method is proposed to simulate the twophase flow–body interaction. The DF/FD does not sacrifice accuracy and robustness by employing a discrete δ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, the easy implementation and the utilization of original governing equation without modification. The main idea is to combine DF/FD method with the level set method in the Cartesian coordinates. We present the results of a number of test cases to illustrate the effectiveness of the proposed method for single‐phase flow–body interaction problem and the two‐phase flows with a stationary body. Eventually, the simulations of various water entry problems have been conducted to validate the capability and the accuracy of the present method on solving the twophase flow–body interaction. Consequently, the present results are found to be in good agreement with those of previous studies. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of dynamic fluid–solid interactions with an improved direct-forcing immersed boundary method

Dynamic fluid–solid interactions are widely found in chemical engineering, such as in particle-laden flows, which usually contain complex moving boundaries. The immersed boundary method (IBM) is a convenient approach to handle fluid–solid interactions with complex geometries. In this work, Uhlmann's direct-forcing IBM is improved and implemented on a supercomputer with CPU–GPU hybrid architecture. The direct-forcing IBM is modified as follows: the Poisson's equation for pressure is solved before evaluation of the body force, and the force is only distributed to the Cartesian grids inside the immersed boundary. A multidirect forcing scheme is used to evaluate the body force. These modifications result in a divergence-free flow field in the fluid domain and the no-slip boundary condition at the immersed boundary simultaneously. This method is implemented in an explicit finite-difference fractional-step scheme, and validated by 2D simulations of lid-driven cavity flow, Couette flow between two concentric cylinders and flow over a circular cylinder. Finally, the method is used to simulate the sedimentation of two circular particles in a channel. The results agree very well with previous experimental and numerical data, and are more accurate than the conventional direct-forcing method, especially in the vicinity of a moving boundary.