Incremental proper orthogonal decomposition for PDE simulation data

We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. The algorithm initializes and efficiently updates the dominant POD eigenvalues and modes during the time stepping in a PDE solver without storing the simulation data. We prove that the algorithm without truncation updates the POD exactly. We demonstrate the effectiveness of the algorithm using finite element computations for a 1D Burgers’ equation and a 2D Navier–Stokes problem.     

Direct simulation for CAD models undergoing parametric modifications

We propose a novel approach—direct simulation—for interactive simulation with accuracy control, for CAD models undergoing parametric modifications which leave Dirichlet boundary conditions unchanged. This is achieved by computing offline a generic solution as a function of the design modification parameters. Using this parametric expression, each time the model parameters are edited, the associated simulation solution for this model instance can be cheaply and quickly computed online by evaluating the derived parametric solution for these parameter values. The proposed approach furthermore works for models undergoing topological changes, and does not need any mesh regeneration or mesh mapping. These results are achieved by use of the proper generalized decomposition model reduction technique, in combination with R-functions. We believe this is the first approach that can interactively simulate the physical properties of a CAD model, even undergoing topological change, without expensive re-computation. The approach is demonstrated for linear elasticity analysis; numerical results demonstrate its simulation accuracy and efficiency in comparison with the classic FE method.     

A turbulence model based on principal components

Literature on turbulence is very wide, providing several models for the power spectral density function of the single-point turbulence components, for the two-point coherence function of the same turbulence component and for the single-point coherence function of different turbulence components. On the other hand, no suitable and simple model seems to be available for representing the two-point coherence function of different turbulence components, in particular of the longitudinal and vertical turbulence components, which would be useful for modelling buffeting actions on bridges. The Proper Orthogonal Decomposition provides efficient tools to formulate a new model of the turbulence field based on principal components. Furthermore, it suggests physical principles and defines mathematical rules to establish an appropriate model of the two-point coherence function of the longitudinal and vertical components, completing the statistical model of turbulence. Embedded in a Monte Carlo framework, this new representation can be used to simulate multi-dimensional and multi-variate random turbulence fields.     

Model reduction for multidisciplinary optimization - application to a 2D wing

Multidisciplinary optimization (MDO) is a growing field in engineering, with various applications in aerospace, aeronautics, car industry, etc. However, the presence of multiple disciplines leads to specific issues, which prevent MDO to be fully integrated in industrial design methodology. In practice, the key issues in MDO lie in the management of the interconnections between disciplines, along with the high number of simulations required to find a feasible multidisciplinary (optimal) solution. Therefore, in this paper, a novel approach is proposed, combining proper orthogonal decomposition to decrease the amount of data exchanged between disciplines, with surrogate models based on moving least squares to reduce disciplines. This method is applied to an original 2D wing demonstrator involving two disciplines (fluid and structure). The numerical results obtained for an optimization task show its benefits in diminishing both the interfaces between disciplines and the overall computational time.     

中石化国际化经营人才英语培训的实践与思考

国际化经营人才英语培训有其自身的特点和规律。不断探索和总结其规律,形成符合实际的由能力模块、培训方式和教学管理构成的培训模式对增强培训效果十分重要。能力模块的构建必须以听说为主,满足受训者出国后工作和生活的需要。培训方式要满足个性发展需要,营造英语环境,帮助学员度过平台期。管理上应体现以人为本、厂校结合、适度施压的原则,打造中石化国际化经营人才英语培训品牌。     

Proper Orthogonal Decomposition and Radial Basis Functions in material characterization based on instrumented indentation

For the mechanical characterization of structural materials non-destructive tests combined with computer simulations and inverse analyses are more and more frequently and advantageously employed in various engineering fields. The contribution to such development presented in this paper can be outlined as follows. With reference to isotropic elastic-plastic material models, indentation test simulations are done preliminarily, once-for-all, by a conventional finite element forward operator. Results of these simulations are employed in a procedure which is centered on Proper Orthogonal Decomposition and Radial Basis Functions approximation and is used for fast interpolations which replace further finite element analyses in the parameter identification process. Comparative computational exercises are presented in order to point out the consequent significant reduction of computing times in test simulations and, hence, in the minimization of the discrepancy function by the Trust Region Algorithm, namely by a traditional first-order mathematical programming method. Such a parameter identification procedure may be carried out routinely and economically on small computers for in situ structural diagnoses. Both the force-penetration relationship (provided by an instrumented indenter) and the average imprint profile (achievable by laser profilometer) are considered as sources of measurable response quantities or experimental data.     

