A fast algorithm for estimating large-scale permeabilities of correlated anisotropic media

The problem of estimating large-scale permeabilities of reservoirs based on knowledge of the small-scale permeabilities is addressed. We present an accurate and fast algorithm to calculate the global permeabilities of two- or three-dimensional correlated and anisotropic block samples, thus providing a fast algorithm for obtaining grid block permeabilities for reservoir simulators from small scale data. The algorithm is tested on both two- and three-dimensional tube networks generated from real images and fractal forgeries modeling porous media. In almost all cases, the algorithm estimates the correct global permeability (calculated using exact but slow algorithms) of the network to better than 5%. The new algorithm is comparable in speed to conventional averaging techniques, such as the geometric mean, but the obtained estimates are always much better.List of Symbols K permeability of network (global permeability - K _e estimated permeability - K K×(L_x×L_y)/L_z - K permeability perpendicular to layering - K permeability parallel with layering - L _x, L_y, L_z Network size inx, y andz-directions - L Size of quadratic (cubic) network - Q global flux through network - U Q/(L_x×L_y), Darcy velocity (flux per unit area) - V volume of network - P pressure drop across network - a,b parameters in Equation (4) - P _i pressure at sitei - q _ij flux between nodesi andj - parameter of Pareto distribution - porosity - K(i) permeability at site (block)i - K _ij permeability of bond between nodesi andj - K _min minimumk(i) for sample - K _max maximumK(i) for sample - fluid viscosity     

A new method for estimating bounds of eigenvalues

A new method for estimating the bounds of eigenvalues is presented. In order to show that the method proposed is as effective as Qiu's, an undamping spring-mass system with 5 nodes and 5 degrees of freedom is given. To illustrate that the present method can be applied to structures which cannot be treated by non-negative decomposition, a plane frame with 202 nodes and 357 beam elements is given. The results show that the present method is effective for estimating the bounds of eigenvalues and is more common than Qiu's. Project supported by the National Natural Science Foundation (No. 19872028) and the Mechanical Technology Development Foundation of China.     

一种新的减基法中的采样方法及误差估计

针对减基法中求解精度受减基空间完备性影响的问题,提出了一种基于向量空间逼近原理的采样方法及相应的误差估计。该方法使每一步采样得到的特征向量与之前已得到的特征向量所张成的向量空间角度最大,从而保证了每步采样所对应的特征向量都具有最弱相关性,进而使最终得到的特征向量基空间更具完备性。并且由该方法产生了一种先验特征值误差界,...     

Comparison of fast algorithms for estimating large-scale permeabilities of heterogeneous media

The problem of upscaling permeability data from the core to the reservoir grid block scale for input into flow simulators is addressed. Two fast, approximate algorithms which have been suggested for this purpose—one based on random walks and the other on real-space renormalisation group methods—are compared using the results of numerical tests performed on 30 different heterogeneous permeability realisations in 3-D. The results show that random walks outperform renormalisation for this problem, being computationally more efficient and demonstrating significantly better accuracy for particular cases.     

A method for estimating wall friction in turbulent wall-bounded flows

We describe a simple method for estimating turbulent boundary layer wall friction using the fit of measured velocity data to a boundary layer model profile that extends the logarithmic profile all the way to the wall. Two models for the boundary layer profile are examined, the power-series interpolation scheme of Spalding and the Musker profile which is based on the eddy viscosity concept. The performance of the method is quantified using recent experimental data in zero pressure gradient flat-plate turbulent boundary layers, and favorable pressure gradient turbulent boundary layers in a pipe, for which independent measurements of wall shear are also available. Between the two model profiles tested, the Musker profile performs much better than the Spalding profile. Results show that the new procedure can provide highly accurate estimates of wall shear with a mean error of about 0.5% in friction velocity, or 1% in shear stress, an accuracy that is comparable to that from independent direct measurements of wall shear stress. An important advantage of the method is its ability to provide accurate estimates of wall shear not only based on many data points in a velocity profile but also very sparse data points in the velocity profile, including only a single data point such as that originating from a near-wall probe.     

