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A note on optimal decay rates for the axisymmetric D-solutions to the steady Navier-Stokes equations

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arXiv 2017年

作者： Weng, Shangkun Xie, Chunjing School of Mathematics and Statistics Computational Science Hubei Key Laboratory Wuhan University Wuhan Hubei Province430072 China Department of Mathematics Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

In this paper, we investigate the decay properties of an axisymmetric D-solutions to stationary incompressible Navier-Stokes systems in R3. We obtain the optimal decay rate |u(x)| | xC|+1 for axisymmetric flows without swirl. Furthermore, we find a dichotomy for the decay rates of the swirl component ua, that is, either O(+11) +1or |ue(r,z)| (C1r)3, where p = Vr2+ z2. In the latter case, we can further deduce that the other two components of the velocity field also attain the optimal decay rates: |ur(r, z)| + |uz(r, z)| C+1-. We do not require any small assumptions on the forcing *** Codes 76D05 Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

Correction to: A Linearized Local Conservative Mixed Finite Element Method for Poisson–Nernst–Planck Equations

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Journal of scientific computing 2018年第2期77卷 818-818页

作者： Gao, Huadong Sun, Pengtao School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan People’s Republic of China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China Department of Mathematical Sciences University of Nevada Las Vegas Las Vegas USA

The original version of this article contained a mistake. There are error in line breaks in Eqs. 4.3 and 4.4 and the word “quad” was included inadvertently in Eq. 4.4.

The original version of this article contained a mistake. There are error in line breaks in Eqs. 4.3 and 4.4 and the word “quad” was included inadvertently in Eq. 4.4.

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A third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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arXiv 2017年

作者： Wu, Chen Shu, Chang Shi, Baochang Chen, Zhen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore119260 Singapore School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third-order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation LBE based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second-order (or lower-order) of accuracy in time splitting scheme as in the conventional high-order Runge-Kutta (RK) based kinetic methods, the present method solves the original BE, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows. Copyright © 2017, The Authors. All rights reserved.

关键词： Boltzmann equation

Dvelopment and application of a fully integrated model for unsaturated-saturated nitrogen reactive transport

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Agricultural Water Management 2017年 180卷 35-49页

作者： Zhu, Yan Yang, Jinzhong Ye, Ming Sun, Huaiwei Shi, Liangsheng State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University WuhanHubei430072 China Department of Scientific Computing Florida State University TallahasseeFL32306 United States School of Hydropower and Information Engineering Huazhong University of Science and Technology Wuhan430074 China

This paper presents a fully integrated model to simulate coupled unsaturated-saturated flow and reactive transport of ammonium and nitrate, the two major nitrogen species. Based on our previous work of developing a coupled model of unsaturated-saturated flow and solute transport of a single species, the key contribution of this study is to develop a new mathematical model and the new computer code for a comprehensive list of biogeochemical reactions, which are necessary for simulating nitrogen reactive transport. The computer code is verified by comparing its simulated results with those obtained using another model for a synthetic case. Model calibration and validation are conducted for two real-world cases to simulate nitrogen reactive transport. The two cases are at the experimental plot scale with the sewage water irrigation and at the field scale with the septic tank effluent infiltration, respectively. Quantitative evaluation of the numerical modeling results indicates that the new model and computer code can accurately simulate field observations of moisture content, water table elevation, and nitrogen concentration. For example, the root mean square error for simulating moisture content can be as small as 0.01. The code is computationally efficient to capture spatial and temporal trends of nitrogen concentrations at the field scale with a large number of computational nodes and time steps. The fully integrated model is a promising tool for large-scale modeling of water flow and nitrogen transformation and transport under complex conditions in agricultural and urban environments. © 2016 Elsevier B.V.

关键词： Mean square error

Slow manifolds for stochastic systems with non-Gaussian stable Lévy noise

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arXiv 2017年

作者： Yuan, Shenglan Hu, Jianyu Liu, Xianming Duan, Jinqiao Center for Mathematical Sciences Huazhong University of Sciences and Technology Wuhan430074 China School of Mathematics and Statistics Huazhong University of Sciences and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the fast variables to reduce the dimension of these coupled dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps understand long time dynamics. The approximation of slow manifolds with error estimate in distribution are also considered. Copyright © 2017, The Authors. All rights reserved.

关键词： Differential equations

Printing of highly conductive solution by alternating current electrohydrodynamic direct-write

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Journal of Physics: Conference Series 2018年第1期986卷

作者： Jiaxin Jiang Gaofeng Zheng Xiang Wang Jianyi Zheng Juan Liu Yifang Liu Wenwang Li Shumin Guo Department of Instrumental and Electrical Engineering Xiamen University Xiamen 361005 China Xiamen Key Laboratory of Optoelectronic Transducer Technology Xiamen 361005 China Fujian Key Laboratory of Universities and Colleges for Transducer Technology Xiamen 361005 China School of Mechanical and Automotive Engineering Xiamen University of Technology Xiamen 361024 China School of Mathematical Sciences Xiamen University Xiamen 361005 China Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

Electrohydrodynamic Direct-Write (EDW) is a novel technology for the printing of micro/nano structures. In this paper, Alternating Current (AC) electrical field was introduced to improve the ejection stability of jet with highly conductive solution. By alternating the electrical field, the polarity of free charges on the surface of jet was changed and the average density of charge, as well as the repulsive force, was reduced to stabilize the jet. When the frequency of AC electrical field increased, the EDW process became more stable and the shape of deposited droplets became more regular. The diameter of printed droplets decreased and the deposition frequency increased with the increase of voltage frequency. The phenomenon of corona discharge was overcome effectively as well. To further evaluate the performance of AC EDW for highly conductive solution, more NaCl was added to the solution and the conductivity was increased to 2810μs/cm. With such high conductivity, the problem of serious corona discharge could still be prevented by AC EDW, and the diameter of printed droplets decreased significantly. This work provides an effective way to accelerate industrial applications of EDW.