纬编间隔床品面料的结构及性能分析

采用3.3 tex涤纶单丝为间隔纱,8.3 tex涤纶和2.2 tex氨纶交织为表层,制备4种不同密度、厚度及间隔纱连接方式的纬编间隔织物。分析织物组织结构和编织工艺,并测试力学性能和热湿舒适性能,分析面料厚度、密度与各项性能关系,用数学模糊分析法对面料进行综合分析。结果表明,间隔纱连接方式对面料拉伸断裂性和顶破性有一定影响,对透气透湿性无明显影响;厚度、密度较小且间隔纱交叉连接的织物综合性能最好;选择床垫面料时考虑厚度、密度及间隔纱连接方式对面料性能影响。     

A hybridized snapshot proper orthogonal decomposition-discrete wavelet transform technique for the analysis of flow structures and their time evolution

A novel hybrid technique has been proposed in order to reveal in a greater detail the turbulent flow structures and their time evolution, and to address the issues and limitations related to the application of snapshot proper orthogonal decomposition (POD) and wavelet transform technique. The proposed hybrid technique combines the inherent abilities of the snapshot proper orthogonal decomposition and the two-dimensional discrete wavelet transform technique. The POD gives us the overall view of the most energetic flow pattern in an ensemble by decomposing the flow field into spatial and temporal modes, while two-dimensional wavelet transform gives us the localized spatial information through scale wise decomposition of the flow field. In this work, we apply the wavelet transform on the POD spatial modes. This enables us to understand the space scale structure of the flow events captured by the spatial POD modes, and the scale wise selectivity of these spatial POD modes. Thus, we are able to relate the most energetic flow events over a period of time (as obtained in spatial modes of snapshot POD) with the localized dominant scales that are contributing to it. Further, this information is utilized in the selection of those pod spatial modes that can effectively reconstruct a flow structure and its time evolution. The proposed technique has also been able to address the issues in the literature concerning the application of POD when the flow is less deterministic, as then a single POD mode may not reveal the flow structure and combination of modes is required to reconstruct it. In the present work, this hybrid methodology has been used to reveal the near wall intermittent events in channel flow: the ascending streaks and the bursts and their time evolution, the vortex tube and leading edge vortices in jet and the Taylor-Couette and irregular small chaotic vortices in Taylor-Couette flow. The planar dataset used for such an analysis has been obtained from particle image velocimetry and large eddy simulation studies.     

Reynolds number scaling of flow in a stirred tank with Rushton turbine. Part II — Eigen decomposition of fluctuation

We consider the question of scaling of flow within a stirred tank with increasing Reynolds number. Experimental results obtained from two different tanks of diameter 15.25 and 29.21 cm with a Rushton turbine operating at a wide range of rotational speed is considered for the scaling analysis. The resulting Reynolds number of the flow ranges from 4000 to about 80,000. Phase locked stereoscopic PIV measurements have been performed in order to obtain all three components of velocity on three different vertical planes close to the impeller. The scaling of plane-averaged mean flow was explored in the companion part-I of the paper. The scaling of rms and skewness of fluctuation about the mean is investigated here. The fluctuation about the mean is explained in terms of time-dependent oscillation of the impeller-induced jet and tip vortex components of the flow. The spatial structure of the instantaneous fluctuation about the mean is investigated in terms of eigenmodes obtained using proper orthogonal decomposition with the method of snapshots. The scaling of energy content of the dominant eigenmodes with Re is investigated.     

Analysis of dominant flow structures and their flow dynamics in chemical process equipment using snapshot proper orthogonal decomposition technique

Snapshot proper orthogonal decomposition (POD) technique has been applied to reveal the dominant flow structures, their dynamics and length scales in six widely used industrial equipments (stirred tank, bubble column, Taylor-Couette flow (annual contactor), ultrasonic reactor, jet reactor, and channel flow). The variation in length scale of structures within an equipment, with change in its operating conditions (Reynolds number and power input) or change in its geometric configuration (sparger and impeller designs), has been brought out in this work. The planar data set for POD analysis was obtained from particle image velocimetry (PIV) and large eddy simulation (LES) studies. The dominant spatial topology was analyzed by using the velocity and vorticity POD modes. The modes have revealed the following flow structures: the ascending streaks and bursts in channel flow, the vortex tube and leading edge vortices in jets, the irregular small chaotic vortices in Taylor-Couette flow, the variation in plume oscillation and flow structures in the vortical region of bubble column resulting from changes in sparger design, the high intensity vortices near the source of ultrasound in the ultrasonic reactor and the effect of impeller designs on dominant flow structures and near blade vortices in the stirred tank. The length scales of structures are obtained by applying image processing on the spatial modes. The dynamics of these flow structures in each of the items of equipment is captured by reconstructing the flow field using appropriate spatial and temporal modes that contribute to these structures. Further, a unique attempt has been made to correlate the length scale distribution with the mixing time.