A fast Godunov method for the water‐hammer problem

An efficient Godunov‐type numerical method with second‐order accuracy was developed to simulate the water‐hammer problem in piping. The exact solutions of the Riemann problem were analysed and illustrated on the intriguing solution diagram by properly introducing dimensionless variables within reasonably practical ranges. Based on the solution diagram, an efficient fast Riemann solver was also developed. Moreover, small perturbation analysis was performed to demonstrate the relations between the primitive variables, velocity and pressure, for the Riemann problem. The typical shock‐tube problem and the water‐hammer problem were implemented as sample ones to test the numerical method. It was shown that the present numerical method incorporated with Van Leer's flux limiter is a promising one to simulate fluid transient problem for piping in the present study. Copyright © 2002 John Wiley & Sons, Ltd.     

大规模动力系统改进的快速精细积分方法

提出一种针对大规模动力系统的改进的快速精细积分方法（FPIM）。以精细积分方法为基础,利用大规模动力系统矩阵的稀疏性和动力问题的物理特性,分析了矩阵指数的特殊结构,并基于此给出一种计算大规模动力系统矩阵指数及其动力响应的高效率方法。     

A fast mesh deformation method for marine propeller flow

ABSTRACT

A fast mesh deformation method for propeller flow is developed based on the elastic solid method. The flow field of a propeller is assumed to be fulfilled with a kind of pseudo elastic solid which does not influence the flow. The vibration equation for the propeller blade-pseudo elastic solid system is derived. During fluid-structure coupling, the nodal displacement for the blade and the flow mesh is computed by modal superposition of the first several modes. Fluid-structure coupling is performed for a highly skewed propeller. The computing time for the dynamic mesh by the present method is about 0.017% of the computing time by the existing elastic solid method. The computing time for the fluid-structure coupling using the present method is 52% less than the computing time by the existing elastic solid method.     

A fast all-in-one method for automated post-processing of PIV data

Post-processing of PIV (particle image velocimetry) data typically contains three following stages: validation of the raw data, replacement of spurious and missing vectors, and some smoothing. A robust post-processing technique that carries out these steps simultaneously is proposed. The new all-in-one method (DCT–PLS), based on a penalized least squares approach (PLS), combines the use of the discrete cosine transform (DCT) and the generalized cross-validation, thus allowing fast unsupervised smoothing of PIV data. The DCT–PLS was compared with conventional methods, including the normalized median test, for post-processing of simulated and experimental raw PIV velocity fields. The DCT–PLS was shown to be more efficient than the usual methods, especially in the presence of clustered outliers. It was also demonstrated that the DCT–PLS can easily deal with a large amount of missing data. Because the proposed algorithm works in any dimension, the DCT–PLS is also suitable for post-processing of volumetric three-component PIV data.     

A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate

We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate $ \left\langle \varepsilon \right\rangle $ in a variety of turbulent flows. The method relies on the validity of the first similarity hypothesis of Kolmogorov (C R (Doklady) Acad Sci R R SS, NS 30:301–305, 1941) (or K41) which implies that spectra of velocity fluctuations scale on the kinematic viscosity ν and $ \left\langle \varepsilon \right\rangle $ at large Reynolds numbers. However, the evidence, based on the DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a ?5/3 inertial subrange only when the Taylor microscale Reynods number R _λ is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30?≤?R _λ?≤?400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of $ \left\langle \varepsilon \right\rangle $ in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.     

A method for estimating the reliability of structural systems with moment-matching and copula concept

It is aimed to propose a copula based systematic quantitative method for system reliability analysis of engineering structures considering multiple dependent failure modes. The principles of the moment matching method, the copula theory and the bound theory are combined to achieve the purpose. As the very first step, the moment estimation of the limit state function of each component is calculated by anchored ANOVA (Analysis of Variance) expansion. The third moment saddle point approximation is then applied to derive the distribution of each performance function and evaluate the reliability index with obtained moments. By introducing copula functions into the narrow bounds theory, the traditional reliability method is improved. The best-fitting copula function is determined to ensure the accuracy of the joint probabilistic modeling between the dependent failure modes. A novel feature of the proposed method is the use of the copula concept, instead of traditional numerical integration commonly used in the joint failure probability estimation. Examples are presented to illustrate the accuracy and applicability of the presented method.     

Stability analysis and estimation of domain of attraction for the endemic equilibrium of an SEIQ epidemic model

This paper mainly addressed the stability analysis and the estimation of domain of attraction for the endemic equilibrium of a class of susceptible-exposed-infected-quarantine epidemic models. Firstly, we discuss the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium in the feasible region D of the epidemic model, respectively. Secondly, we use a geometric approach to investigate the global stability of the endemic equilibrium in a positive invariant region \(D_s(\subset D)\). Furthermore, we estimates the domain of attraction for the endemic equilibrium via sum of squares optimization method, and obtain the optimal estimation by solving an semidefinite programming problem with sum of squares polynomial constraints. Finally, numerical simulation is examined to demonstrate the feasibility and effectiveness of the research results.     

A fast and robust fictitious domain method for modelling viscous flows in complex mixers: The example of propellant make‐down

This work deals with the development of a fast three‐dimensional numerical strategy for the simulation of viscous fluid flow in complex mixing systems. The proposed method is based on a distributed Lagrange multiplier fictitious domain method and the use of the low‐cost MINI finite element. Contrary to the previous fictitious domain method developed by our group a few years ago, the underlying partial differential equations are solved here in a coupled manner using a consistent penalty technique. The method is discussed in detail and its precision is assessed by means of experimental data in the case of an agitated vessel. A comparison made with our existing fictitious domain method and its decoupled Uzawa‐based solver clearly shows the advantages of resorting to the MINI finite element and fully coupled solution strategy. The new technique is then applied to the simulation of the flow of a Newtonian viscous fluid in a three‐blade planetary mixer in the context of the production of solid propellants. Copyright © 2008 John Wiley & Sons, Ltd.     

A three-dimensional fictitious domain method for incompressible fluid flow problems

A new Galerkin finite element method for the solution of the Navier–Stokes equations in enclosures containing internal parts which may be moving is presented. Dubbed the virtual finite element method, it is based upon optimization techniques and belongs to the class of fictitious domain methods. Only one volumetric mesh representing the enclosure without its internal parts needs to be generated. These are rather discretized using control points on which kinematic constraints are enforced and introduced into the mathematical formulation by means of Lagrange multipliers. Consequently, the meshing of the computational domain is much easier than with classical finite element approaches. First, the methodology will be presented in detail. It will then be validated in the case of the two-dimensional Couette cylinder problem for which an analytical solution is available. Finally, the three-dimensional fluid flow inside a mechanically agitated vessel will be investigated. The accuracy of the numerical results will be assessed through a comparison with experimental data and results obtained with a standard finite element method. © 1997 John Wiley & Sons, Ltd.     

Improved linear regression method for estimating Weibull parameters

In the linear regression method for estimating parameters of a Weibull distribution, multiple flaw distributions may be further evidenced by derivation form the linearity of data from a single Weibull distribution. In this paper, a new technique of estimating multiple Weibull parameters is conducted, compared to commonly used regression probability estimator.     

一种船舶漂浮状态下捷联惯导快速自对准方法

为解决无外部参考信息船舶SINS漂浮状态下捷联惯导快速自对准问题,提出了在粗对准阶段采用时变参数罗经法、精对准阶段采用卡尔曼滤波精对准的方案.传统方案中罗经对准方案常常被用于精对准,这里采用大方位失准角条件下时变参数的罗经法进行粗对准,代替目前成熟的凝固法粗对准方案,在大方位失准角条件下同时利用东向通道和北向通道的速度...     

A fast and practical method to pack spheres for mesh generation

Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.