改进Guyan～递推减缩技术

本文基于广义逆技术和逐级逼近思想,既建立了精度显著提高的改进Guyan减缩法,又提出了“物理型”近似减缩技术方面精度最好的准动态k级速推减缩公式,然而这些方法的执行时间却与其它“同一级”方法大抵相同．因此说,本方为工程界提供了至今综合效果最好的一类准动态模型减缩技术。     

Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

Order reduction strategies aim to alleviate the computational burden of the four‐dimensional variational data assimilation by performing the optimization in a low‐order control space. The proper orthogonal decomposition (POD) approach to model reduction is used to identify a reduced‐order control space for a two‐dimensional global shallow water model. A reduced second‐order adjoint (SOA) model is developed and used to facilitate the implementation of a Hessian‐free truncated‐Newton (HFTN) minimization algorithm in the POD‐based space. The efficiency of the SOA/HFTN implementation is analysed by comparison with the quasi‐Newton BFGS and a nonlinear conjugate gradient algorithm. Several data assimilation experiments that differ only in the optimization algorithm employed are performed in the reduced control space. Numerical results indicate that first‐order derivative methods are effective during the initial stages of the assimilation; in the later stages, the use of second‐order derivative information is of benefit and HFTN provided significant CPU time savings when compared to the BFGS and CG algorithms. A comparison with data assimilation experiments in the full model space shows that with an appropriate selection of the basis functions the optimization in the POD space is able to provide accurate results at a reduced computational cost. The HFTN algorithm benefited most from the order reduction since computational savings were achieved both in the outer and inner iterations of the method. Further experiments are required to validate the approach for comprehensive global circulation models. Copyright © 2006 John Wiley & Sons, Ltd.     

An extended mixture model for the simultaneous treatment of small‐scale and large‐scale interfaces

The aim of this work is to present a new model based on the volume of fluid method and the algebraic slip mixture model in order to solve multiphase gas–fluid flows with different interface scales and the transition among them. The interface scale is characterized by a measure of the grid, which acts as a geometrical filter and is related with the accuracy in the solution; in this sense, the presented coupled model allows to reduce the grid requirements for a given accuracy. With this objective in mind, a generalization of the algebraic slip mixture model is proposed to solve problems involving small‐scale and large‐scale interfaces in an unified framework taking special care in preserving the conservativeness of the fluxes. This model is implemented using the OpenFOAM^® libraries to generate a tool capable of solving large problems on high‐performance computing facilities. Several examples are solved as a validation for the presented model, including new quantitative measurements to assess the advantages of the method. Copyright © 2014 John Wiley & Sons, Ltd.     

Running large‐scale CFD applications on Intel‐KNL–based clusters

Intel's latest Xeon Phi processor, Knights Landing (KNL), has the potential to provide over 2.6 TFLOPS. However, to obtain maximum performance on the KNL, significant refactoring and optimization of application codes are still required to exploit key architectural innovations that KNL features—wide vector units, many‐core node design, and deep memory hierarchy. The experience and insights gained in porting and running FEFLO (a typical edge‐based finite element code for the solution of compressible and incompressible flows) on the KNL platform are described in this paper. In particular, optimizations used to extract on‐node parallelism via vectorization and multithreading and improve internode communication are considered. These optimizations resulted in a 2.3× performance gain on a 16 node runs of FEFLO, with the potential for larger performance gains as the code is scaled beyond 16 nodes. The impact of the different configurations of KNL's on‐package MCDRAM (Multi‐Channel DRAM) memory on FEFLO's performance is also explored. Finally, the performance of the optimized versions of FEFLO for KNL and Haswell (Intel Xeon) is compared.     

Efficient identification of uncertain parameters in a large‐scale tidal model of the European continental shelf by proper orthogonal decomposition

The adjoint method can be used to identify uncertain parameters in large‐scale shallow water flow models. This requires the implementation of the adjoint model, which is a large programming effort. The work presented here is inverse modeling based on model reduction using proper orthogonal decomposition (POD). An ensemble of forward model simulations is used to determine the approximation of the covariance matrix of the model variability and the dominant eigenvectors of this matrix are used to define a model subspace. An approximate linear reduced model is obtained by projecting the original model onto this reduced subspace. Compared with the classical variational method, the adjoint of the tangent linear model is replaced by the adjoint of a linear reduced forward model. The minimization process is carried out in reduced subspace and hence reduces the computational costs. In this study, the POD‐based calibration approach has been implemented for the estimation of the depth values and the bottom friction coefficient in a large‐scale shallow sea model of the entire European continental shelf with approximately 10⁶ operational grid points. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. The results demonstrate that the POD calibration method with little computational effort and without the implementation of the adjoint code can be used to solve large‐scale inverse shallow water flow problems. Copyright © 2011 John Wiley & Sons, Ltd.     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Multi‐scale simulation with a hybrid Boussinesq‐RANS hydrodynamic model

A hybrid wave model is developed for simulation of water wave propagation from deep water to shoreline. The constituent wave models are the irrotational, 1‐D horizontal Boussinesq and 2‐D vertical Reynolds‐averaged Navier–Stokes (RANS). The models are two‐way coupled, and the interface is placed at a location where turbulence is relatively small. Boundary conditions on the interfacing side of each model are provided by its counterpart model through data exchange. Prior to the exchange, a data transformation step is carried out due to the differences in physical variables and approximations employed in both models. The hybrid model is tested for both accuracy and speedup performance. Tests consisting of idealized solitary and standing wave motions and wave overtopping of nearshore structures show that: (1) the simulation results of the current hybrid model compare well with the idealized data, experimental data, and pure RANS model results and (2) the hybrid model saves computational time by a factor proportional to the reduction in the size of the RANS model domain. Finally, a large‐scale tsunami simulation is provided for a numerical setup that is practically unapproachable using RANS model alone; not only does the hybrid model offer more rapid simulation of relatively small‐scale problems, it provides an opportunity to examine very large total domains with the fine resolution typical of RANS simulations. Copyright © 2009 John Wiley & Sons, Ltd.     

基于Kriging代理模型的迭代更新高效反演方法

为提高混凝土坝等大体积结构参数反演效率和精度,减少由于应用有限元进行大量正分析而产生的计算机时,建立了一种结合Kriging代理模型和粒子群优化(PSO)算法的迭代更新反演方法。通过拉丁超立方抽样(LHS)方法确定初始样本点的空间分布,并使用有限元正分析获取对应的响应值,构建粗糙的初始代理模型,结合具有全局寻优能力的PSO算法,反演大体积结构的分区弹性模量,随之再代入有限元模型中,计算获取新的位移响应,并将其作为新样本加入到样本集中,通过迭代更新获得局部更高精度的代理模型。工程实际算例表明,该方法对混凝土坝等大体积结构参数反演精度较高和适用性好,且能大幅减少传统有限元模型反演方法所需消耗的正分析机时,提高反演效率。     

Statistical detection of structural damage based on model reduction

This paper proposes a statistical method for damage detection based on the finite element （FE） model reduction technique that utilizes measured modal data with a limited number of sensors. A deterministic damage detection process is formulated based on the model reduction technique. The probabilistie process is integrated into the deterministic damage detection process using a perturbation technique, resulting in a statistical structural damage detection method. This is achieved by deriving the first- and second-order partial derivatives of uncertain parameters, such as elasticity of the damaged member, with respect to the measurement noise, which allows expectation and covariance matrix of the uncertain parameters to be calculated. Besides the theoretical development, this paper reports numerical verification of the proposed method using a portal frame example and Monte Carlo simulation.     

Comparative study of implicit and subgrid‐scale model large‐eddy simulation techniques for low‐Reynolds number airfoil applications

A computational study of a high‐fidelity, implicit large‐eddy simulation (ILES) technique with and without the use of the dynamic Smagorinsky subgrid‐scale (SGS) model is conducted to examine the contributions of the SGS model on solutions of transitional flow over the SD7003 airfoil section. ILES without an SGS model has been shown in the past to produce comparable and sometimes favorable results to traditional SGS‐based large‐eddy simulation (LES) when applied to canonical turbulent flows. This paper evaluates the necessity of the SGS model for low‐Reynolds number airfoil applications to affirm the use of ILES without SGS‐modeling for a broader class of problems such as those pertaining to micro air vehicles and low‐pressure turbines. It is determined that the addition of the dynamic Smagorinsky model does not significantly affect the time‐mean flow or statistical quantities measured around the airfoil section for the spatial resolutions and Reynolds numbers examined in this study. Additionally, the robustness and reduced computational cost of ILES without the SGS model demonstrates the attractiveness of ILES as an alternative to traditional LES. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Very large‐scale computation of very small‐scale motions in a fully developed pipe flow

Local isotropy theory is examined using direct numerical simulation in a fully developed pipe flow at two Reynolds numbers Re_τ=1285.6 and 684.8. The approach to local isotropy is assessed with reference to the two Kolmogorov classical equations for longitudinal and transverse velocity structure functions. The results for the second‐order longitudinal structure functions in both the dissipative and inertial ranges indicate an improved agreement with the local isotropy hypothesis as the centreline is approached. However, the transverse structure functions satisfy isotropy neither in the dissipative range or in the inertial range. The distribution of the longitudinal and transverse structure functions also shows a substantial Reynolds number dependance in the logarithmic region of the flow and beyond. The results for the third‐order longitudinal structure function demonstrate an increased Reynolds number influence, and a deteriorating tendency to local isotropy for large separations. Contour images of axial velocity differences in the dissipative and inertial ranges have exhibited interesting patterns in relation to those of the instantaneous axial velocity. Finally, the results obtained in this investigation are in very good agreement with other published experimental and numerical data on channel and duct flows. Copyright © 2010 John Wiley & Sons, Ltd.     

A general optimal formulation for the dynamic Smagorinsky subgrid‐scale stress model

In this paper, a general optimal formulation for the dynamic Smagorinsky subgrid‐scale (SGS) stress model is reported. The Smagorinsky constitutive relation has been revisited from the perspective of functional variation and optimization. The local error density of the dynamic Smagorinsky SGS model has been minimized directly to determine the model coefficient C_S. A sufficient and necessary condition for optimizing the SGS model is obtained and an orthogonal condition (OC), which governs the instantaneous spatial distribution of the optimal dynamic model coefficient, is formulated. The OC is a useful general optimization condition, which unifies several classical dynamic SGS modelling formulations reported in the literature. In addition, the OC also results in a new dynamic model in the form of a Picard's integral equation. The approximation tensorial space for the projected Leonard stress is identified and the physical meaning for several basic grid and test‐grid level tensors is systematically discussed. Numerical simulations of turbulent Couette flow are used to validate the new model formulation as represented by the Picard's integral equation for Reynolds numbers ranging from 1500 to 7050 (based on one half of the velocity difference of the two plates and the channel height). The relative magnitudes of the Smagorinsky constitutive parameters have been investigated, including the model coefficient, SGS viscosity and filtered strain rate tensor. In general, this paper focuses on investigation of fundamental mathematical and physical properties of the popular Smagorinsky constitutive relation and its related dynamic modelling optimization procedure. Copyright © 2005 John Wiley & Sons Ltd.     

基于聚类算法和自由度集结的柔性结构模型降阶研究

提出了采用k-means聚类算法对动力相似自由度进行自动集结的模型降阶方法。考虑动力荷载空间分布,给出了根据模态参与系数选取原模型重要模态的方法,并讨论了次要方向自由度舍弃的方法。根据重要模态中各自由度振型值的相似性,应用聚类算法对自由度进行自动分类,从柔度矩阵元素的定义入手推导了结构矩阵显式条件下柔度法降阶的统一表达式,并证明了降阶模型的正定性、对称性及正交关系。最后通过一榀40层混凝土框架结构模型由240自由度降阶为8自由度的算例,说明了柔度法降阶的有效性及降阶模型评判指标的合理性。     

Semi‐automatic porting of a large‐scale CFD code to multi‐graphics processing unit clusters

A typical large‐scale CFD code based on adaptive, edge‐based finite‐element formulations for the solution of compressible and incompressible flow is taken as a test bed to port such codes to graphics hardware (graphics processing units, GPUs) using semi‐automatic techniques. In previous work, a GPU version of this code was presented, in which, for many run configurations, all mesh‐sized loops required throughout time stepping were ported. This approach simultaneously achieves the fine‐grained parallelism required to fully exploit the capabilities of many‐core GPUs, completely avoids the crippling bottleneck of GPU–CPU data transfer, and uses a transposed memory layout to meet the distinct memory access requirements posed by GPUs. The present work describes the next step of this porting effort, namely to integrate GPU‐based, fine‐grained parallelism with Message‐Passing‐Interface‐based, coarse‐grained parallelism, in order to achieve a code capable of running on multi‐GPU clusters. This is carried out in a semi‐automated fashion: the existing Fortran–Message Passing Interface code is preserved, with the translator inserting data transfer calls as required. Performance benchmarks indicate up to a factor of 2 performance advantage of the NVIDIA Tesla M2050 GPU (Santa Clara, CA, USA) over the six‐core Intel Xeon X5670 CPU (Santa Clara, CA, USA), for certain run configurations. In addition, good scalability is observed when running across multiple GPUs. The approach should be of general interest, as how best to run on GPUs is being presently considered for many so‐called legacy codes. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of free‐stream turbulence on large‐scale coherent structures of separated boundary layer transition

It has been well established that large‐scale structures, usually called coherent structures, exist in many transitional and turbulent flows. The topology and range of scales of those large‐scale structures vary from flow to flow such as counter‐rotating vortices in wake flows, streaks and hairpin vortices in turbulent boundary layer. There has been relatively little study of large‐scale structures in separated and reattached transitional flows. Large‐eddy simulation (LES) is employed in the current study to investigate a separated boundary layer transition under 2% free‐stream turbulence on a flat plate with a blunt leading edge. The Reynolds number based on the inlet free stream velocity and the plate thickness is 6500. A dynamic subgrid‐scale model is employed to compute the subgrid‐scale stresses more accurately in the current transitional flow case. Flow visualization has shown that the Kelvin–Helmholtz rolls, which have been so clearly visible under no free‐stream turbulence (NFST) are not as apparent in the present study. The Lambda‐shaped vortical structures which can be clearly seen in the NFST case can hardly be identified in the free‐stream turbulence (FST) case. Generally speaking, the effects of free‐stream turbulence have led to an early breakdown of the boundary layer, and hence increased the randomization in the vortical structures, degraded the spanwise coherence of those large‐scale structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of Smagorinsky‐based subgrid‐scale models in a finite‐volume computation

Smagorinsky‐based models are assessed in a turbulent channel flow simulation at Re_b=2800 and Re_b=12500. The Navier–Stokes equations are solved with three different grid resolutions by using a co‐located finite‐volume method. Computations are repeated with Smagorinsky‐based subgrid‐scale models. A traditional Smagorinsky model is implemented with a van Driest damping function. A dynamic model assumes a similarity of the subgrid and the subtest Reynolds stresses and an explicit filtering operation is required. A top‐hat test filter is implemented with a trapezoidal and a Simpson rule. At the low Reynolds number computation none of the tested models improves the results at any grid level compared to the calculations with no model. The effect of the subgrid‐scale model is reduced as the grid is refined. The numerical implementation of the test filter influences on the result. At the higher Reynolds number the subgrid‐scale models stabilize the computation. An analysis of an accurately resolved flow field reveals that the discretization error overwhelms the subgrid term at Re_b=2800 in the most part of the computational domain. Copyright © 2002 John Wiley & Sons, Ltd.     

RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network (RNN) model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.     

A time‐implicit high‐order compact differencing and filtering scheme for large‐eddy simulation

This work investigates a high‐order numerical method which is suitable for performing large‐eddy simulations, particularly those containing wall‐bounded regions which are considered on stretched curvilinear meshes. Spatial derivatives are represented by a sixth‐order compact approximation that is used in conjunction with a tenth‐order non‐dispersive filter. The scheme employs a time‐implicit approximately factored finite‐difference algorithm, and applies Newton‐like subiterations to achieve second‐order temporal and sixth‐order spatial accuracy. Both the Smagorinsky and dynamic subgrid‐scale stress models are incorporated in the computations, and are used for comparison along with simulations where no model is employed. Details of the method are summarized, and a series of classic validating computations are performed. These include the decay of compressible isotropic turbulence, turbulent channel flow, and the subsonic flow past a circular cylinder. For each of these cases, it was found that the method was robust and provided an accurate means of describing the flowfield, based upon comparisons with previous existing numerical results and experimental data. Published in 2003 by John Wiley & Sons, Ltd.