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Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues

arXiv

引用

arXiv 2022年

作者： Chai, Zhenhua Yuan, Xiaolei Shi, Baochang 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 College of Mathematics and Information Science Hebei University Baoding071002 China

In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equation (NCDE) by extending our recent unified framework of MRT-LB method [Z.H. Chai and B.C. Shi, Phys. Rev. E 102, 023306 (2020)], where a rectangular equilibrium distribution function (REDF) [J.H. Lu et al, Phil. Trans. R. Soc. A 369, 2311-2319 (2011)] on a rectangular lattice is utilized. Due to the anisotropy of discrete velocities on a rectangular lattice, the third-order moment of REDF is inconsistent with that of popular LB method, and thus the previous unified framework of MRT-LB method cannot be directly applied to the NSEs using the REDF on the rectangular rDdQq (q discrete velocities in d-dimensional space, d ≥ 1) lattice. The macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method by properly selecting the relaxation sub-matrix S2 which is related to kinetic viscosity and bulk viscosity. While the rectangular lattice does not lead to the change of the zero-th, first and second-order moments of REDF, thus the unified framework of MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, while there are no rectangular D3Q13 and D3Q15 lattices within this framework of RMRT-LB method. Thanks to the block-lower triangular-relaxation matrix introduced in the unified framework, the RMRT-LB versions (if existed) of the previous MRT-LB models can be obtained, including those based on raw (natural)-moment, central-moment, Hermite-moment, and central Hermite-moment, respectively. It is also found that when the standard or regular lattice is used, and the sound speed is taken as an adjustable parameter, the present RMRT-LB method becomes a new class of MRT-LB method for the NSEs and NCDE, and the commonly used MRT-LB

关键词： Navier Stokes equations

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Lattice QCD determination of unpolarized TMDPDFs of the nucleon 10

Lattice QCD determination of unpolarized TMDPDFs of the nucl...

引用

10th International Conference on Quarks and Nuclear Physics, QNP 2024

作者： Zhang, Qi-An He, Jin-Chen Chu, Min-Huan Hua, Jun Ji, Xiangdong Schäfer, Andreas Su, Yushan Wang, Wei Yang, Yi-Bo Zhang, Jian-Hui School of Physics Beihang University Beijing102206 China Yang Yuanqing Scientific Computering Center Tsung-Dao Lee Institute Shanghai Jiao Tong University Shanghai200240 China School of Physics and Astronomy Shanghai Jiao Tong University Shanghai200240 China Department of Physics University of Maryland College ParkMD20742 United States 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 Beijing China School of Physical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Science and Engineering The Chinese University of HongKong Shenzhen518172 China Center of Advanced Quantum Studies Department of Physics Beijing Normal University Beijing100875 China

We present a first calculation of the unpolarized nucleon’s isovector transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD, which are essential to predict observables of multi-scale, semi-inclusive processes in the standard model. We use a Nf = 2 + 1 + 1 MILC ensemble with valence clover fermions on a highly improved staggered quark (HISQ) sea to compute the quark momentum distributions in a large-momentum nucleon on the lattice. The state-of-the-art techniques in renormalization and extrapolation in the correlation distance on the lattice are adopted. The perturbative kernel up to next-to-next-to-leading order is taken into account, and the dependence on the pion mass and the hadron momentum is explored. Our results are qualitatively comparable with phenomenological TMDPDFs, which provide an opportunity to predict high energy scatterings from first principles. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).

关键词： Crystal lattices

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Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Function

arXiv

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arXiv 2021年

作者： Xiao, Nachuan Liu, Xin The Institute of Operations Research and Analytics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible, namely, are the first-order stationary points of the original optimization problem, or far from the Stiefel manifold. Besides, the original problem and ExPen share the same second-order stationary points. Remarkably, the exact gradient and Hessian of ExPen are easy to compute. As a consequence, abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen. Copyright © 2021, The Authors. All rights reserved.

关键词： Optimization

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Cell-Free Massive MIMO-OFDM for High-Speed Train Communications

arXiv

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arXiv 2022年

作者： Zheng, Jiakang Zhang, Jiayi Björnson, Emil Li, Zhetao Ai, Bo The School of Electronic and Information Engineering Beijing Jiaotong University Beijing100044 China The Department of Computer Science KTH Royal Institute of Technology Kista Sweden The Hunan International Scientific and Technological Cooperation Base of Intelligent Network Key Laboratory of Intelligent Computing & Information Processing Ministry of Education Xiangtan University Hunan411105 China The State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing100044 China

