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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

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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

Three-dimensional coherent x-ray diffractive imaging from a single view

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Three-dimensional coherent x-ray diffractive imaging from a ...

作者： Sandberg, Richard L. Raines, Kevin S. Salha, Sara Jiang, Huaidong Rodríguez, Jose A. Fahimian, Benjamin P. Kapteyn, Henry C. Murnane, Margaret M. Du, Jincheng Miao, Jianwei Department of Physics JILA University of Colorado at Boulder Boulder CO 80309-0440 United States Physical Chemistry and Applied Spectroscopy Los Alamos National Laboratory Los Alamos NM 8 7545 United States Department of Physics and Astronomy California NanoSystems Institute University of of California Los Angeles CA 90095 United States Molecular Biology Institute University of California Los Angeles CA 90095 United States Department of Materials Science and Engineering Center for Advanced Scientific Computing and Modeling University of North Texas Denton TX 76203 United States

We demonstrate that high numerical aperture coherent diffractive imaging enables three-dimensional imaging from a single exposure angle under certain conditions. We demonstrate this technique, called ankylography, wit... 详细信息

ISBN: (纸本)9781557528902

关键词： X ray lasers

A stochastic pitchfork bifurcation in most probable phase portraits

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arXiv 2018年

作者： Wang, Hui Chen, Xiaoli Duan, Jinqiao Center for Mathematical Sciences School of Mathematics and Statistics Hubei Key Laboratory for Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan430074 China

We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i) When the non-Gaussianity parameter in Lévy noise varies, there is either one, two or none backward pitchfork type bifurcations;(ii) When a parameter in the vector field varies, there are two or three forward pitchfork bifurcations;(iii) The non-Gaussian Lévy noise clearly leads to fundamentally more complex bifurcation scenarios, since in the special case of Gaussian noise, there is only one pitchfork bifurcation which is reminiscent of the deterministic situation. Copyright © 2018, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

Group Projected Subspace Pursuit for Block Sparse Signal Reconstruction: Convergence Analysis and Applications

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arXiv 2024年

作者： He, Roy Y. Liu, Haixia Liu, Hao Department of Mathematics City University of Hong Kong Kowloon Tong Hong Kong School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT), Journal of Computational Physics, 494, 112526) and extend its application to general tasks of block sparse signal recovery. We prove that when the sampling matrix satisfies the Block Restricted Isometry Property (BRIP) with a sufficiently small Block Restricted Isometry Constant (BRIC), GPSP exactly recovers the true block sparse signals. When the observations are noisy, this convergence property of GPSP remains valid if the magnitude of the true signal is sufficiently large. GPSP selects the features by subspace projection criterion (SPC) for candidate inclusion and response magnitude criterion (RMC) for candidate exclusion. We compare these criteria with counterparts of other state-of-the-art greedy algorithms. Our theoretical analysis and numerical ablation studies reveal that SPC is critical to the superior performances of GPSP, and that RMC can enhance the robustness of feature identification when observations contain noises. We test and compare GPSP with other methods in diverse settings, including heterogeneous random block matrices, inexact observations, face recognition, and PDE identification. We find that GPSP outperforms the other algorithms in most cases for various levels of block sparsity and block sizes, justifying its effectiveness for general applications. © 2024, CC BY.

关键词： Face recognition

A prediction-correction based iterative convolution-thresholding method for topology optimization of heat transfer problems

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arXiv 2024年

作者： Chen, Huangxin Dong, Piaopiao Wang, Dong Wang, Xiao-Ping School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian361005 China School of Science and Engineering The Chinese University of Hong Kong Guangdong Shenzhen518172 China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data Guangdong518172 China

In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM. Copyright © 2024, The Authors. All rights reserved.

关键词： Convolution

Large contributions from optical phonons to thermal transport in hexagonal carbon-boron-nitrogen monolayers

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Physical Review B 2023年第23期108卷 235420-235420页

作者： Xue-Kun Chen (陈学坤) Yue Zhang (张越) Qing-Qing Luo (罗青清) Xue Chen (陈雪) Pin-Zhen Jia (贾聘真) Wu-Xing Zhou (周五星) School of Mathematics and Physics and Hunan Key Laboratory of Mathematical Modeling and Scientific Computing University of South China Hengyang 421001 China Department of Mathematics and Physics Hunan Institute of Technology Hengyang 421002 China School of Materials Science and Engineering and Hunan Provincial Key Laboratory of Advanced Materials for New Energy Storage and Conversion Hunan University of Science and Technology Xiangtan 411201 People's Republic of China

As representative semiconducting hexagonal carbon-boron-nitride lattices, C6BN and C2BN are experimentally realized two-dimensional (2D) plane materials and have recently become the focus of research. Herein, combining first-principles calculations with the Boltzmann transport equation, we performed a comprehensive study on the phonon interaction and thermal conductivity in C6BN and C2BN monolayers. It is found that the thermal conductivities of C6BN and C2BN monolayers at room temperature are reduced by 79% and 73%, respectively, due to four-phonon scattering, compared with the results including three-phonon scattering only. We can attribute this phenomenon to giant four-phonon scattering exclusive for the heat-carrying out-of-plane acoustic (ZA) phonons, because the reflection symmetry allows four-ZA processes much higher than three-ZA processes, and the quasiparallel behavior between the ZA and low-lying out-of-plane optical (ZO) branches contribute to a broad phase space for four-phonon scattering as well. Moreover, C6BN monolayer exhibits unusual behavior that optical phonons contribute about ∼60% to the overall thermal conductivity under the four-phonon picture, which differs from the traditional case that acoustic phonons dominate thermal conductivity. Unexpectedly, two low-lying ZO modes have as high as 38% contributions to the thermal transport at 300 K under the four-phonon picture, causing 60% contribution of optical phonon modes, apparently larger than that of the three-phonon case (15%) and many other 2D materials, also indicating the four-phonon scattering has a more significant effect on acoustic phonons than on optical phonons. This finding not only highlights insight into the nature of phonon transport, but also provides a promising strategy for manipulation of heat transport based on optical phonon modes.

关键词： Phonons Thermal conductivity Boron nitride Graphene First-principles calculations Lattice-Boltzmann methods

ASYMPTOTIC BEHAVIOR OF THE PRINCIPAL EIGENVALUE OF A LINEAR SECOND ORDER ELLIPTIC OPERATOR WITH LARGE ADVECTION AND GENERAL BOUNDARY CONDITIONS

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arXiv 2023年

作者： Peng, Rui Zhang, Guanghui Zhou, Maolin School of Mathematical Sciences Zhejiang Normal University Zhejiang Jinhua321004 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 Chern Institute of Mathematics and LPMC Nankai University Tianjin300071 China

Consider the eigenvalue problem of a linear second order elliptic operator: − D∆ − 2α∇m(x) · ∇ + V (x) = λ in Ω, complemented by the Dirichlet boundary condition or the following general Robin boundary condition: (Formula Presented) is a bounded smooth domain, n(x) is the unit exterior normal to ∂Ω at x ∈ ∂Ω, D > 0 and α > 0 are, respectively, the diffusion and advection coefficients, m ∈ C2(Ω), V ∈ C(Ω), β ∈ C(∂Ω) are given functions, and β allows to be positive, sign-changing or negative. In [41], the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as D → 0 or D → ∞ was studied. In this paper, when N ≥ 2, under proper conditions on the advection function m, we establish the asymptotic behavior of the principal eigenvalue as α → ∞, and when N = 1, we obtain a complete characterization for such asymptotic behavior provided m0 changes sign at most finitely many times. Our results complement or improve those in [4, 7, 44] and also partially answer some questions raised in [4]. © 2023, CC0.

关键词： Advection

Deepstsnet: Reconstructing the Quantum State-Resolved Thermochemical Nonequilibrium Flowfield Using Deep Neural Operator Learning With Scarce Data

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SSRN

SSRN 2023年

作者： Lv, Jiaqi Hong, Qizhen Wang, Xiaoyong Mao, Zhiping Sun, Quanhua State Key Laboratory of High Temperature Gas Dynamics Institute of Mechanics Chinese Academy of Sciences Beijing100190 China School of Engineering Science University of Chinese Academy of Sciences Beijing100049 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen361005 China

The hypersonic flow is in a thermochemical nonequilibrium state due to the high-temperature caused by the strong shock compression. In a thermochemical nonequilibrium flow, the distribution of molecular internal energy levels strongly deviates from the equilibrium distribution (i.e., the Boltzmann distribution). It is intractable to directly obtain the microscopic nonequilibrium distribution from existed experimental measurements usually described by macroscopic field variables such as temperature or velocity. Motivated by the idea of deep multi-scale multi-physics neural network (DeepMMNet) proposed in [Mao et al, J. Comput. Phys., 2021], we develop in this paper a data assimilation framework called DeepStSNet to accurately reconstruct the quantum state-resolved thermochemical nonequilibrium flowfield by using sparse experimental measurements of vibrational temperature and pre-trained deep neural operator networks (DeepONets). In particular, we first construct several DeepONets to express the coupled dynamics between field variables in the thermochemical nonequilibrium flow and to approximate the state-to-state (StS) approach, which traces the variation of each vibrational level of molecule accurately. These proposed DeepONets are then trained by using the numerical simulation data, and would later be served as building blocks for the DeepStSNet. We demonstrate the effectiveness and accuracy of DeepONets with different test cases showing that the density and energy of vibrational groups as well as the temperature and velocity fields are predicted with high accuracy. We then extend the architectures of DeepMMNet by considering a simplified thermochemical nonequilibrium model, i.e., the 2T model, showing that the entire thermochemical nonequilibrium flowfield is well predicted by using scattered measurements of full or even partial field variables. We next consider a more accurate and complex thermochemical nonequilibrium model, i.e., the StS-CGM model, and develop a

关键词： Multiphysics

The macroscopic finite-difference scheme and modified equations of the general propagation multiple-relaxation-time lattice Boltzmann model

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arXiv 2023年

作者： Chen, Ying Liu, Xi Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Organization Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Organization Hubei Wuhan430074 China

In this paper, we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations (MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation (NACDE) and Navier-Stokes equations (NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, two benchmark problems, Gauss hill problem and Poiseuille flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results are not only in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations