3D conforming power diagrams for radial LGR in CPG reservoir grids

Mesh generation becomes a crucial step in reservoir flow simulation of new generation. The mesh must faithfully represent the architecture of the reservoir and its heterogeneity. In (Flandrin et al. in IJNME 65(10):1639–1672, 2006) a three-dimensional hybrid mesh model was proposed to capture the radial characteristics of the flow around the wells. In this hybrid mesh, the reservoir is described by a non-uniform Cartesian structured mesh and the drainage areas around the wells are represented by structured radial circular meshes. Unstructured polyhedral meshes are used to connect these two kinds of structured grids. The construction of these transition meshes is based on 3D power diagrams (Aurenhammer in SIAM J Comput 16(1):78–96, 1987) to ensure finite volume properties such as mesh conformity, dual orthogonality and cell convexity. In this paper, we propose an extension of this hybrid model to the case where the reservoir is described by a corner point geometry (CPG) grid. At first, the CPG grid is mapped, in a reference space, into a non-uniform Cartesian grid by minimizing the mapping deformation. Then, a hybrid mesh is generated in this reference space using the previous method. Finally, this mesh is mapped back into the real space. Some quality criterions are introduced to measure and improve the quality of the polyhedral transition mesh.     

2D-Shape Analysis Using Conformal Mapping

The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural distances between 2D shapes creates a metric space of shapes, whose mathematical structure is inherently relevant to the classification task. One intriguing metric space comes from using conformal mappings of 2D shapes into each other, via the theory of Teichmüller spaces. In this space every simple closed curve in the plane (a “shape”) is represented by a ‘fingerprint’ which is a diffeomorphism of the unit circle to itself (a differentiable and invertible, periodic function). More precisely, every shape defines to a unique equivalence class of such diffeomorphisms up to right multiplication by a Möbius map. The fingerprint does not change if the shape is varied by translations and scaling and any such equivalence class comes from some shape. This coset space, equipped with the infinitesimal Weil-Petersson (WP) Riemannian norm is a metric space. In this space, the shortest path between each two shapes is unique, and is given by a geodesic connecting them. Their distance from each other is given by integrating the WP-norm along that geodesic. In this paper we concentrate on solving the “welding” problem of “sewing” together conformally the interior and exterior of the unit circle, glued on the unit circle by a given diffeomorphism, to obtain the unique 2D shape associated with this diffeomorphism. This will allow us to go back and forth between 2D shapes and their representing diffeomorphisms in this “space of shapes”. We then present an efficient method for computing the unique shortest path, the geodesic of shape morphing between each two end-point shapes. The group of diffeomorphisms of S¹ acts as a group of isometries on the space of shapes and we show how this can be used to define shape transformations, like for instance ‘adding a protruding limb’ to any shape.     

Statistical properties of differences between low and high resolution CMAQ runs with matched initial and boundary conditions

Numerical simulations of air quality models provide unique and different outputs for different choices of grid size. Thus, an important task is to understand the characteristics of model outcomes as a function of grid size in order to assess the quality of the model as to its fitness for meeting a specific design objective. This type of assessment is somewhat different than that of traditional operational performance and diagnostic type model evaluation. There, the objective is towards assessing errors in numerical models of air quality and utilizing concentration measurements from monitors to provide the bases for guidance towards model improvement and for their assessment of ability to predict and retrospectively map air quality. However, observations used as “truth” to assess model performance have themselves properties unique to the data collection protocols, siting and spatial density of deployment. In the data assimilation community, the term “model error” is used for the difference between model output given perfect inputs and the “truth” (Kalnay, 2003). In this paper, we are concerned with one aspect of this “model error”, the discrepancy due to discretization of space by choice of grid size in the model. To understand discrepancy due to discretization, outputs from the Community Multiscale Air Quality model (CMAQ) at two resolutions are studied. The lower resolution run is carried out so that its initial and boundary conditions are as similar as possible to those for the higher resolution run, thus minimizing this source of discrepancies and allowing us to isolate discrepancies due to discretization. Differences are analyzed from a statistical perspective by comparing marginal distributions of two outputs and considering spatial variation of the differences. Results indicate sharp increases in spatial variation of the differences for the first few hours of running the model, followed by small increases thereafter. The spatial variation of the differences depends on the individual spatial structure of the original processes, which we show varies with the time of day. We also show that the spatial variations on sub-regions depend on whether the sub-region is in a rural or an urban area.     

A parallel sparse grid construction algorithm based on the shared memory architecture and its application to flash calculations

The study of sparse grids has been done in a lot of works, but none of them pay special attention on the concept of “layer”, not to mention the further research on this new concept. This work presents the layer concept at first, and then based on it a new parallel sparse grid construction algorithm is proposed, which fills the niche that few works design such kind of algorithm on shared memory architecture. With the superiorities of the layer concept, the sparse grids can be constructed in a “layer by layer” manner on a much easier structure which is the simplified tree. Different from the classical tree structures used in the former sparse grid construction algorithm, the simplified tree reduces the number of sparse grid points further and at the same time avoids many unnecessary usages of pointers. Moreover, the correctness of the algorithm is guaranteed by the two correctness criterions, and its main advantages include that it can achieve load balance among the threads easily and that it can be applied in the function domains of any kinds of configurations, which is demonstrated by theory. After that, the algorithm is tested on flash calculations which are an important application from reservoir simulations. According to the characteristics of the issue, a modified version of the algorithm is given. By comparing the tested results with those of the former algorithm, it is found that a great quantity of construction time is saved by this algorithm.     

混合重叠网格通信优化算法

重叠网格技术广泛应用在复杂外型和运动边界问题的流场数值模拟中.本文在并行重叠网格隐式挖洞算法实现的基础上,提出了笛卡尔辅助网格和多块结构网格的混合重叠网格方法.通过笛卡尔辅助网格实现重叠网格洞边界和网格插值关系的快速建立.通过定义重叠区域网格权重、部件网格与背景网格绑定的方法,建立了混合网格的并行分配模式,有效减少重叠插值信息在各进程间的通信,实现计算负载和通信负载在各个进程的均匀分配.测试表明该方法可应用于数千万量级的重叠网格系统,可扩展至千核规模,高效的实现多个物体构成的复杂网格系统的重叠关系建立.     

Symbolic path-based protocol verification

The principal problem in protocol verification is state explosion problem. In our work (W.C. Liu, C.G. Chung, Path-based Protocol Verification Approach, Technical Report, Department of Computer Science and Information Engineering, National Chiao-Tung University, Hsin-Chu, Taiwan, ROC, 1998), we have proposed a “divide and conquer” approach to alleviate this problem, the path-based approach. This approach separates the protocol into a set of concurrent paths, each of which can be generated and verified independently of the others. However, reachability analysis is used to identify the concurrent paths from the Cartesian product of unit paths, and it is time-consuming. Therefore, in this paper, we propose a simple and efficient checking algorithm to identify the concurrent paths from the Cartesian product, using only Boolean and simple arithmetic operations.     

Flow simulations in arbitrarily complex cardiovascular anatomies – An unstructured Cartesian grid approach

Image guided computational fluid dynamics is attracting increasing attention as a tool for refining in vivo flow measurements or predicting the outcome of different surgical scenarios. Sharp interface Cartesian/Immersed-Boundary methods constitute an attractive option for handling complex in vivo geometries but their capability to carry out fine-mesh simulations in the branching, multi-vessel configurations typically encountered in cardiovascular anatomies or pulmonary airways has yet to be demonstrated. A major computational challenge stems from the fact that when such a complex geometry is immersed in a rectangular Cartesian box the excessively large number of grid nodes in the exterior of the flow domain imposes an unnecessary burden on both memory and computational overhead of the Cartesian solver without enhancing the numerical resolution in the region of interest. For many anatomies, this added burden could be large enough to render comprehensive mesh refinement studies impossible. To remedy this situation, we recast the original structured Cartesian formulation of Gilmanov and Sotiropoulos [Gilmanov A, Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. J Comput Phys 2005;207(2):457–92] into an unstructured Cartesian grid layout. This simple yet powerful approach retains the simplicity and computational efficiency of a Cartesian grid solver, while drastically reducing its memory footprint. The method is applied to carry out systematic mesh refinement studies for several internal flow problems ranging in complexity from flow in a 90° pipe bend to flow in an actual, patient-specific anatomy reconstructed from magnetic resonance images. Finally, we tackle the challenging clinical scenario of a single-ventricle patient with severe arterio-venous malformations, seeking to provide a fluid dynamics prospective on a clinical problem and suggestions for procedure improvements. Results from these simulations demonstrate very complex cardiovascular flow dynamics and underscore the need for high-resolution simulations prior to drawing any clinical recommendations.     

基于“两个细则”的一次调频影响因素分析与对策研究

并网机组的一次调频功能对于电网的稳定性来说至关重要。随着“两个细则”的发布,电网对一次调频功能的考核越来越严格。在此背景下,本文总结了影响一次调频的11个因素并给出了相应的解决措施,具有一定的借鉴意义。     

Absolute Permeability Upscaling for Superelement Modeling of Petroleum Reservoir

A technique for local upscaling of absolute permeability is proposed intended for the superelement modeling of petroleum reservoir development. The upscaling is performed for every block of an unstructured superelement grid based on solving a series of stationary one-phase flow in reservoir problems on a refined grid with the initial permeability field under various boundary conditions reflecting the characteristic structural variants of the filtrational flow and taking into account the presence or absence of wells inside the block. The resulting components of the effective permeability tensor in each superelement are sought from the solution of the problem on minimizing the deviations of the normal flows through the faces of the superelement averaged on a refined computational grid from those approximated on a coarse superelement grid. The application of the method is demonstrated by examples of the reservoir of the periodic and nonperiodic structure. The method is compared with the traditional techniques for local upscaling.     

A FORTRAN program for constrained sequence-slotting based on minimum combined path length

This paper describes a program for combining or “slotting” together two ordered sequences of observations into a single combined sequence with the minimum possible “combined path length” while preserving the stratigraphic ordering within each original sequence. A dynamic programming approach is used to minimize the total length or distance through the combined sequence, taking as input user-defined distances or dissimilarities between each pair of observations. This optimization criterion in some situations may be more appropriate than other criteria. The program enables the user to specify, using simple mnemonic codes, any number of additional order constraints of 12 different types. The program is illustrated on a set of data comprising gamma, sonic, and induction logs from two wells. Detailed input instructions and a listing of the program are given.     

An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods

A Cartesian grid method with adaptive mesh refinement and multigrid acceleration is presented for the compressible Navier-Stokes equations. Cut cells are used to represent boundaries on the Cartesian grid, while ghost cells are introduced to facilitate the implementation of boundary conditions. A cell-tree data structure is used to organize the grid cells in a hierarchical manner. Cells of all refinement levels are present in this data structure such that grid level changes as they are required in a multigrid context do not have to be carried out explicitly. Adaptive mesh refinement is introduced using phenomenon-based sensors. The application of the multilevel method in conjunction with the Cartesian cut-cell method to problems with curved boundaries is described in detail. A 5-step Runge-Kutta multigrid scheme with local time stepping is used for steady problems and also for the inner integration within a dual time-stepping method for unsteady problems. The inefficiency of customary multigrid methods on Cartesian grids with embedded boundaries requires a new multilevel concept for this application, which is introduced in this paper. This new concept is based on the following novelties: a formulation of a multigrid method for Cartesian hierarchical grid methods, the concept of averaged control volumes, and a mesh adaptation strategy allowing to directly control the number of refined and coarsened cells.     

Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids

Freestream and vortex preservation properties of a weighted essentially nonoscillatory scheme (WENO) and a weighted compact nonlinear scheme (WCNS) on curvilinear grids are investigated. While the numerical technique used for the compact difference scheme can be applied to WCNS, applying it to WENO is difficult. This difference is caused by difference in the formulation of numerical fluxes. WENO computed in the generalized coordinate system does not work well for either freestream or vortex preservation, whereas WENO computed in the Cartesian coordinate system works well for both freestream and vortex preservation, but its resolution is lower than that of WCNS. In addition, WENO in the Cartesian coordinate system costs three times as much as WENO or WCNS in the generalized coordinate system. Therefore, WENO in the Cartesian coordinate system is not suitable for solving Euler equations on a curvilinear grid. On the other hand, WCNS computed in the generalized coordinate system works well for freestream and vortex preservation when used with the numerical technique proposed for the compact difference scheme. The results show that WCNS with this numerical technique can be used for an arbitrary grid system. In this paper, the excellent freestream and vortex preservation properties of WCNS when used with the numerical technique, compared with those of WENO, are shown for the first time.     

