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Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

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arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Wang, Huili Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 China 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

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

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

On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization

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On the worst-case complexity of nonlinear stepsize control a...

作者： Grapiglia, G.N. Yuan, J. Yuan, Y. Department of Mathematics Federal University of Paraná Curitiba Brazil State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

A Nonlinear Stepsize Control (NSC) framework has been proposed by Toint [Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization, *** Softw. 28 (2013), pp. 82-95] for unconstrained optimization, generalizing many trust-region and regularization algorithms. More recently, worst-case complexity bounds for the generic NSC framework were proved by Grapiglia et al. [On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization, Math. Program. 152 (2015), pp. 491-520] in the context of non-convex problems. In this paper, improved complexity bounds are obtained for convex and strongly convex objectives. © 2015 Taylor & Francis.

关键词： Optimization

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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A parallel thermal reservoir simulator on distributed-memory supercomputers

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A parallel thermal reservoir simulator on distributed-memory...

SPE Asia Pacific Oil and Gas Conference and Exhibition 2016

作者： Zhong, He Liu, Hui Cui, Tao Wang, Kun Yang, Bo Yang, Min Chen, Zhangxin Dept. of Chemical and Petroleum Engineering University of Calgary 2500 University Drive NW CalgaryAB Canada State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

ISBN: (纸本)9781510835849

This paper describes the algorithms and implementation of a parallel thermal reservoir simulator designed for heavy oil simulation using distributed-memory supercomputers that can solve prohibitive problems efficiently. The thermal simulator inherits the features of a sequential thermal simulator. The performance of supercomputers is proportional to the number of CPUs. As a result, thermal problems can be solved thousands of times faster using supercomputers. This parallel simulator is based on our in-house platform, which provides grid management, data management, linear solvers and a visualization module. The exchange of information between CPUs is achieved by using the message passing interface standard, MPI. Results indicate that this simulator exhibits excellent scalability on the IBM Blue Gene/Q system and is thousands of times faster than serial simulators on a workstation. The simulator is also capable of simulating models with billions of grid blocks and fine resolution results can be obtained. © 2016 Society of Petroleum Engineers. All rights reserved.

关键词： Simulators

DASHMM accelerated adaptive fast multipole poisson-boltzmann solver on distributed memory architecture

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arXiv 2017年

作者： Zhang, B. DeBuhr, J. Niedzielski, D. Mayolo, S. Lu, B. Sterling, T. Center for Research in Extreme Scale Technologies School of Informatics Computing and Engineering Indiana University BloomingtonIN47404 United States Department of Physics Rensselaer Polytechnic Institute TroyNY12180 United States Department of Computer Science Tennessee Technological University CookevilleTN38505 United States State Key Laboratory of Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190

We present an updated version of the AFMPB package for fast calculation of molecular solvation-free energy. The main feature of the new version is the successful adoption of the DASHMM library, which enables AFMPB to operate on distributed memory computers. As a result, the new version can easily handle larger molecules or situations with higher accuracy requirements. To demonstrate the updated code, we applied the new version to a dengue virus system with more than one million atoms and a mesh with approximately 20 million triangles, and were able to reduce the time-to-solution from 10 hours reported in the previous release on a shared memory computer to less than 30 seconds on a Cray XC30 cluster using 12, 288 cores. Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary element method

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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Uniqueness and traveling waves in a cell motility model

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arXiv 2017年

作者： Mizuhara, Matthew S. Zhang, Peng Department of Mathematics Pennsylvania State University University ParkPA16802 United States Institute of Natural Sciences Department of Mathematics Shanghai Jiao Tong University Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Ministry of Education 800 Dongchuan Road Shanghai200240 China

We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic cells on a substrate. We establish uniqueness of solutions to the sharp interface limit equation in the so-called subcritical parameter regime. The proof relies on a Grönwall estimate for a specially chosen weighted L2 norm. Next, as persistent motion of crawling cells is of central interest to biologists we study the existence of traveling wave solutions. We prove that traveling wave solutions exist in the supercritical parameter regime provided the non-linear term of the sharp interface limit equation possesses certain asymmetry (related, e.g., to myosin contractility). Finally, we numerically investigate traveling wave solutions and simulate their dynamics. Due to non-uniqueness of solutions of the sharp interface limit equation we simulate a related, singularly perturbed PDE system which is uniquely solvable. Our simulations predict instability of traveling wave solutions and capture both bipedal wandering cell motion as well as rotating cell motion;these behaviors qualitatively agree with recent experimental and theoretical *** Codes 35Q92, 35K55, 65-04 Copyright © 2017, The Authors. All rights reserved.

关键词： Cytology

Singularity formation and global existence of classical solutions for one dimensional rotating shallow water system

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arXiv 2017年

作者： Cheng, Bin Peng, Q.U. Chunjing, X.I.E. Department of Mathematics University of Surrey Guildford United Kingdom School of Mathematical Sciences Fudan University Shanghai 200433 China Department of mathematics Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing SHL-MAC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China

We study classical solutions of one dimensional rotating shallow water system which plays an important role in geophysical fluid dynamics. The main results contain two contrasting aspects. First, when the solution crosses certain threshold, we prove finite-time singularity formation for the classical solutions by studying the weighted gradients of Riemann invariants and utilizing conservation of physical energy. In fact, the singularity formation will take place for a large class of C1 initial data whose gradients and physical energy can be arbitrarily small and higher order derivatives should be large. Second, when the initial data have constant potential vorticity, global existence of small classical solutions is established via studying an equivalent form of a quasilinear Klein-Gordon equation satisfying certain null conditions. In this global existence result, the smallness condition is in terms of the higher order Sobolev norms of the initial data.2010 Mathematics Subject Classification. 35L40, 35L67, 35L72, 35Q86, 76U05. Copyright © 2017, The Authors. All rights reserved.

关键词： Equations of motion