Topological shape optimization of power flow problems at high frequencies using level set approach

Using a level set method we develop a topological shape optimization method applied to power flow problems in steady state. Necessary design gradients are computed using an efficient adjoint sensitivity analysis method. The boundaries are implicitly represented by the level set function obtainable from the “Hamilton–Jacobi type” equation with the “Up-wind scheme.” The implicit function is embedded into a fixed initial domain to obtain the finite element response and sensitivity. The developed method defines a Lagrangian function for the constrained optimization. It minimizes a generalized compliance, satisfying the constraint of allowable volume through the variations of implicit boundary. During the optimization, the boundary velocity to integrate the Hamilton–Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the established topology optimization method, the developed one has no numerical instability such as checkerboard problems and easy representation of topological shape variations.     

Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow

This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.     

高斯牛顿技术求解偶应力反问题

建立了便于敏度分析的偶应力反问题数值求解模型,给出了直接法和伴随法两种敏度计算格式.在反演计算中采用了高斯牛顿技术对未知本构参数进行识别,探讨了测点数目、初值选取和数据噪音对反演结果的影响,数值算例给出了令人满意的结果.     

A study of reduced‐order 4DVAR with a finite element shallow water model

Four‐dimensional variational data assimilation (4DVAR) is frequently used to improve model forecasting skills. This method improves a model consistency with available data by minimizing a cost function measuring the model–data misfit with respect to some model inputs and parameters. Associated with this type of method, however, are difficulties related to the coding of the adjoint model, which is needed to compute the gradient of the 4DVAR cost function. Proper orthogonal decomposition (POD) is a model reduction method that can be used to approximate the gradient calculation in 4DVAR. In this work, two ways of using POD in 4DVAR are presented, namely model‐reduced 4DVAR and reduced adjoint 4DVAR (RA‐4DVAR). Both techniques employ POD to obtain a reduced‐order approximation of the forward linear tangent operator. The difference between the two methods lies in the treatment of the forward model. Model‐reduced 4DVAR performs minimization entirely in the POD‐reduced space, thereby achieving very low computational costs, but sacrificing accuracy of the end result. On the other hand, the RA‐4DVAR uses POD to approximate only the adjoint model. The main contribution of this study is a comparative performance analysis of these 4DVAR methodologies on a nonlinear finite element shallow water model. The sensitivity of the methods to perturbations in observations and the number of observation points is examined. The results from twin experiments suggest that the RA‐4DVAR method is easy to implement and computationally efficient and provides a robust approach for achieving reasonable results in the context of variational data assimilation. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct sensitivity analysis of multibody systems with holonomic and nonholonomic constraints via an index-3 augmented Lagrangian formulation with projections

Optimizing the dynamic response of mechanical systems is often a necessary step during the early stages of product development cycle. This is a complex problem that requires to carry out the sensitivity analysis of the system dynamics equations if gradient-based optimization tools are used. These dynamics equations are often expressed as a highly nonlinear system of ordinary differential equations or differential-algebraic equations, if a dependent set of generalized coordinates with its corresponding kinematic constraints is used to describe the motion. Two main techniques are currently available to perform the sensitivity analysis of a multibody system, namely the direct differentiation and the adjoint variable methods. In this paper, we derive the equations that correspond to the direct sensitivity analysis of the index-3 augmented Lagrangian formulation with velocity and acceleration projections. Mechanical systems with both holonomic and nonholonomic constraints are considered. The evaluation of the system sensitivities requires the solution of a tangent linear model that corresponds to the Newton–Raphson iterative solution of the dynamics at configuration level, plus two additional nonlinear systems of equations for the velocity and acceleration projections. The method was validated in the sensitivity analysis of a set of examples, including a five-bar linkage with spring elements, which had been used in the literature as benchmark problem for similar multibody dynamics formulations, a point-mass system subjected to nonholonomic constraints, and a full-scale vehicle model.     