Cell-free (CF) massive multiple-input multiple-output (MIMO) systems show great potentials in low-mobility scenarios, due to cell boundary disappearance and strong macro diversity. However, the great Doppler frequency offset (DFO) leads to serious inter-carrier interference in orthogonal frequency division multiplexing (OFDM) technology, which makes it difficult to provide high-quality transmissions for both high-speed train (HST) operation control systems and passengers. In this paper, we focus on the performance of CF massive MIMO-OFDM systems with both fully centralized and local minimum mean square error (MMSE) combining in HST communications. Considering the local maximum ratio (MR) combining, the large-scale fading decoding (LSFD) cooperation and the practical effect of DFO on system performance, exact closed-form expressions for uplink spectral efficiency (SE) expressions are derived. We observe that cooperative MMSE combining achieves better SE performance than uncooperative MR combining. In addition, HST communications with small cell and cellular massive MIMO-OFDM systems are compared in terms of SE. Numerical results reveal that the CF massive MIMO-OFDM system achieves a larger and more uniform SE than the other systems. Finally, the train antenna centric (TA-centric) CF massive MIMO-OFDM system is designed for practical implementation in HST communications, and three power control schemes are adopted to optimize the propagation of TAs for reducing the impact of the DFO. Copyright © 2022, The Authors. All rights reserved.

关键词： MIMO systems

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A Stochastic Galerkin Lattice Boltzmann Method for Incompressible Fluid Flows with Uncertainties

SSRN

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SSRN 2024年

作者： Zhong, Mingliang Xiao, Tianbai Krause, Mathias J. Frank, Martin Simonis, Stephan Scientific Computing Center Karlsruhe Institute of Technology Eggenstein-Leopoldshafen76344 Germany State Key Laboratory of High Temperature Gas Dynamics Centre for Interdisciplinary Research in Fluids Institute of Mechanics Chinese Academy of Sciences Beijing100190 China School of Engineering Science University of Chinese Academy of Sciences Beijing100049 China Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76131 Germany Institute of Mechanical Process Engineering and Mechanics Karlsruhe Institute of Technology Karlsruhe76131 Germany Lattice Boltzmann Research Group Karlsruhe Institute of Technology Karlsruhe76131 Germany

Efficient modeling and simulation of uncertainties in computational fluid dynamics (CFD) remains a crucial challenge. In this paper, we present the first stochastic Galerkin (SG) lattice Boltzmann method (LBM) built upon the generalized polynomial chaos (gPC). The proposed method offers an efficient and accurate approach that depicts the propagation of uncertainties in stochastic incompressible flows. Formal analysis shows that the SG LBM preserves the correct Chapman-Enskog asymptotics and recovers the corresponding macroscopic fluid equations. Numerical experiments, including the Taylor-Green vortex flow, lid-driven cavity flow, and isentropic vortex convection, are presented to validate the solution algorithm. The results demonstrate that the SG LBM achieves the expected spectral convergence and the computational cost is significantly reduced compared to the sampling-based non-intrusive approaches, e.g., the routinely used Monte Carlo method. We obtain a speedup factor of 5.72 compared to Monte Carlo sampling in a randomized two-dimensional Taylor-Green vortex flow test case. By leveraging the accuracy and flexibility of LBM and the efficiency of gPC-based SG, the proposed SG LBM provides a powerful framework for uncertainty quantification in CFD practice. © 2024, The Authors. All rights reserved.

关键词： Computational fluid dynamics

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Study on attrition of spherical-shaped Mo/HZSM-5 catalyst for methane dehydro-aromatization in a gas–solid fluidized bed

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Chinese Journal of Chemical engineering 2021年第10期34卷 172-183页

作者： Xinzhuang Zhang Yunda Han Dapeng Li Zhanguo Zhang Xiaoxun Ma School of Chemical Engineering Northwest UniversityXi’an 710069China Research Institute of Shaanxi Yanchang Petroleum(Group)Co. Ltd.Xi’an 710065China Chemical Engineering Research Center of the Ministry of Education(MOE)for Advanced Use Technology of Shanbei Energy Xi’an 710069China Shaanxi Research Center of Engineering Technology for Clean Coal Conversion Xi’an 710069China Collaborative Innovation Center for Development of Energy and Chemical Industry in Northern Shaanxi Xi’an 710069China International Scientific and Technological Cooperation Base of the Ministry of Science and Technology(MOST)for Clean Utilization of Hydrocarbon Resources Xi’an 710069China Hydrocarbon High-efficiency Utilization Technology Research Center of Shaanxi Yanchang Petroleum(Group)Co. Ltd.Xi’an 710065China Key Laboratory on Resources Chemicals and Materials Shenyang University of Chemical TechnologyShenyang 110142China Longdong University Qingyang 745000China