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Simulations of fractal star cluster formation: I. new insights for measuring mass segregation of star clusters with substructure

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arXiv 2017年

作者： Yu, Jincheng Puzia, Thomas H. Lin, Congping Zhang, Yiwei Institute of Astrophysics Pontificia Universidad Católica de Chile Av. Vicuna Mackenna 4860 Macul Santiago7820436 National Astronomical Observatories Chinese Academy of Sciences 20A Datun Road Beijing100012 Center for Mathematical Science Huazhong University of Science and Technology 1037 Luoyu Road Wuhan4370074 Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology 1037 Luoyu road Wuhan430074 School of Mathematics and Statistics Huazhong University of Science and Technology 1037 Luoyu Road Wuhan4370074

We compare the existent methods including the minimum spanning tree based method and the local stellar density based method, in measuring mass segregation of star clusters. We find that the minimum spanning tree method reflects more the compactness, which represents the global spatial distribution of massive stars, while the local stellar density method reflects more the crowdedness, which provides the local gravitational potential information. It is suggested to measure the local and the global mass segregation simultaneously. We also develop a hybrid method that takes both aspects into account. This hybrid method balances the local and the global mass segregation in the sense that the predominant one is either caused either by dynamical evolution or purely accidental, especially when such information is unknown a priori. In addition, we test our prescriptions with numerical models and show the impact of binaries in estimating the mass segregation value. As an application, we use these methods on the Orion Nebula Cluster (ONC) observations and the Taurus cluster. We find that the ONC is significantly mass segregated down to the 20th most massive stars. In contrast, the massive stars of the Taurus cluster are sparsely distributed in many different subclusters, showing a low degree of compactness. The massive stars of Taurus are also found to be distributed in the high-density region of the subclusters, showing significant mass segregation at subcluster scales. Meanwhile, we also apply these methods to discuss the possible mechanisms of the dynamical evolution of the simulated substructured star clusters. Copyright © 2017, The Authors. All rights reserved.

关键词： Numerical methods

A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media

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Procedia Computer Science 2016年 80卷 1324-1333页

作者： Huangxin Chen Shuyu Sun School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian 361005 China and King Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955-6900 Saudi Arabia King Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955-6900 Saudi Arabia

In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two- dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.

关键词： Fractured porous media two-scale discrete fracture model embedded fracture model mixed finite element method

Simulation of nitrogen transport in a surficial aquifer and estimation of nitrogen load from septic systems in the Indian River Lagoon Area, Florida

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Simulation of nitrogen transport in a surficial aquifer and ...

World Environmental and Water Resources Congress 2015: Floods, Droughts, and Ecosystems

作者： Sayemuzzaman, Mohammad Ye, Ming Zhu, Yun Hicks, Richard Shi, Liangsheng Department of Scientific Computing Florida State University United States State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan Hubei China Florida Department of Environmental Protection TallahasseeFL United States

ISBN: (数字)9780784479162

ISBN: (纸本)9780784479162

Onsite sewage treatment and disposal system (OSTDS) or septic systems, is one of the significant sources of nitrogen in groundwater and surface water, poseing serious threats to human health and the environment. The ArcGIS-based Nitrate Load Estimation Toolkit (ArcNLET) has been used to simulate nitrogen transport and estimate nitrogen load from septic systems to surface waterbodies through the surficial aquifer. It is based on a simplified conceptual model of groundwater flow and nitrogen transport. This study utilizes the ArcNLET tool for the Main-South Canal (MSC) drainage basins of Indian River County (IRC) area which discharge to the Indian River Lagoon (IRL), FL. The purpose of this study is to estimate the nitrogen load from 12,735 septic systems to the IRL and other surface waterbodies in MSC drainage basins. This study found, all the waterbodies(574 in number) including the IRL have been receiving a total nitrogen load of 13,742 lbs/yr. Twenty out of the 574 watebodies receive 50.5% (6,802 lbs/yr) of the total load. Among the 12,735 septic systems, only 358 septic systems contributed nitrogen load directly to the IRL, which is 2.01% (271 lbs/yr) of the total load. It is also found that the estimated ground water load of nitrogen to the southern drainage basin is greater than the estimated septic tank load to the main drainage basin. The estimation of nitrogen load exhibits spatial variability, which is useful to facilitate decisions on the sewering of residential areas served by OSTDS to reduce nitrogen load to the canals and the IRL. The modeling results may change when new data are available for model calibration. © 2015 ASCE.

关键词： Aquifers