A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes

A block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual time-stepping method is developed for moving body problems with hybrid dynamic grids. To simulate flows over complex configurations, a hybrid grid method is adopted in this paper. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. With the motion of moving bodies, the quad grids move with the bodies, while the adaptive Cartesian grid remains stationary. Meanwhile, the triangular grids are deformed according to the motion of solid bodies with a ‘spring’ analogy approach. If the triangular grids become too skewed, or the adaptive Cartesian grid crosses into the quad grids, the triangular grids are regenerated. Then the flow solution is interpolated from the old to the new grid. The fully implicit equation is solved using a dual time-stepping solver. A Godunov-type scheme with Roe’s flux splitting is used to compute the inviscid flux. Several sub-iteration schemes are investigated in this study. Both supersonic and transonic unsteady cases are tested to demonstrate the accuracy and efficiency of the method.     

A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations

A hybrid dynamic grid generation technique for two-dimensional (2D) morphing bodies and a block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual-time-stepping method for unsteady incompressible flows are presented for external bio-fluid simulations. To discretize the complicated computational domain around 2D morphing configurations such as fishes and insect/bird wings, the initial grids are generated by a hybrid grid strategy firstly. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. During the unsteady movement of morphing bodies, the dynamic grids are generated by a coupling strategy of the interpolation method based on ‘Delaunay graph’ and local remeshing technique. With the motion of moving/morphing bodies, the grids are deformed according to the motion of morphing body boundaries firstly with the interpolation strategy based on ‘Delaunay graph’ proposed by Liu and Qin. Then the quality of deformed grids is checked. If the grids become too skewed, or even intersect each other, the grids are regenerated locally. After the local remeshing, the flow solution is interpolated from the old to the new grid. Based on the hybrid dynamic grid technique, an efficient implicit finite volume solver is set up also to solve the unsteady incompressible flows for external bio-fluid dynamics. The fully implicit equation is solved using a dual-time-stepping approach, coupling with the artificial compressibility method (ACM) for incompressible flows. In order to accelerate the convergence history in each sub-iteration, a block lower-upper symmetric Gauss-Seidel implicit method is introduced also into the solver. The hybrid dynamic grid generator is tested by a group of cases of morphing bodies, while the implicit unsteady solver is validated by typical unsteady incompressible flow case, and the results demonstrate the accuracy and efficiency of present solver. Finally, some applications for fish swimming and insect wing flapping are carried out to demonstrate the ability for 2D external bio-fluid simulations.     

A new index for molecular property correlation in halomethanes

“Geometric volume”, a new index, has been proposed for correlating boiling point, melting point, density and refractive index of 43 halomethanes. The index is a simple and straightforward approximation of the unit molecular volume in space. The index has been found to work well for other molecular properties and for other class of molecules as well.     

New inverse kinematic algorithms for redundant robots

New inverse kinematic algorithms for generating redundant robot joint trajectories are proposed. The algorithms utilize the kinematic redundancy to improve robot motion performance (in joint space or Cartesian space) as specified by certain objective functions. The algorithms are based on the extension of the existing “joint-space command generator” technique in which a null space vector is introduced which optimizes a specific objective function along the joint trajectories. In this article, the algorithms for generating the joint position and velocity (PV) trajectories are extensively developed. The case for joint position, velocity, and acceleration (PVA) generation is also addressed. Application of the algorithms to a four-link revolute planar robot manipulator is demonstrated through simulation. Several motion performance criteria are considered and their results analyzed.     