Continuum-Based Shape Sensitivity Analysis for 2D Coupled Atomistic/Continuum Simulations Using Bridging Scale Decomposition

In this paper, we propose the first attempt to perform shape sensitivity analysis for two-dimensional coupled atomistic and continuum problems using bridging scale decomposition. Based on a continuum variational formulation of the bridging scale, the sensitivity expressions are derived in a continuum setting using both direct differentiation method and adjoint variable method. To overcome the issue of discontinuity in shape design due to the discrete nature of the molecular dynamics (MD) simulation, we define design velocity fields in a way that the shape of the MD region does not change. Another major challenge is that the discrete finite element (FE) mass matrix in bridging scale is not continuous with respect to shape design variables. To address this issue, we assume an evenly distributed mass density when evaluating the material derivative of the FE mass matrix. In order to support accuracy verification of sensitivity results using overall finite difference method, we use regular-shaped finite elements and only allow shape change in one direction in our example problems, so that design perturbations can be made to the discrete FE mass matrix. However, the sensitivity formulation is sufficiently general to support irregular-shaped finite elements and arbitrary design velocity fields. The sensitivity analysis results, verified using overall finite difference method, reveal the impact of macroscopic shape design changes on microscopic atomistic responses.     

饱和-非饱和土壤中污染物运移过程的数值模拟

本文提出了一个模拟饱和 非饱和土壤中溶和污染物运移过程的数值模型．模拟的控制污染物运移的物理 化学现象包括：对流，机械逸散，分子弥散，吸附，蜕变，不动水效应．发展了一个修正的特征线Ｇａｌｅｒｋｉｎ方法以离散污染物运移过程的控制方程并导出了一个用于有限元方程求解的显式算法．数值例题结果表明所提出模型和算法的功能     

热结构稳态响应的耦合灵敏度分析方法

研究结构稳态热变形和热应力的灵敏度分析方法，给出了直接法和伴随法两种算法。考虑了温度场的耦合作用，在直接法中需要计算温度场对设计变量的导数，在伴随法中需要计算热载荷对温度场的导数。对尺寸和形状两类设计变量的灵敏度分析算例，验证了本文方法的精度。伴随法在应用程序中的实现，为大型结构优化提供了高效率的灵敏度计算方法。     

Discretization of the vorticity field of a planar jet

In data assimilation, information from sensors is used to correct the state variables of a numerical model. This has been used to great advantage by the weather prediction community in the context of direct numerical simulation (DNS) models, but has seen comparatively little use in point-vortex models. This is due in large part to data-processing issues. In order to keep up with the speeds necessary for effective data assimilation, one must extract and discretize the vortex structures from velocity field data in a computationally efficient fashion—i.e., using as few discrete vortices as possible to model the measured flow. This paper describes a new strategy for accomplishing this and evaluates the results using data from a laboratory-scale vortex-dominated planar jet. Large-scale vortex structures are found using a family of variants on traditional vortex extraction methods. By augmenting these methods with simple computational topology techniques, one obtains a new method that finds the boundaries of the coherent structures in a manner that naturally follows the geometry of the flow. This strategy was evaluated in the context of two standard vortex extraction methods, vorticity thresholding and Okubo–Weiss, and tested upon velocity field data from the experimental fluid flow. The large-scale structures found in this manner were then modeled with collections of discrete vortices, and the effects of the grain size of the discretization and the parameters of the discrete vortex model were studied. The results were evaluated by comparing the instantaneous velocity field induced by the discrete vortices to that measured in the jet. These comparisons showed that the two extraction techniques were comparable in terms of sensitivity and error, suggesting that the computationally simpler vorticity thresholding method is more appropriate for applications where speed is an issue, like data assimilation. Comparisons of different discretization strategies showed that modeling each large-scale vortex structure with a single discrete vortex provided the best compromise between mean-squared error and computational effort. These results are of potential interest in any situation where one must balance accuracy and expense while extracting vortices from a snapshot of a flow field; data assimilation is only one example.     

Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Criteria of optimality for sensors' location are addressed using an interpolation error transformed by especial adjoint problems. The considered criteria correspond to the analysis error in certain Hessian‐based metrics and to the error of some forecast aspect. Both criteria are obtained using adjoint problems that provide computation without the direct use of the Hessian. For a linear inverse heat conduction problem, these criteria are compared and demonstrated promising results when compared with a criterion based on the norm of the interpolation error of observation data. Approaches to sensor set modification using either redistribution of sensors' or refinement of the sensors grid (insertion of additional sensors) are also compared. Copyright © 2009 John Wiley & Sons, Ltd.     

强迫谐振动下连续体结构拓扑优化

应用结构拓扑优化ICM(独立连续映射)方法,对强迫谐振动下结构拓扑优化问题建立了以重量极小为目标,位移幅值为约束的优化模型.位移幅值采用一阶泰勒展式近似,由于拓扑优化中设计变量数目通常很多,对强迫谐振动位移幅值的敏度分析推导了伴随法公式,使得一次敏度分析可以计算出对所有设计变量的偏导数,克服了采用直接法敏度分析中一次只能计算出对一个设计变量的偏导数的不足.算例表明用伴随法分析敏度在结构拓扑优化中可以大幅提高计算效率,ICM方法采用独立于截面及形状参数的拓扑优化设计变量更清晰地反映了拓扑优化的本质.     

Sensitivity Analysis and Optimal Design of Nonlinear Beams and Plates

A uniform formulation of sensitivity analysis for beams and plates is presented in terms of generalized stresses and strains. Both physical and geometric nonlinearities can be treated within this formulation. Next, optimal design problems for stress and deflection constraints are formulated and the relevant optimality conditions are derived using the concept of a linear adjoint structure. Finally, several numerical solutions of optimal design problems of beams are presented.     

Effect of random perturbations on adaptive observation techniques

An observation sensitivity (OS) method to identify targeted observations is implemented in the context of four‐dimensional variational (4D‐Var) data assimilation. This methodology is compared with the well‐established adjoint sensitivity (AS) method using a nonlinear Burgers equation as a test model. Automatic differentiation software is used to implement the first‐order adjoint model (ADM) to calculate the gradient of the cost function required in the 4D‐Var minimization algorithm and in the AS computations and the second‐order ADM to obtain information on the Hessian matrix of the 4D‐Var cost that is necessary in the OS computations. Numerical results indicate that the observation‐targeting is particularly successful in reducing the forecast error for moderate Reynolds numbers. The potential benefits of the OS targeting approach over the AS are investigated. The effect of random perturbations on the performance of these adaptive observation techniques is also analyzed. Copyright © 2011 John Wiley & Sons, Ltd.     

广义变分原理的结构形状优化伴随法灵敏度分析

提出了一种利用伴随变量进行结构形状优化灵敏度分析的新方法. 基于广义变分原理， 考虑了形状优化中位移边界条件的变化对结构响应的影响. 新方法弥补了Arora 等人所提出的形状优化灵敏度分析变分原理中的缺陷，为采用伴随法进行灵敏度分析提供了 新的框架.     

Optimal estimation of eddy viscosity for a quasi-three-dimensional numerical tidal and storm surge model

It is shown that the eddy viscosity profile in a quasi-three-dimensional numerical tidal and storm surge model can be estimated by assimilation of velocity data from one or more current meters located on the same vertical line. The computational model used is a simplified version of the so-called vertical/horizontal splitting algorithm proposed by Lardner and Cekirge. We have estimated eddy viscosity both as a constant and as a variable parameter. The numerical scheme consists of a two-level leapfrog method to solve the depth-averaged equations and a generalized Crank-Nicolson scheme to compute the vertical profile of the velocity field. The cost functional in the adjoint scheme consists of two terms. The first term is a certain norm of the difference between computed and observed velocity data and the second term measures the total variation in the eddy viscosity function. The latter term is not needed when the data are exact for the model but is necessary to smooth out the instabilities associated with ‘noisy’ data. It is shown that a satisfactory minimization can be accomplished using either the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm or Nash's truncated Newton algorithm. Very effective estimation of eddy viscosity profiles is shown to be achieved even when the amount of data is quite small.     

Advective transport in a multilayered system of aquifers

A three-dimensional model of transport in porous media, consisting of several aquifers and aquitards, is presented. In the solution procedure a two-dimensional flow model has been adapted to incorporate three-dimensional velocity components. This procedure enables to observe the way particles of a pollutant are being transported through the system of aquifers and aquitards, while maintaining the Dupuit assumption of zero vertical gradients of the hydraulic head in the aquifers. The governing equations are solved using a finite element technique. The transport of pollutants is restricted to advective transport and linear adsorption.     

