Robust globally divergence-free weak Galerkin finite element methods for natural convection problems

This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity, pressure, and temperature approximations in the interior of elements, respectively, and piecewise polynomials of degrees l, k, l(l = k-1,k) for the numerical traces of velocity, pressure and temperature on the interfaces of elements. The methods yield globally divergence-free velocity solutions. Well-posedness of the discrete scheme is established, optimal a priori error estimates are derived, and an unconditionally convergent iteration algorithm is presented. Numerical experiments confirm the theoretical results and show the robustness of the methods with respect to Rayleigh number.Comment: 32 pages, 13 figure

1-(2-Hydr­oxy-4,5-dimeth­oxyphen­yl)propan-1-one

In the title compound, C11H14O4, isolated from the stems of Trigonostemon xyphophylloides, an intra­molecular O—H⋯O hydrogen bond helps to establish an essentially planar conformation for the mol­ecule (r.m.s. deviation = 0.044 Å)

Water invasion performance of complex fracture-vuggy gas reservoirs based on classification modeling

   The complexity of the pore structure, spatial development, fractures, and pore distribution of fractured-vuggy carbonate reservoirs influences the water invasion dynamics of gas reservoirs, which is crucial in the dynamic research of strongly heterogeneous reservoirs. In this study, the collocation relationship of pore-vuggy fractures is described by the quantitative characterization of their attribute parameters. The discrete fracture network model is used to match and construct the fractures in different modes. The distribution classification method is used to model three-dimensional geological reservoirs in terms of their geometric and attribute characteristics. Bottom-water and edge-water gas reservoirs are constructed separately using numerical simulation, and the dynamic characteristics of water invasion are described. The results show that the proposed method is suitable for the geological modeling of fractured-vuggy gas reservoirs with strong heterogeneity and complexity. The modeling accuracy is improved because the gas reservoir heterogeneity and water invasion’s dynamic characteristics can be described accurately. Six stages of water invasion are identified from the numerical simulation of water invasion. This method provides theoretical guidance for the study of heterogeneous gas reservoirs with water.Cited as: Han, X., Tan, X., Li, X., Pang, Y., Zhang, L. Water invasion performance of complex fracture-vuggy gas reservoirs based on classification modeling. Advances in Geo-Energy Research, 2021, 5(2): 222-232, doi: 10.46690/ager.2021.02.1

Physics-Based Gaussian Process Method for Predicting Average Product Lifetime in Design Stage

The average lifetime or the mean time to failure (MTTF) of a product is an important metric to measure the product reliability. Current methods of evaluating the MTTF are mainly based on statistics or data. They need lifetime testing on a number of products to get the lifetime samples, which are then used to estimate the MTTF. The lifetime testing, however, is expensive in terms of both time and cost. The efficiency is also low because it cannot be effectively incorporated in the early design stage where many physics-based models are available. We propose to predict the MTTF in the design stage by means of a physics-based Gaussian process (GP) method. Since the physics-based models are usually computationally demanding, we face a problem with both big data (on the model input side) and small data (on the model output side). The proposed adaptive supervised training method with the Gaussian process regression can quickly predict the MTTF with a reduced number of physical model calls. The proposed method can enable continually improved design by changing design variables until reliability measures, including the MTTF, are satisfied. The effectiveness of the method is demonstrated by three examples

Approximation to Multivariate Normal Integral and Its Application in Time-Dependent Reliability Analysis

It is common to evaluate high-dimensional normal probabilities in many uncertainty-related applications such as system and time-dependent reliability analysis. An accurate method is proposed to evaluate high-dimensional normal probabilities, especially when they reside in tail areas. The normal probability is at first converted into the cumulative distribution function of the extreme value of the involved normal variables. Then the series expansion method is employed to approximate the extreme value with respect to a smaller number of mutually independent standard normal variables. The moment generating function of the extreme value is obtained using the Gauss-Hermite quadrature method. The saddlepoint approximation method is finally used to estimate the cumulative distribution function of the extreme value, thereby the desired normal probability. The proposed method is then applied to time-dependent reliability analysis where a large number of dependent normal variables are involved with the use of the First Order Reliability Method. Examples show that the proposed method is generally more accurate and robust than the widely used randomized quasi Monte Carlo method and equivalent component method

Robust Quantized Generalized H

This paper deals with the problem of robust generalized H2 filter design for uncertain discrete-time fuzzy systems with output quantization. Firstly, the outputs of the system are quantized by a memoryless logarithmic quantizer before being transmitted to a filter. Then, attention is focused on the design of a generalized H2 filter to mitigate quantization effects, such that the filtering error systems ensure the robust stability with a prescribed generalized H2 noise attenuation level. Via applying Finsler lemma to introduce some slack variables and using the fuzzy Lyapunov function, sufficient conditions for the existence of a robust generalized H2 filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach