线性与非线性流固耦合动力学数值方法的进展及应用

本文综述了线性与非线性流固耦合问题数值方法的进展及工程应用。讨论了四种数值分析方法：(1)混合有限元–子结构–子区域数值模型,以求解有限域线性流固耦合问题,如流体晃动,声腔–结构耦合,流体中的压力波,化工容器的地震响应,坝水耦合等;(2)混合有限元–边界元数值模型,以求解涉及无限域的线性流固耦合问题,如大型浮体承受飞机降落冲击,船舰的炮击回应等;(3)混合有限元–有限差分(体积)数值模型,以求解不涉及破浪和两相分离的非线性流固耦合问题;(4)混合有限元–光滑粒子数值模型,以求解涉及破浪和两相分离的非线性流固耦合问题。文中推荐分区迭代求解过程,以便应用现有的固体及流体求解器,于毎一时间步长分别求解固体及流体的方程,通过耦合迭代收敛,向前推进以达问题求解。文中选用的工程应用例子包含气–液–壳三相耦合,液化天然气船水晃动,人体步行冲击引起的声腔–建筑结构耦合,大型浮体承受飞机降落冲击的瞬态动力回应,涉及破浪和两相分离的气–翼耦合及结构于水上降落的冲击。数值分析结果与可用的实验或计算结果作了比较,以说明所述方法的精度及工程应用价值。文中列出了基于流固耦合的波能采积装置模型,以应用线性系统的共振及非线性系统的周期解原理,有效地采积波能。本文列出了231篇参考文献,以便读者进一步研讨所感兴趣方法。     

NUMERICAL MODELING FOR FLUID-STRUCTURE INTERACTION UNDER BLAST AND IMPACT LOADING RESPONSE

建立了基于位移相等条件的流固耦合数值模拟程序框架,通过串联弱耦合方式对爆炸冲击波作用下流固耦合效应进行数值模拟. 其中非线性固体位移场采用基于Lagrange方法描述的时域间断伽辽金有限元方法进行处理. 基于修正弹簧近似的非结构动网格新技术,非定常流场采用格心格式的有限体积方法进行求解. 数值模拟结果表明: 该文所发展的弱耦合分析程序在流固耦合数值模拟过程中具有可靠的计算精度. 同时,程序对于爆炸强间断气动冲击载荷冲击作用下固体变形引起流场的反射和叠加效应, 以及流场变化引起复杂的固体响应具有良好的耦合求解能力.     

面向对象的土石坝参数随机反演程序设计

将储液容器流固耦合系统中的液体和容器分别视为理想可压缩流体和线弹 性固体，采用流体压力单元和固体壳单元对流固耦合系统进行有限元离散，得到一个非对称 的大型流固耦合有限元方程. 采用Arnoldi方法求解上面这个大型有限元方程的非对称特征 值问题，以得到储液容器的动力特性. 通过移频技术避免了处理零频问题，并构造了迭代格 式计算Arnoldi向量. 数值算例表明所用解法对于流固耦合系统都是非常有效的.     

A new numerical technique for the analysis of parametrically excited nonlinear systems

A new computational scheme using Chebyshev polynomials is proposed for the numerical solution of parametrically excited nonlinear systems. The state vector and the periodic coefficients are expanded in Chebyshev polynomials and an integral equation suitable for a Picard-type iteration is formulated. A Chebyshev collocation is applied to the integral with the nonlinearities reducing the problem to the solution of a set of linear algebraic equations in each iteration. The method is equally applicable for nonlinear systems which are represented in state-space form or by a set of second-order differential equations. The proposed technique is found to duplicate the periodic, multi-periodic and chaotic solutions of a parametrically excited system obtained previously using the conventional numerical integration schemes with comparable CPU times. The technique does not require the inversion of the mass matrix in the case of multi degree-of-freedom systems. The present method is also shown to offer significant computational conveniences over the conventional numerical integration routines when used in a scheme for the direct determination of periodic solutions. Of course, the technique is also applicable to non-parametrically excited nonlinear systems as well.     

Numerical investigation of ice breaking by a high-pressure bubble based on a coupled BEM-PD model

In this paper, by combining the boundary element method (BEM) and peridynamics (PD), a bubble-ice interaction model is established, which can investigate the dynamic interactions between a high-pressure bubble and an ice plate with particular focus on the mechanical behaviors of ice breaking. The bubble dynamics are solved by BEM based on the potential flow theory. Ice cracks initiation and propagation are simulated by the bond-based peridynamics which is validated by a three-point bending test. The fluid–structure interaction (FSI) is achieved by matching the normal velocity and hydrodynamic loads at the fluid–structure interface. To validate the proposed FSI model, an experiment is carried out in which an oscillating bubble is generated under an ice plate by underwater discharge system. The whole interaction process is captured by a Phantom V711 high-speed camera. Qualitative agreements are achieved between the numerical and experimental results. The underlying mechanism of cracks initiation, propagation, branching, and coalescence of the ice plate is found to highly depend on three parameters, i.e., bubble–ice distance, ice thickness and bubble size. The present study is expected to provide further assists in the understanding of ice breaking problems.     

Internal waves in a two‐layer system using fully nonlinear internal‐wave equations

In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.     

IMPROVEMENTS OF GEOMETRICALLY NONLINEAR ANALYSIS ALGORITHMS FOR SPATIAL FRAME STRUCTURES

以几何精确梁理论为基础,分别采用高阶拉格朗日插值和埃米特插值构造高精度空间梁单元。提出基于单元层次平衡迭代的自由度凝聚方法,以保证单元的通用性。实现了基于载荷控制或柱面弧长控制的结构几何非线性分析算法。算例研究结果表明,提出的改进方法不但提高了计算效率,而且还具有较高的数值稳定性;特别是基于三次埃米特插值构造的单元表现出较好的性态,适用于结构屈曲后分析。     

A brief survey on discontinuous Galerkin methods in computational fluid dynamics

间断Galerkin （DG）方法结合了有限元法（具有弱形式、有限维解和试验函数空间）和有限体积法（具有数值通量、非线性限制器）的优点,特别适合对流占优问题（如激波等线性和非线性波）的模拟研究,本文述评DG 方法,强调其在计算流体力学（CFD）中的应用,文中讨论了DG 方法的必要构成要素和性能特点,并介绍了该方法的一些最近研究进展,相关工作促进了DG 方法在CFD 领域的应用,     

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.      

二维定常不可压缩粘性流动N-S方程的数值流形方法

将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法.     

Soil stress and deformation determination under a landing airplane on an unsurfaced airfield

This paper presents a multidisciplinary approach to a problem of soil–wheel interaction during the landing of an airplane on a grass airfield, with terramechanical analysis of the forces acting between a wheel and the surface. The experiment on stress and deformation state in soil under a wheel on touchdown was performed in the field. The soil stress state (major stress S1, minor stresses S2 and S3, stress invariant in an octahedral system, MNS and OCTSS) was determined with the use of an SST (stress state transducer), which was installed at 15 cm depth. Soil deformation was determined with an inertial measuring system, integrated with the SST. These soil data were captured exactly at the moment touchdown. In the experiment, a four-passenger, STOL multirole airplane was used and pilots performed two landing patterns: normal landing and emergency landing (without propeller thrust).     

AN APPLICATION OF THE CBS SCHEME IN THE FLUID-MEMBRANE INTERACTION

提出了一种不可压缩流体与弹性薄膜耦合问题的特征线分裂有限元解法. 首先, 给出了流场和结构的控制方程. 然后, 对流场、结构以及流固耦合的具体求解过程进行了描述. 其中, 流场求解采用改进特征线分裂方法和双时间步方法相结合的隐式求解方式, 并利用艾特肯加速法对每个时间步的迭代收敛过程进行了加速处理;结构部分的空间离散和时间积分分别采用伽辽金有限元方法和广义方法, 并通过牛顿迭代法对所得非线性代数方程组进行了求解;流场网格的更新采用弹簧近似法;流场、结构两求解模块之间采用松耦合方式.最后, 采用该方法对具有弹性底面的方腔顶盖驱动流问题进行了求解, 验证了算法的准确性和稳定性.此外, 计算结果表明艾特肯加速法可以显著地提高双时间步方法迭代求解过程的收敛速度.     

基于ALE方法的飞机水面降落过程

为了研究飞机水面降落过程中的动态响应规律,采用arbitrary Lagrangian-Eulerian(ALE)方法开展了飞机水面降落的动力学分析。研究了飞机水面降落过程的速度变化规律,结果表明,降落速度和飞行速度在飞机入水的初始阶段变化较快,随后变化幅度趋于平缓。分析了不同降落速度、飞行速度和降落仰角下的机身结构响应,得到了飞机水面降落时结构响应随时间的变化规律。机身结构应力在入水的初始阶段达到最大值,随后迅速下降,最后保持稳定。飞机结构的最大变形也出现在入水的初始阶段,随后迅速回复到初始状态。对比了降落速度、飞行速度和降落仰角对飞机结构响应的影响程度,结果表明降落速度对结构响应的影响程度最大,降落仰角次之,飞行速度的影响最小。 更多还原     

STUDY OF PARAMETRIC VIBRATION OF GYROSCOPIC CONTINUA BASED ON NONLINEAR NORMAL MODES AND A NUMERICAL ITERATIVE APPROACH

以脉动流输流管为例,利用非线性模态技术和一种数值迭代法研究陀螺连续体的非线性参数振动响应问题. 通过谐波平衡法将系统非线性非自治控制方程转化为拟自治方程,并在状态空间上利用不变流形法构造系统的非线性模态. 以对应自治系统的解为初值,采用一种数值迭代法来求解拟自治控制方程的模态系数,结果证明了该迭代法的快速收敛性. 在频域分析中得到了幅频响应和相空间上的不变流形,而在时域复模态分析中则发现了参激陀螺系统的正交相位差和行波振动现象.     