Ghost-Cell Method with far-field coarsening and mesh adaptation for Cartesian grids

Cartesian grid methods for inviscid computational fluid dynamics offer great promise for the development of very rapid conceptual design tools. The present paper deals with a number of new features for Cartesian grid methods which appear to be particularly well suited for this application. A key ingredient is the implementation of non-penetration boundary conditions at solid walls which is based upon the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall. This method was shown to be substantially more accurate than traditional surface boundary condition approaches. This improved boundary condition has been adapted to a Cartesian mesh formulation, which we termed the Ghost-Cell Method. In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges, without any cut cells which complicate other Cartesian mesh methods. Another typical drawback of non-adaptive Cartesian grid methods is that any Cartesian grid clustering near the body must be maintained to the far field boundary. To address this issue, we have introduced a far-field grid coarsening, based on the iblanking approach, which maintains the structured nature of the grid while computing only the active cell centers. In addition, to highlight the advantages of grid adaptation in connection with Cartesian mesh methods, we have introduced a rudimentary procedure which detects the shock position and automatically refines the mesh by locally reducing the grid dimension to one fourth of its original dimension. The merits of the Ghost-Cell Method are established by the computation of the compressible flow about circular cylinders. The results show the surface non-penetration condition to be satisfied in the limit of vanishing cell size and the method to be second-order accurate in space. The results of the far-field grid coarsening indicate that the numerical solutions are unaffected by the coarsening, while the number of the computed cells and the CPU time are reduced to less than 50% of the uncoarsened solution values. The results computed using the mesh adaptation at the shock indicate that the method is effective in reducing the shock transition region thickness, without modifying the flow solution away from the shock. Finally, some test cases with airfoils located at different positions have been considered and the results are proven to be practically independent of the position of the body with respect to the grid. Although this paper is limited to two-dimensional applications, the methodology is well-suited for general three-dimensional geometries, which will be the subject of future research.     

A parallel computing framework for big data

Big data has received great attention in research and application. However, most of the current efforts focus on system and application to handle the challenges of “volume” and “velocity”, and not much has been done on the theoretical foundation and to handle the challenge of “variety”. Based on metric-space indexing and computationalcomplexity theory, we propose a parallel computing framework for big data. This framework consists of three components, i.e., universal representation of big data by abstracting various data types into metric space, partitioning of big data based on pair-wise distances in metric space, and parallel computing of big data with the NC-class computing theory.     

Optimal Scheduling for UET/UET-UCT Generalizedn-Dimensional Grid Task Graphs

Then-dimensional grid is one of the most representative patterns of data flow in parallel computation. Many scientific algorithms, which require nearest neighbor communication in a lattice space, are modeled by a task graph with the properties of a simple or enhanced grid. The two most frequently used scheduling models for grids are the unit execution time-zero communication delay (UET) and the unit execution time–unit communication time (UET-UCT). In this paper we introduce an enhanced model of then-dimensional grid by adding extra diagonal edges and allowing unequal boundaries for each dimension. For this generalized grid topology we establish the optimal makespan for both cases of UET/UET-UCT grids. Then we give a closed formula that calculates the minimum number of processors required to achieve the optimal makespan. Finally, we propose a low-complexity optimal time and processor scheduling strategy for both cases.     

Assessing classifiers in terms of the partial area under the ROC curve

Assessing classifiers using the partial area under the ROC curve (PAUC) (or its equivalent, “separability”, that is a function of the chosen threshold of the decision variable) is considered. The population properties of the “separability” as a function only of the trained classifier and the selected threshold are derived. Next, the nonparametric estimation of the “separability” and its mean, for which we assume the availability of only one dataset, using the leave-pair-out bootstrap-based estimator is considered. In addition, the influence function approach to estimate the uncertainty of that estimate is used. The major contributions are the inclusion of the effect of the training set on the properties of the “separability”, and also on its nonparametric estimator, in both the mean and the variance; this is a key difference from the PAUC literature and its use in medical community. The mathematical properties are confirmed by a set of experiments using simulated and real datasets. Finally, the true performance (not its estimate) of classifiers measured in “separability” may vary significantly with varying the training set, while its estimate yet has a small estimated variance. This accounts for having “good” estimate for “bad” performance.