As a potential methane efficient conversion process,non-oxidative aromatization of methane in fluidized bed requires a catalyst with good attrition resistance,especially in the states of high temperature,longtime rapid movement and chemical *** evaluation methods for attrition resistance,such as ASTM D5757 and Jet Cup test,are targeted for fresh catalysts at ambient temperature,which cannot well reflect the real *** this study,spherical-shaped Mo/HZSM-5 catalyst prepared by dipping and spray drying was placed in a self-made apparatus for attrition testing,in which the catalyst attrition under different system temperatures,running time and process factors was investigated with percent mass loss(PML),particle size-mass distribution(PSMD)and scanning electron microscope(SEM).Carbon deposition on the catalyst before and after activation,aromatization and regeneration was analyzed by thermogravimetry(TG),and the attrited catalysts were evaluated for methane dehydro-aromatization(MDA).The results show that the surface abrasion and body breakage of catalyst particles occur continuously,with the increase of system temperature and running time,and make the PML rise *** process factors of activation,aromatization and regeneration can cause the catalyst attrition and carbon deposits,which broaden the PSMD in varying degrees,and the carbon-substances on catalysts greatly improve their attrition resistance at high *** attrition has a certain influence on its catalytic performance,and the main reasons point to particle breakage and fine powder escape.

关键词： Attrition Mo/HZSM-5 Fluidized-bed Catalyst activation Methane dehydro-aromatization

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DENSITY CONVERGENCE OF A FULLY DISCRETE FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION

arXiv

引用

arXiv 2022年

作者： Hong, Jialin Jin, Diancong Sheng, Derui LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn-Hilliard equation driven by multiplicative space-time white noises. The main difficulty lies in the control of the drift coefficient that is neither globally Lipschitz nor one-sided Lipschitz. To handle this difficulty, we propose a novel localization argument and derive the strong convergence rate of the numerical solution to estimate the total variation distance between the exact and numerical solutions. This along with the existence of the density of the numerical solution finally yields the convergence of density in L1() of the numerical solution. Our results partially answer positively to the open problem emerged in [J. Cui and J. Hong, J. Differential Equations (2020)] on computing the density of the exact solution numerically. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite difference method

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Convergence analysis of a finite difference method for stochastic Cahn-Hilliard equation

arXiv

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arXiv 2022年

This paper presents the convergence analysis of the spatial finite difference method (FDM) for the stochastic Cahn–Hilliard equation with Lipschitz nonlinearity and multiplicative noise. Based on fine estimates of the discrete Green function, we prove that both the spatial semi-discrete numerical solution and its Malliavin derivative have strong convergence order 1. Further, by showing the negative moment estimates of the exact solution, we obtain that the density of the spatial semi-discrete numerical solution converges in L1(R) to the exact one. Finally, we apply an exponential Euler method to discretize the spatial semi-discrete numerical solution in time and show that the temporal strong convergence order is nearly 83, where a difficulty we overcome is to derive the optimal Hölder continuity of the spatial semi-discrete numerical solution. Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

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A GENERAL CLASS OF ONE-STEP APPROXIMATION FOR INDEX-1 STOCHASTIC DELAY-DIFFERENTIAL-ALGEBRAIC *EQUATIONS

引用

Journal of Computational Mathematics 2019年第2期37卷 151-169页

作者： Tingting Qin Chengjian Zhang School of Mathematics and Statistics Huazhong University of Science and Technology. Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations. The existence and uniqueness theorem of strong solutions of index-1 equations is given. A strong convergence criterion of the methods is derived, which is applicable to a series of one-step stochastic numerical methods. Some specific numerical methods, such as the Euler-Maruyama method, stochastic ^-methods, split-step ^-methods are proposed, and their strong convergence results are given. Numerical experiments further illustrate the theoretical results.

关键词： Stochastic delay differential-algebraic equations One-step discretization schemes Strong convergence

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Xdn: towards efficient inference of residual neural networks on cambricon chips 2nd

Xdn: towards efficient inference of residual neural networks...

引用

2nd International Symposium on Benchmarking, Measuring, and Optimization, Bench 2019

作者： Li, Guangli Wang, Xueying Ma, Xiu Liu, Lei Feng, Xiaobing State Key Laboratory of Computer Architecture Institute of Computing Technology Chinese Academy of Sciences Beijing China School of Computer Science and Technology University of Chinese Academy of Sciences Beijing China College of Computer Science and Technology Jilin University Changchun China MOE Key Laboratory of Symbolic Computation and Knowledge Engineering Jilin University Changchun China

ISBN: (纸本)9783030495558

In this paper, we present XDN, an optimization and inference engine for accelerating residual neural networks on Cambricon chips. We leverage a channel pruning method to compress the weights of ResNet-50. By exploring the optimization opportunities in computational graphs, we propose a layer fusion strategy, which dramatically decreases the number of scalar computation layers, such as Batch Normalization, Scale. Furthermore, we design an efficient implementation of XDN, including data preprocessing, hyper-parameter auto-tuning, etc. The experimental results show that the ResNet-50 model can achieve significant speedup without accuracy loss by using our XDN engine. © Springer Nature Switzerland AG 2020.

关键词： Engines

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