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A Phase-Field-Based Multiple-Relaxation-Time Lattice Boltzmann Method for Incompressible Multiphase Flows with Density and Viscosity Contrasts

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SSRN

SSRN 2022年

作者： Yuan, Xiaolei Wu, Yao Zhang, Chunhua Chai, Zhenhua Shi, Baochang College of Mathematics and Information Science Hebei University Baoding071002 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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 Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Guangdong Shenzhen518055 China

In this work, we present a unified framework of phase-field-based multiple-relaxation-time lattice Boltzmann (MRT-LB) method for incompressible multiphase flows with density and viscosity contrasts where a block-lower-triangular relaxation matrix is introduced. The present framework includes the classic MRT-LB model and central-moments-based LB model (CLBM, a particular version of the MRT-LB model). The governing equations of incompressible multiphase flows can be reproduced precisely through the direct Taylor expansion method at the second-order of expansion parameters. In this work, the pressure $p$ is re-estimated, and we prove that the present pressure expression is suitable for classic MRT model, CLBM and various lattice structures. In addition, theoretical analysis and modeling are both carried out in the velocity space. As a result, the present model has a similar structure to the traditional Bhatnagar-Gross-Krook (BGK) model and is very easy to analyze and implement. We then test the present model (mainly CLBM) by five classic physical problems. The results show that the present model is found to be accurate and has better numerical stability over the BGK model, and has the ability to simulate multiphase flow problems with large density ratio ($1000$). © 2022, The Authors. All rights reserved.

关键词： Multiphase flow

A parallel scalable domain decomposition preconditioner for elastic crack simulation using XFEM

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arXiv 2021年

作者： Tian, Wei Jingjing, Huang Chen, Rongliang Jiang, Yi Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen518055 China Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen518055 China Department of Rehabilitation Medicine Shenzhen University General Hospital Shenzhen518055 China

In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the computational mesh into two types of subdomains: the regular subdomains and the crack tip subdomains based on the observation that the crack tips have a significant impact on the convergence of the iterative method while the impact of the crack lines is not that different from those of regular mesh points. The tip subdomains consist of mesh points at crack tips and all neighboring points where the branch enrichment functions are applied. The regular subdomains consist of all other mesh points, including those on the crack lines. To overcome the mismatch between the number of subdomains and the number of processor cores, the proposed method is divided into two steps: solve the crack tip problem and then the regular subdomain problem during each iteration. The proposed method was used to develop a parallel XFEM package which is able to test different types of iterative methods. To achieve good parallel efficiency, additional methods were introduced to reduce communication and to maintain the load balance between processors. Numerical experiments indicate that the proposed method significantly reduces the number of iterations and the total computation time compared to the classical methods. In addition, the method scales up to 8192 processor cores with over 70% parallel efficiency to solve problems with more than 2 × 108 degrees of freedom. Copyright © 2021, The Authors. All rights reserved.

关键词： Crack tips

Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel

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arXiv 2023年

作者： Chu, Min-Huan He, Jin-Chen Hua, Jun Liang, Jian Ji, Xiangdong Schäfer, Andreas Shu, Hai-Tao Su, Yushan Walter, Lisa Wang, Wei Wang, Ji-Hao Yang, Yi-Bo Zeng, Jun Zhang, Qi-An INPAC Shanghai Key Laboratory for Particle Physics and Cosmology Key Laboratory for Particle Astrophysics and Cosmology MOE School of Physics and Astronomy Shanghai Jiao Tong University Shanghai200240 China Yang Yuanqing Scientific Computering Center Tsung-Dao Lee Institute Shanghai Jiao Tong University Shanghai200240 China Department of Physics University of Maryland College ParkMD20742 United States Key Laboratory of Atomic and Subatomic Structure and Quantum Control MOE Institute of Quantum Matter South China Normal University Guangzhou510006 China Guangdong Provincial Key Laboratory of Nuclear Science Institute of Quantum Matter South China Normal University Guangzhou510006 China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Southern Nuclear Science Computing Center South China Normal University Guangzhou510006 China Institut für Theoretische Physik Universität Regensburg RegensburgD-93040 Germany Institute of Modern Physics Chinese Academy of Sciences Guangdong Province Huizhou516000 China CAS Key Laboratory of Theoretical Physics Institute of Theoretical Physics Chinese Academy of Sciences Beijing100190 China School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced Study UCAS Hangzhou310024 China International Centre for Theoretical Physics Asia-Pacific Hangzhou Beijing China School of Physical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Physics Beihang University Beijing102206 China

We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudo-scalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton. Copyright © 2023, The Authors. All rights reserved.

关键词： Wave functions

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

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Applied Mathematics and Mechanics(English Edition) 2019年第2期40卷 215-236页

作者： Le FANG Hongkai ZHAO Weidan NI Jian FANG Lipeng LU Laboratoire de Mecanique Physique (LMP) Ecole Centrale de P'ekinBeihang University National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics School of Energy and Power Engineering Beihang University Scientific Computing Department Science and Technology Facilities Council (STFC)Daresbury Laboratory

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.

关键词： non-equilibrium turbulence backward ramp direct numerical simulation(DNS)

A DECOUPLING TWO-GRID METHOD FOR THE STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS

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Journal of Computational Mathematics 2019年第4期37卷 556-578页

作者： Ying Yang Benzhuo Lu Yan Xie School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing the National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.

关键词： Poisson-Nernst-Planck equations Two-grid finite element method Decoupling method Error analysis Gummel iteration

Prediction of multi-parameters in the inverse heat conduction problems

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Prediction of multi-parameters in the inverse heat conductio...

2020 International Conference on Physics, Mechanics and Mathematical Science, PMMS 2020

作者： Abdelhamid, Talaat Chen, Rongliang Alam, Mahbub Shenzhen Institutes of Advanced Technology Chinese Academy of Science Shenzhen China Institute for Turbulence-Noise-Vibration Interaction and Control Shenzhen Graduate School Harbin Institute of Technology Shenzhen China Physics and Mathematical Engineering Department Faculty of Electronic Engineering Menoufiya University Menouf Egypt Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen China

This paper studies the prediction of the spatial-dependent-heat transfer coefficient γ(x) and- heat flux q(x), using the modified conjugate gradient method (MCGM). The mathematical formulation of the problem well defined and the existence of the minimizer is investigated. We establish the sensitivity and adjoint equations for computing the gradient with respect to γ(x) and q(x). The proposed algorithm 4.1 is derived for reconstructing γ(x) and q(x) using the MCGM. The numerical experiments are examined to show the efficiency and accuracy of the proposed method. Finally, some conclusions and remarks are given. © Published under licence by IOP Publishing Ltd.

关键词： Conjugate gradient method

Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

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arXiv 2020年

作者： Ma, Ganggang Xu, Jie Liu, Ya-Feng Vedady Moghadam, Mohammad R. Shenzhen China Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China TransferFi Pte Ltd Singapore

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the nonlinear radio frequency (RF) to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the "convex-concave" shape of the RF-DC power relation at ERs. By considering a particular time duration for WPT, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation. In order to solve the non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy harvesting

Multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: Modeling, analysis, and elements

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Physical Review E 2020年第2期102卷 023306-023306页

作者： Zhenhua Chai (柴振华) Baochang Shi (施保昌) School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China and Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this paper, we first present a unified framework of multiple-relaxation-time lattice Boltzmann (MRT-LB) method for the Navier-Stokes and nonlinear convection-diffusion equations where a block-lower-triangular-relaxation matrix and an auxiliary source distribution function are introduced. We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion, and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes and nonlinear convection-diffusion equations from the MRT-LB method and show that from mathematical point of view, these four analysis methods can give the same equations at the second-order of expansion parameters. Finally, we give some elements that are needed in the implementation of the MRT-LB method and also find that some available LB models can be obtained from this MRT-LB method.

关键词： Lattice-Boltzmann methods

Spiking hierarchy in an adaptive exponential integrate-and-fire network synchronization

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arXiv 2021年

作者： Wu, Xiaoyue Lin, Congping Zhang, Yiwei School of Mathematics and Statistics Huazhong University of Sciences and Technology Wuhan China Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China

Neuronal network synchronization has received wide interests. Network connection structure is known to play a key role in its synchronization. In the present manuscript, we study the influence of initial membrane potentials together with network topology on bursting synchronization, in particular the sequential spiking order in stabilized inter bursts. We find a hierarchical phenomenon on spiking order. We grade neurons into different layers: Primary neurons are those initiate the spike and lower-layer neurons are then determined via network connections successively. This constructs a directed graph to indicate spiking propagation among different layers of neurons. Neurons in upper layers spike earlier than those in lower layers. More interestingly, we find that among the same layer, neuron spiking order is mainly associated with stimuli they receive from upper layer via network connections;more stimuli leads to earlier spiking. Furthermore, we find that with effectively the same stimuli from upper layer, neurons with less connections spike earlier. © 2021, CC BY.

关键词： Neurons