成型充填过程的ALE有限元模拟

在ALE框架中提出了一个用于成型充填过程有限元数值模拟的模型。应用ALE参考构形及ALE参考粒子速度描写充填过程中的熔体质量运动。摒弃了Hele-Shaw近似假定,因而所提出的模型能用于非薄壁型腔中高分子材料充填过程的数值模拟。应用基于时域分步算法的Taylor-Galerkin方法,对控制成型充填过程的守恒方程建立了弱形式。对移动自由面附近的充填材料区构造了网格生成算法与网格重划分方案。给出了在几种不同形状的典型腔体中充填过程的数值模拟结果,表明了所提出的ALE有限元模型模拟充填过程的有效性。     

饱和颗粒土-维冰分凝模型及数值模拟

基于相平衡和力甲衡提出了一个关于饱和颗粒土的冰分凝模型，引入了冰分凝时未冻水迁移的驱动势，基于Clapeyron方程和吸附膜的观点简要叙述了相变区内未冻水含量与温度及孔隙水压的关系，数值模拟了饱和颗粒士的一维冻结过程，得到了冰分层分凝的计算结果，与已有实验所观测到的现象较为吻合，计算所得的冻胀量的变化趋势与已有实验所测结果是相符的．     

基于计算流体力学的“虚拟飞行”技术及初步应用

以动态混合网格技术为基础, 通过耦合求解刚体动力学方程、流体力学控制方程以及飞行控制律, 建立了适用于飞行器"虚拟飞行" 过程研究的一体化数值模拟技术. 通过典型的外挂物投放算例对流体力学控制方程/动力学方程的耦合算法进行了测试, 并对某导弹的姿态角控制过程、过载控制过程以及变马赫数条件下的控制过程进行了数值模拟, 得到了与实验非常一致的结果. 这些算例证明该一体化算法已经初步具备了针对复杂飞行器"数值虚拟飞行" 的应用能力.      

饱和土动力学有限元分析的改进稳定分步算法

基于Blot理论，控制饱和变形多孔介质中固相位移u和孔隙压力pw演变的场方程的空间半离散化导致u-pw型混合有限元方程。在固体颗粒和孔隙液体不可压缩以及零渗透性情况下，基本未知量u，pw的近似插值函数必须满足Babuska—Brezzi条件或者与之等价的Zienkiewicz和Taylor分片试验。采用相同低阶u-pw插值的有限元(如线性三角形单元和双线性四边形单元)不能满足B—B条件。分步算法作为一种稳定技术的引入可以绕开B—B条件，但现有分步算法在瞬态问题中仍存在虚假数值振荡和不稳定现象。本文在现有分步算法的基础上引入迭代过程，有效地缓解和克服了数值振荡现象，使低阶u-pw单元得以正常应用。应用双线性四节点u-pw单元的数值结果表明了所提出的包含迭代过程的改进分步算法的有效性。     

植物固沙区土壤水热运移耦合模型研究

根据Ｐｈｉｌｉｐ与Ｖｒｉｅｓ提出的土壤中水热交换的耦合理论，建立了植物固沙区土壤水热运移的耦合模型，考虑了液态水和汽态水运移对温度的变化，分析了植物根系吸水对土壤水热交换的影响，给出了植物蒸腾量、土壤蒸发量、根系汲水率及土壤表面热通量等有关变量的计算公式．利用本模式并采用具有二阶精度的Ｃｒａｎｋ－Ｎｉｃｏｌｓｏｎ格式对非线性扩散方程进行离散，对沙坡头植物固沙区土壤水热交换过程进行了数值模拟，模拟结果和实测值进行了比较，总体上符合较好，证明本模型具有实用价值，可为改造沙漠提供科学依据     

植物固沙区土壤水热运移耦合模型研究

根据Ｐｈｉｌｉｐ与Ｖｒｉｅｓ提出的土壤中水热交换的耦合理论，建立了植物固沙区土壤水热运移的耦合模型，考虑了液态水和汽态水运移对温度的变化，分析了植物根系吸水对土壤水热交换的影响，给出了植物蒸腾量、土壤蒸发量、根系汲水率及土壤表面热通量等有关变量的计算公式．利用本模式并采用具有二阶精度的Ｃｒａｎｋ－Ｎｉｃｏｌｓｏｎ格式对非线性扩散方程进行离散，对沙坡头植物固沙区土壤水热交换过程进行了数值模拟，模拟结果和实测值进行了比较，总体上符合较好，证明本模型具有实用价值，可为改造沙漠提供科学依据     

高速冲击过程数值分析的再生核质点法

利用新型的无网格方法-再生核质点方法对高速冲击过程进行数值模拟，给出了控制 方程，分析中引入Bordner-Partom本构模型来实现材料高速冲击条件下的大应变和高应变 率的特性，提出了新的接触面处理方法，介绍了速度配点法来实现接触面及其它本质边界的 速度条件. 数值模拟表明，再生核质点法能够准确模拟高速冲击过程，具有较高的计算精度.     

除尘管道内铝粉运移及沉积的数值研究

基于DPM(Discrete Phase Model)模型，研究了长直通风管道内粒径服从Rosin-Rammler 分布的铝粉的运移与沉积规律．基于颗粒与壁面的碰撞过程中的能量分析，建立了粉尘沉积-回弹模型，得出了粉尘沉积的判定准则及脱离壁面时的回弹速度．利用UDF 将沉积-回弹模型嵌入Fluent，完成了对管道内粉尘运移和沉积的数值模拟．粉尘沉积的数值结果与实验结果符合得较好，验证了所提模型的有效性．数值结果表明风速的增大使管道内粉尘浓度明显降低，管壁粉尘沉积率也降低；粒径的增大对粉尘浓度的大小影响不明显，主要影响粉尘浓度在管道内的分布情况，同时会增大粉尘在管壁的沉积率．     

高温条件下混凝土墙体的非线性分析研究

本文建立了一个弹塑性-损伤耦合本构模型用于数值模拟高温下混凝土的真实破坏过程。导出了一个利用Newton-Raphson迭代的一般的直接应力返回映射算法。同时求解应力向量和塑性、损伤的内状态变量。并推导了用于化学-热-湿-力学耦合分析的全局守恒方程Newton-Raphson迭代过程的一致性切线模量矩阵。建议了一个用于弹塑性-损伤耦合分析的两级求解过程。给出的数值例题结果显示了所提出的数法和公式的正确性,表明了所发展的弹塑性-损伤耦合本构模型在模拟高温下混凝土墙体中复杂破坏过程的能力。     

多组份流体质量扩散的格子Boltzmann方法

建立了多组份流体、多速度格子Ｂｏｌｔｚｍａｎｎ模型．利用Ｃｈａｐｍａｎ－Ｅｎｓｋｏｇ渐近展开法推导了流体质量扩散方程和运动方程，并且给出了相应的扩散系数和粘性系数表达式．通过正弦波的衰减过程测量了两流体间的扩散系数．测量值与理论预测值相吻合．作为本模型的一个应用实例，对圆形区域内的静止流体在具有均匀来流速度的另外一种流体中的对流扩散问题进行了数值模拟．     

Numerical modelling of shear-dependent mass transfer in large arteries

A numerical scheme for the simulation of blood flow and transport processes in large arteries is presented. Blood flow is described by the unsteady 3D incompressible Navier–Stokes equations for Newtonian fluids; solute transport is modelled by the advection–diffusion equation. The resistance of the arterial wall to transmural transport is described by a shear-dependent wall permeability model. The finite element formulation of the Navier–Stokes equations is based on an operator-splitting method and implicit time discretization. The streamline upwind/Petrov–Galerkin (SUPG) method is applied for stabilization of the advective terms in the transport equation and in the flow equations. A numerical simulation is carried out for pulsatile mass transport in a 3D arterial bend to demonstrate the influence of arterial flow patterns on wall permeability characteristics and transmural mass transfer. The main result is a substantial wall flux reduction at the inner side of the curved region. © 1997 John Wiley & Sons, Ltd.     

An Approach to Transport in Heterogeneous Porous Media Using the Truncated Temporal Moment Equations: Theory and Numerical Validation

In the last decade, the characterization of transport in porous media has benefited largely from numerical advances in applied mathematics and from the increasing power of computers. However, the resolution of a transport problem often remains cumbersome, mostly because of the time-dependence of the equations and the numerical stability constraints imposed by their discretization. To avoid these difficulties, another approach is proposed based on the calculation of the temporal moments of a curve of concentration versus time. The transformation into the Laplace domain of the transport equations makes it possible to develop partial derivative equations for the calculation of complete moments or truncated moments between two finite times, and for any point of a bounded domain. The temporal moment equations are stationary equations, independent of time, and with weaker constraints on their stability and diffusion errors compared to the classical advection–dispersion equation, even with simple discrete numerical schemes. Following the complete theoretical development of these equations, they are compared firstly with analytical solutions for simple cases of transport and secondly with a well-performing transport model for advective–dispersive transport in a heterogeneous medium with rate-limited mass transfer between the free water and an immobile phase. Temporal moment equations have a common parametrization with transport equations in terms of their parameters and their spatial distribution on a grid of discretization. Therefore, they can be used to replace the transport equations and thus accelerate the achievement of studies in which a large number of simulations must be carried out, such as the inverse problem conditioned with transport data or for forecasting pollution hazards.     

Robust Multi-D Transport Schemes with Reduced Grid Orientation Effects

In this paper we investigate truly multi-D upwind schemes for simulating adverse mobility ratio displacements in porous media. Due to an underlying physical instability at the simulation scale, numerical results are highly sensitive to discretization errors and hence the orientation of the underlying computational grid. We use modified equations analysis to predict preferred flow angles on structured grids for several popular methods and present a conservative, multi-D framework for designing positive upwind schemes for general velocity fields. After placing the common schemes in this framework, we go on to develop a novel scheme with “minimal” constant transverse (cross-wind) diffusion. Results for miscible gas injection into homogeneous and heterogeneous media demonstrate that truly multi-D schemes, and in particular our new scheme, greatly reduce grid orientation effects and numerical biasing as compared to dimensional upwinding.     

The two‐dimensional streamline upwind scheme for the convection–reaction equation

This paper is concerned with the development of the finite element method in simulating scalar transport, governed by the convection–reaction (CR) equation. A feature of the proposed finite element model is its ability to provide nodally exact solutions in the one‐dimensional case. Details of the derivation of the upwind scheme on quadratic elements are given. Extension of the one‐dimensional nodally exact scheme to the two‐dimensional model equation involves the use of a streamline upwind operator. As the modified equations show in the four types of element, physically relevant discretization error terms are added to the flow direction and help stabilize the discrete system. The proposed method is referred to as the streamline upwind Petrov–Galerkin finite element model. This model has been validated against test problems that are amenable to analytical solutions. In addition to a fundamental study of the scheme, numerical results that demonstrate the validity of the method are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

A dynamic coupling numerical model for pollutant transport under wave condition

In order to study the diffusion, migration, and distribution of pollutants among overlying water-body and porous seabed under wave conditions, a dynamic coupling numerical model is proposed. In this model, the coupling between wave field of overlying water-body and seepage of porous bed, the capture and release of pollutants in porous media, and the transport process between the two different regions are taken into account. We use the unified equations for pressure correction and pollutant concentration to solve the numerical model, which avoids repeated iteration on the interface boundary. The model is verified by several case studies. Afterwards, the processes involving release of pollutant from porous seabed and transportation to overlying water-body under different wave conditions are investigated. The results show that the water depth, wave height,and wave period have great influences on the release, capture, and transport processes for phosphorus pollutant.     

Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D

A two‐dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first order upwind technique is applied to solve the flux terms in both the flow and solute equations and the bed slope source terms and a centred discretization is applied to the diffusion and friction terms. The convenience of considering the fully coupled system of equations is indicated and the methodology is well explained. Three options are suggested and compared in order to deal with the diffusion terms. Some comparisons are carried out in order to show the performance in terms of accuracy and computational effort of the different options. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiphase flow in heterogeneous porous media: A classical finite element method versus an implicit pressure–explicit saturation‐based mixed finite element–finite volume approach

Various discretization methods exist for the numerical simulation of multiphase flow in porous media. In this paper, two methods are introduced and analyzed—a full‐upwind Galerkin method which belongs to the classical finite element methods, and a mixed‐hybrid finite element method based on an implicit pressure–explicit saturation (IMPES) approach. Both methods are derived from the governing equations of two‐phase flow. Their discretization concepts are compared in detail. Their efficiency is discussed using several examples. Copyright © 1999 John Wiley & Sons, Ltd.     

Solution of the 2‐D shallow water equations with source terms in surface elevation splitting form

A vertex‐centred finite‐volume/finite‐element method (FV/FEM) is developed for solving 2‐D shallow water equations (SWEs) with source terms written in a surface elevation splitting form, which balances the flux gradients and source terms. The method is implemented on unstructured grids and the numerical scheme is based on a second‐order MUSCL‐like upwind Godunov FV discretization for inviscid fluxes and a classical Galerkin FE discretization for the viscous gradients and source terms. The main advantages are: (1) the discretization of SWE written in surface elevation splitting form satisfies the exact conservation property (??‐Property) naturally; (2) the simple centred‐type discretization can be used for the source terms; (3) the method is suitable for both steady and unsteady shallow water problems; and (4) complex topography can be handled based on unstructured grids. The accuracy of the method was verified for both steady and unsteady problems, including discontinuous cases. The results indicate that the new method is accurate, simple, and robust. Copyright © 2007 John Wiley & Sons, Ltd.     

极坐标系下Fourier-Legendre谱元方法与有限差分法数值扩散的比较

提出一种Fourier-Legendre谱元方法用于求解极坐标系下的Navier-Stokes方程,其中极点所在单元的径向采用Gauss-Radau积分点,避免了r=0处的1/r坐标奇异性。时间离散采用时间分裂法,引入数值同位素模型跟踪同位素的输运过程验证数值模拟的精度,分别利用谱元法和有限差分法的迎风差分格式求解匀速和加速坩埚旋转流动中的同位素方程。计算结果表明,有限差分法中的一阶迎风差分格式存在严重的数值假扩散,二阶迎风差分格式的数值结果较精确,增加节点可以有效地缓解数值扩散。然而,谱元法具有以较少节点得到高精度解的优势。     

Analysis of a second‐order upwind method for the simulation of solute transport in 2D shallow water flow

A two‐dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first‐order upwind technique, a second order in space and time and an extended first‐order method are applied to solve the non‐diffusive terms in both the flow and solute equations and a centred implicit discretization is applied to the diffusion terms. The stability constraints are studied and the form to avoid oscillatory results in the solute concentration in the presence of complex flow situations is detailed. Some comparisons are carried out in order to show the performance in terms of accuracy of the different options. Copyright © 2007 John Wiley & Sons, Ltd.