基于ALE有限元法的流固耦合强耦合数值模拟

针对不同流固耦合问题,提出一种基于任意拉格朗日-欧拉(ALE)有限元技术的分区强耦合算法.运用半隐式特征线分裂算法求解ALE描述下的不可压缩黏性流体Navier-Stokes方程.分别考虑一般平面运动刚体和几何非线性固体,采用复合隐式时间积分法推进结构运动方程,故可选用较大时间步长;进一步应用单元型光滑有限元法求解几何非线性固体大变形,获得更精确结构解且不影响计算效率.运用子块移动技术结合正交-半扭转弹簧近似法高效更新流体动网格;同时将一质量源项引入压力泊松方程满足几何守恒律,无需复杂构造网格速度差分格式.采用简单高效的固定点法配合Aitken动态松弛技术实现各场耦合,可灵活选择先进单场求解技术,具备较好程序模块性.运用本文算法分别模拟了H型桥梁截面颤振问题和均匀管道流内节气阀涡激振动问题.研究表明,数值结果与已有文献数据吻合,计算精度和求解效率均令人满意.     

基于ALE有限元法的流固耦合强耦合数值模拟

针对不同流固耦合问题,提出一种基于任意拉格朗日--欧拉(ALE)有限元技术的分区强耦合算法. 运用半隐式特征线分裂算法求解ALE描述下的不可压缩黏性流体Navier-Stokes方程. 分别考虑一般平面运动刚体和几何非线性固体,采用复合隐式时间积分法推进结构运动方程,故可选用较大时间步长;进一步应用单元型光滑有限元法求解几何非线性固体大变形,获得更精确结构解且不影响计算效率. 运用子块移动技术结合正 交--半扭转弹簧近似法高效更新流体动网格;同时将一质量源项引入压力泊松方程满足几何守恒律,无需复杂构造网格速度差分格式. 采用简单高效的固定点法配合Aitken动态松弛技术实现各场耦合,可灵活选择先进单场求解技术,具备较好程序模块性. 运用本文算法分别模拟了H型桥梁截面颤振问题和均匀管道流内节气阀涡激振动问题. 研究表明,数值结果与已有文献数据吻合,计算精度和求解效率均令人满意.      

高黏性流动有限元模拟的迭代稳定分步算法

分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于 某个临界值方能使算法稳定. 然而在高黏性流动模拟中，已有的显式和半隐式分步算法由于 其显式本质，必须采用小时间步长计算，不但降低了计算效率，同时也常与为使分步算法稳 分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于 某个临界值方能使算法稳定. 然而在高黏性流动模拟中，已有的显式和半隐式分步算法由于 其显式本质，必须采用小时间步长计算，不但降低了计算效率，同时也常与为使分步算法稳 定必须满足的最小时间步长要求冲突. 本文目的是构造一种含迭代格式的分步算法，它能在 保证精度的前提下大幅度地增大时间步长. 方腔流和平面Poisseuille流数值计算结果证实 了此特点，该方法被有效应用于充填流动过程的数值模拟.     

全机绕流Euler方程多重网格分区计算方法

全机三维复杂形状绕流数值求解只能采用分区求解的方法,本文采用可压缩Euler方程有限体积方法以及多重网格分区方法对流场进行分区计算。数值方法采用改进的van Leer迎风型矢通量分裂格式和MUSCL方法,基于有限体积方法和迎风型矢通量分裂方法,建立一套处理子区域内分界面的耦合条件。各个子区域之间采用显式耦合条件,区域内部采用隐式格式和局部时间步长等,以加快收敛速度。计算结果飞机表面压力分布等气动力特性与实验值进行了比较,二者基本吻合。计算结果表明采用分析“V”型多重网格方法,能提高计算效率,加快收敛速度达到接近一个量级。根据全机数值计算结果和可视化结果讨论了流场背风区域旋涡的形成过程。     

基于同步交替法求解流体-弹性板耦合作用

基于预测-多步校正方法提出了流固耦合同步交替求解方法.采用ALE描述流固耦合问题.基于SUPG有限元对流体动量方程进行空间离散,以消除对流项引起的数值振荡.时间域上的积分采用预测-多步校正(predictor-multicorrector)方法.对流体和结构同时进行预测,在多步校正的过程中对流体和固体域动力学方程进行交替求解,从而在时间上达到同步推进.基于上述同步交替法,编程计算了流体-弹性板耦合作用问题,取得了良好的数值计算结果.     

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.     

基于DES的高雷诺数空腔噪声数值模拟

发展出一套基于SA-DES和SST—DES模型,对三维超音速空腔流动进行数值模拟的方法和程序。采用混合网格有限体积方法求解非定常流场,时间离散采用基于LU—SGS隐式格式的双时间步长方法。采用可压缩物面函数来减少进行高雷诺数数值模拟时物面粘性网格的数量。对比了一方程SA-DES和两方程SST—DES计算得到的涡量和压强...     

基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

采用浸没边界格子Boltzmann(immersed boundary-lattice Boltzmann,IB-LB)模型执行动边界绕流数值模拟时,信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率.基于隐式扩散界面,一种改进的直接力格式IB-LB模型被提出.边界力表达式基于欧拉/拉格朗日变量同一性准...     

磁流体力学数值计算处理方法

介绍电磁内爆实验中求解磁流体力学方程组的处理方法。方程组采用分裂法以克服非线性耦合可能引起的数值不稳定性；采用隐式差分格式避免过小时间步长限制。隐式格式采用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法叠代求解，使用比较简单的叠代初值的给定方法。对一些特殊边界处理作了说明。     

高温激波管化学非平衡流动数值模拟研究

为了预测氢氧定容燃烧驱动的高温激波管性能,需要准确分析激波管非定常化学非平衡流动过程.本文在破膜前的驱动段定容燃烧以及破膜后的化学非平衡流动数值模拟中,引入双时间步长方法,发展高温激波管化学非平衡流动数值模拟方法,该方法在时间上具有二阶精度.计算结果与目前存在的激波管流动解析解以及零维化学反应系统的数值解进行了比较,吻合较好.对于典型高温激波管状态,采用有限体积方法离散准一维流动Euler控制方程,并通过将流动过程和化学反应动力学过程耦合求解,获得了激波管内部的化学非平衡流动特征.     

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method. The English text was polished byYunming Chen.     

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effiectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.     

A high-order discontinuous Galerkin method for simulating incompressible fluid-thermal-structural interaction problems

This paper presents a framework for the application of the discontinuous Galerkin(DG) finite element method to the multi-physics simulation of the solid thermal deformation interacting with incompressible flow problems in two-dimensions. Recent applications of the DG method are primarily for thermoelastic problems in a solid domain or fluid-structure interaction problems without heat transfer. Based on a recently published conjugate heat transfer solver, the incompressible Navier-Stokes equation, the fluid advection-diffusion equation, the Boussinesq term, the solid heat equation and the solid linear elastic equation are solved using an explicit DG formulation. A Dirichlet-Neumann partitioning strategy has been implemented to achieve the data exchange process via the numerical flux computed at interface quadrature points in the fluid-solid interface. Formal hp convergence studies employing the method of manufactured solutions demonstrate that the expected order of accuracy is achieved for each solver. The algorithm is then further validated against several existing benchmark cases including the in-plane loaded square, the Timoshenko Beam, the laminated beam subject to thermal-loads and the lid-driven cavity with a flexible bottom wall. The computational effort demonstrates that for all cases the highest order accurate algorithm has several magnitudes lower error than the second-order schemes for a given computational effort. It is a strong justification for the development of such high order discretisations. The solver can be employed to predict thermal deformation of a structure due to convective and conductive heat transfer at low Mach, such as chip deformation on a printed circuit board, wave-guide structure optimization, thermoelectric cooler simulation, and optics mounting method verification.     

Finite Element Modeling of Liquid Deuterium Flow and Heat Transfer in a Cold-neutron Source

A finite element simulation of flow and heat transfer in the moderator cell of a cold-neutron source (CNS), in which liquid deuterium subject to internal heat generation is flowing, is reported. The numerical scheme consists of a stabilized equal-order method. A time-accurate approach is adopted to resolve the large-scale eddies of the flow, with a Smagorinsky's model for the subgrid-scale effects. The thermal coupling follows a staggered strategy, with SUPG-type upwinding. A specific wall-law is developed that accounts for the correct partition of the heat deposited at the wall by radiation between the liquid deuterium and the helium gas flowing at the outer side of the wall. The average flow and thermal structure are presented. The turbulent fluctuations are both illustrated in physical space and decomposed into spectral components. The wavenumber spectrum suggests that adequate resolution of the large-scale eddies has been attained with just 200,000 nodes, while a DNS analysis would have required at least 1010 nodes. Usefulness of the approach in the design process of the CNS is highlighted.     

求解三维流固耦合问题的一种全隐全耦合区域分解并行算法

三维流固耦合问题的非结构网格数值算法在很多工程领域都有重要应用, 目前现有的数值方法主要基于分区算法, 即流体和固体区域分别进行求解, 因此存在收敛速度较慢以及附加质量导致的稳定性问题, 此外, 该类算法的并行可扩展性不高, 在大规模应用计算方面也受到一定限制．本文针对三维非定常流固耦合问题, 提出一种基于区域分解的全隐全耦合可扩展并行算法．首先基于任意拉格朗日?欧拉框架建立流固耦合控制方程, 然后时间方向采用二阶向后差分隐式格式、空间方向采用非结构稳定化有限元方法进行离散．对于大规模非线性离散系统, 构造一种结合非精确Newton法、Krylov子空间迭代法与区域分解Schwarz预条件子的Newton-Krylov-Schwarz (NKS) 并行求解算法, 实现流体、固体和动网格方程的一次性整体求解．采用弹性障碍物绕流的标准测试算例对数值方法的准确性进行了验证, 数值性能测试结果显示本文构造的全隐全耦合算法具有良好的稳定性, 在不同的物理参数下具有良好的鲁棒性, 在“天河二号”超级计算机上, 当并行规模从192增加到3072个处理器核时获得了91%的并行效率．性能测试结果表明本文构造的NKS算法有望应用于复杂区域流固耦合问题的大规模数值模拟研究中．      

A spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications

We present a spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for fluid–solid conjugate heat transfer applications. Using the discrete Boltzmann equation, we propose a numerical scheme for conjugate heat transfer applications on unstructured, non‐uniform grids. We employ a double‐distribution thermal lattice Boltzmann model to resolve flows with variable Prandtl (Pr) number. Based upon its finite element heritage, the spectral‐element discontinuous Galerkin discretization provides an effective means to model and investigate thermal transport in applications with complex geometries. Our solutions are represented by the tensor product basis of the one‐dimensional Legendre–Lagrange interpolation polynomials. A high‐order discretization is employed on body‐conforming hexahedral elements with Gauss–Lobatto–Legendre quadrature nodes. Thermal and hydrodynamic bounce‐back boundary conditions are imposed via the numerical flux formulation that arises because of the discontinuous Galerkin approach. As a result, our scheme does not require tedious extrapolation at the boundaries, which may cause loss of mass conservation. We compare solutions of the proposed scheme with an analytical solution for a solid–solid conjugate heat transfer problem in a 2D annulus and illustrate the capture of temperature continuities across interfaces for conductivity ratio γ > 1. We also investigate the effect of Reynolds (Re) and Grashof (Gr) number on the conjugate heat transfer between a heat‐generating solid and a surrounding fluid. Steady‐state results are presented for Re = 5?40 and Gr = 10⁵?10⁶. In each case, we discuss the effect of Re and Gr on the heat flux (i.e. Nusselt number Nu) at the fluid–solid interface. Our results are validated against previous studies that employ finite‐difference and continuous spectral‐element methods to solve the Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Stabilized finite element solution to handle complex heat and fluid flows in industrial furnaces using the immersed volume method

We consider the numerical simulation of conjugate heat transfer, incompressible turbulent flows for multicomponents systems using a stabilized finite element method. We present an immersed volume approach for thermal coupling between fluids and solids for heating high‐alloy steel inside industrial furnaces. It consists in considering a single 3D grid of the furnace and solving one set of equations with different thermal properties. A distance function enables to define precisely the position and the interface of any objects inside the volume and to provide homogeneous physical and thermodynamic properties for each subdomain. An anisotropic mesh adaptation algorithm based on the variations of the distance function is then applied to ensure an accurate capture of the discontinuities that characterize the highly heterogeneous domain. The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfers and turbulent flows in an industrial furnace with the presence of three conducting solid bodies. Copyright © 2010 John Wiley & Sons, Ltd.     

固体非傅立叶温度场的时域间断Galerkin有限元法

运用时域间断Galerkin有限元法[1],对高频非傅立叶热波动问题[2-3]进行分析。其主要特点是:取温度及温度的时间导数为基本未知量,对其分别进行3次Hermite插值和线性插值。在保证节点温度自动保持连续的基础上,温度的时间导数在离散时域存在间断。数值结果表明所提出的方法能够滤掉虚假的数值震荡,能够良好地模拟固体中的非傅立叶热波动行为。     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method based on the velocity–pressure–vorticity formulation was proposed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to the saddle point problem of the classic mixed method and can thus accommodate equal-order interpolations. The method has no parameter to tune. The associated algebraic system is symmetric and positive definite. In order to show the validity of the method for high-Reynolds-number problems, this paper provides numerical results for cavity flow at Reynolds number up to 10 000 and backward-facing step flow at Reynolds number up to 900.