大涡模拟建筑物对近源大气污染物扩散的影响

采用大涡模拟(LES)方法对一个由上风低源排放的烟流在孤立建筑物周围扩散的现象进行了数值模拟。模拟中,离散网格的尺度控制在100倍Kolmogorov湍流尺度的量级以内,亚格子应力由Smagorinsky模型加以模拟,并采用了随机数方法生成符合指定湍流特征的入流边界条件。数值模拟结果表明:建筑物尾流区平均浓度场的分布和大小不仅取决于局地流场的影响,在很大程度上也受到因建筑物阻挡出现的烟流抬升和马蹄涡对烟流的捕获的影响。通过对比风洞试验数据显示:大涡模拟方法能较好地再现气流绕建筑物的流动形态和建筑物周围的浓度分布,因而具有广泛的应用前景。     

Density-driven Transport of Volatile Organic Compounds and its Impact on Contaminated Groundwater Plume Evolution

Density-driven advection of gas phase due to vaporization of chlorinated volatile organic compounds (VOCs) has a significant effect on fate and transport of contaminants. In this study, we investigated the effects of density-driven advection, infiltration, and permeability on contaminant plume evolution and natural attenuation of VOCs in the subsurface system. To analyze these effects, multiphase flow and contaminant transport processes were simulated using a three-dimensional Galerkin-finite-element-based model. Trichloroethylene (TCE) is selected as a target contaminant. Density-driven advection of gas phase elevated the potential of groundwater pollution in the saturated zone by accelerating downward migration of vaporized contaminant in the unsaturated zone. The advection contributed to increased removal rates of non-aqueous phase liquid (NAPL) TCE source and reduced dissolved TCE plume development in the downstream area. Infiltration reduced the velocity of the density-driven advection and its influence zone, but raised TCE transfer from the unsaturated to the saturated zone. The variation in soil permeability showed greater impact on contaminant migration within water phase in the saturated zone than within gas phase in the unsaturated zone. Temporal variations of TCE mass within two-dimensional (2D) and three-dimensional (3D) domains under several modeling conditions were compared. These results are important in evaluation of natural attenuation processes, and should be considered to effectively design monitored natural attenuation as a remedial option.     

A FE‐based algorithm for the inverse natural convection problem

Several numerical algorithms for solving inverse natural convection problems are revisited and studied. Our aim is to identify the unknown strength of a time‐varying heat source via a set of coupled nonlinear partial differential equations obtained by the so‐called finite element consistent splitting scheme (CSS) in order to get a good approximation of the unknown heat source from both the measured data and model results, by minimizing a functional that measures discrepancies between model and measured data. Viewed as an optimization problem, the solutions are obtained by means of the conjugate gradient method. A second‐order CSS in time involving the direct problem, the adjoint problem, the sensitivity problem and a system of sensitivity functions is used in order to enhance the numerical accuracy obtained for the unknown heat source function. A spatial discretization of all field equations is implemented using equal‐order and mixed finite element methods. Numerical experiments validate the proposed optimization algorithms that are in good agreement with the existing results. Copyright © 2010 John Wiley & Sons, Ltd.     

再悬浮底泥中非吸附性污染物释放的数值模拟

环境水动力学中, 湖库底泥中污染物释放是人们研究的主要问题之一. 在水动力学条件作用下, 污染底泥再悬浮使大量污染物被重新释放出来, 造成水体的二次污染. 本文基于水槽实验研究提供的大量实测数据, 建立上覆水体-底泥-污染物的耦合力学模型. 在上覆水体不同流速条件下, 数值模拟底泥起动再悬浮过程以及污染物释放过程. 分析流场特性和污染物浓度之间的关系, 得到速度、颗粒体积分数、污染物浓度、湍动能以及时间等参数之间的定量关系. 研究表明, 底泥再悬浮污染物释放过程, 是由上覆水体-底泥-污染物构成的耦合过程. 迅速进入上覆水体的底泥颗粒, 影响了上覆水体流动特性, 进而影响到污染物的释放. 对于非吸附性污染物, 底泥起动后复杂的流场特性是底泥再悬浮污染物释放的主要影响因素. 当流场特性(如雷诺数)改变时, 对流和湍流扩散作用在污染物输运过程贡献不同. 建立上覆水体-底泥-污染物的耦合模型, 研究水动力学条件与底泥污染物释放规律的定量化关系, 可为构建湖库区域水污染模型提供支撑.