Numerical simulation of interaction between wind and 2D freak waves

This paper presents a newly developed approach for the numerical modelling of wind effects on the generation and dynamics of freak waves. In this approach, the quasi arbitrary Lagrangian–Eulerian finite element method (QALE-FEM) developed by the authors of this paper is combined with a commercial software (StarCD). The former is based on the fully nonlinear potential model, in which the wind-excited pressure is modelled using a modified Jeffreys' model [9]. The latter has a volume of fluid (VOF) solver which can handle violent air–wave interaction problems. The combination can simulate the interaction between freak waves and winds with an improved computational efficiency. The numerical approach is validated by comparing its predictions with experimental data. Satisfactory agreements are achieved. Detailed numerical investigations of the interaction between winds and 2D freak waves are carried out, which not only explore different air flow states but also reveal the wind effects on the change of freak wave profiles. Both breaking and non-breaking freak waves are considered.     

An Analysis of Turbulent Motions In and Around a Differentially Forced Density Interface

The Rapid-Distortion-Theory-based analysis proposed by Fernando and Hunt [1] is extended to study the nature of turbulence in and around a density interface sandwiched between turbulent layers with dissimilar properties. It is shown that interfacial motions consist of low-frequency, resonantly excited, nonlinear internal waves and high-frequency, linear internal waves driven by background turbulence. Based on the assumptions that (i) all resonant waves and some nonresonant waves having frequencies close to the resonant frequencies grow rapidly, break, and cause interfacial mixing, (ii) the spectral amplitude of the vertical velocity in the wave-breaking regime is constant, and (iii) kinetic energy is equipartitioned between linear and nonlinear breaking wave regimes, the r.m.s. vertical velocity at the interface and the turbulent kinetic energy flux into the interface are calculated. The migration velocity of the interface is calculated using the additional assumption that the buoyancy flux into a given turbulent layer is a fixed fraction of the turbulent kinetic energy flux supplied to the interface by the same layer. The calculations are found to be in good agreement with the entrainment data obtained in previous laboratory experiments in the parameter regime where the interface is dominated by internal wave dynamics. Received 23 July 1997 and accepted 8 January 1999     

自由液面大晃动的流固耦合数值分析方法研究进展

本文较为全面地评述了国内外对具有自由液面大晃动的流固耦合问题的研究。在第2节,以两种典型的工程问题（石油化工储液罐抗震性和提高机理问题和液态金属快中子增殖堆主容器流固耦合问题）为背景全面评述了这类流固耦合问题的有关研究进展;文章的第3节较为深入讨论了这类流固耦合问题中所采用的分析方法（包括解析方法、半解析方法和数值方法以及问题描述的ALE格式等）和分析模型（包括位移－位移模型和多种的位移－势模型等）;第4节首先从问题求解方面,说明了具有自由液面大晃动的流固耦合问题的性质和特点,然后讨论了交替求解方法及其对求解此类问题的特别适应性;最后,本文给出了这方面今后应进一步研究的问题。     

Nonlinear Lamb waves in plate/shell structures

鉴于常规超声检测技术对分布式材料细微损伤和接触类结构损伤的检测效果不佳,近年来非线性超声技术逐渐引起广泛关注.超声波在板壳结构中通常以兰姆波的形式进行传播,然而由于兰姆波的频散及多模特性,使得非线性兰姆波的理论和实验研究进展缓慢.本文从经典非线性理论出发,总结了源于材料固有非线性诱发的非线性兰姆波的理论和实验两个方面的研究进展,并综述了兰姆波的二次谐波发生效应在材料损伤评价方面的若干应用;从接触声非线性理论出发,讨论了目前由于接触类结构损伤诱发的非线性兰姆波的研究现状.最后展望了非线性兰姆波的未来研究重点及发展趋势.     

Numerical study of flow-induced vibrations of cylinders under the action of nonlinear energy sinks (NESs)

An isolated two-dimensional circular cylinder with two linear degrees of freedom, parallel and perpendicular to the free-stream direction, and owning a nonlinear energy sink (NES) is investigated by fluid–structure interaction (FSI) simulations to assess vortex-induced vibrations (VIV) at moderate Reynolds numbers. Subsequently, the wake-induced vibration (WIV) of a pair of identical cylinders under the action of two NES in a tandem arrangement and in a proximity–wake interference regime is explored using the same approach. The NES parameters (mass, nonlinear stiffness and damping) are investigated to determine their effects on the dynamic response of a single degree of freedom (in transverse flow direction) coupled system by a reduced-order model based on an experimentally validated van der Pol oscillator. The CFD model coupled with FSI method is also validated against VIV experimental data for an isolated cylinder in a uniform flow. The study is aimed to investigate the effect of the passive suppression NES device on VIV and WIV. The amplitude response, trajectories of cylinder motion and temporal evolutions of vortex shedding are obtained by conducting a series of numerical simulations. It is found that placing a tuned NES in the cylinders can provide good suppression effect; however, the effectiveness is function of the reduced velocity.     

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Robust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd.