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arXiv 2024年

作者： Dutta, Tanmay Mohan, Dasari Shenoy, Saurav Attar, Nasir Kalokhe, Abhikshek Sagar, Ajay Bhure, Swapnil Pradhan, Swaroop S. Praharaj, Jitendriya Mridha, Subham Kushwaha, Anshika Shah, Vaishali Gururajan, M.P. Shenoi, V. Venkatesh Phanikumar, Gandham Bhattacharyya, Saswata Choudhury, Abhik Department of Materials Engineering Indian Institute of Science Karnataka Bangalore560012 India Department of Metallurgical and Materials Engineering IIT Madras Tamil Nadu Chennai600036 India Department of Materials Science and Metallurgical Engineering IIT Hyderabad Telangana Hyderabad502284 India Center for development of Advanced Computing Pune University Campus Maharashtra Pune411007 India Department of Metallurgical Engineering and Materials Science IIT Bombay Powai Maharashtra Mumbai400076 India Department of Scientific Computing Modeling and Simulation Savitribai Phule Pune University Maharashtra Pune411007 India

The phase-field method has become a useful tool for the simulation of classical metallurgical phase transformations as well as other phenomena related to materials science. The thermodynamic consistency that forms the basis of these formulations lends to its strong predictive capabilities and utility. However, a strong impediment to the usage of the method for typical applied problems of industrial and academic relevance is the significant overhead with regard to the code development and know-how required for quantitative model formulations. In this paper, we report the development of an open-source phase-field software stack that contains generic formulations for the simulation of multi-phase and multi-component phase transformations. The solvers incorporate thermodynamic coupling that allows the realization of simulations with real alloys in scenarios directly relevant to the materials industry. Further, the solvers utilize parallelization strategies using either multiple CPUs or GPUs to provide cross-platform portability and usability on available supercomputing machines. Finally, the solver stack also contains a graphical user interface to gradually introduce the usage of the software. The user interface also provides a collection of post-processing tools that allow the estimation of useful metrics related to microstructural evolution. © 2024, CC BY-NC-SA.

关键词： Technology transfer

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Phase-field-based lattice Boltzmann method for the transport of insoluble surfactant in two-phase flows

arXiv

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arXiv 2024年

作者： Zhan, Chengjie Liang, Hong Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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 Physics Hangzhou Dianzi University Hangzhou310018 China

In this work, we present a general second-order phase-field model for the transport of insoluble surfactant in incompressible two-phase flows. In this model, the second-order local Allen-Cahn equation is applied for interface capturing, a general form of the simple scalar transport equation [S. S. Jain, J. Comput. Phys. 515, 113277 (2024)] is adopted for interface-confined surfactant, and the consistent and conservative Navier-Stokes equations with the Marangoni force is used for fluid flows. To solve this model, we further developed a mesoscopic lattice Boltzmann (LB) method, in which the LB model for surfactant transport equation is proposed under the general LB framework for the convection-diffusion type equation, and it can correctly recover the governing equation for surfactant transport. The accuracy of the present LB method is tested by several benchmark problems, and the numerical results show it has a good performance for the transport of the insoluble surfactant in two-phase flows. © 2024, CC BY-NC-ND.

关键词： Navier Stokes equations

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EFFICIENT 3D AFFINELY EQUIVARIANT CNNS WITH ADAPTIVE FUSION OF AUGMENTED SPHERICAL FOURIER-BESSEL BASES

arXiv

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arXiv 2024年

作者： Zhao, Wenzhao Albert, Steffen Wichtmann, Barbara D. Maurer, Angelika Attenberger, Ulrike Zöllner, Frank G. Hesser, Jürgen School of Information Engineering Nanjing University of Finance and Economics Interdisciplinary Center for Scientific Computing Mannheim Institute for Intelligent Systems in Medicine Medical Faculty Mannheim Heidelberg University Germany Computer Assisted Clinical Medicine Mannheim Institute for Intelligent Systems in Medicine Medical Faculty Mannheim Heidelberg University Germany Clinic of Neuroradiology University Hospital Bonn Germany Department of Diagnostic and Interventional Radiology University Hospital Bonn Germany Department of Biomedical Imaging and Image-guided Therapy Medical University of Vienna Austria Interdisciplinary Center for Scientific Computing Central Institute for Computer Engineering CSZ Heidelberg Center for Model-Based AI Data Analysis and Modeling in Medicine Mannheim Institute for Intelligent Systems in Medicine Medical Faculty Mannheim Heidelberg University Germany

Filter-decomposition-based group equivariant convolutional neural networks (CNNs) have shown promising stability and data efficiency for 3D image feature extraction. However, these networks, which rely on parameter sharing and discrete transformation groups, often underperform in modern deep neural network architectures for processing volumetric images, such as the common 3D medical images. To address these limitations, this paper presents an efficient non-parameter-sharing continuous 3D affine group equivariant neural network for volumetric images. This network uses an adaptive aggregation of Monte Carlo augmented spherical Fourier-Bessel filter bases to improve the efficiency and flexibility of 3D group equivariant CNNs for volumetric data. Unlike existing methods that focus only on angular orthogonality in filter bases, the introduced spherical Bessel Fourier filter base incorporates both angular and radial orthogonality to improve feature extraction. Experiments on four medical image segmentation datasets show that the proposed methods achieve better affine group equivariance and superior segmentation accuracy than existing 3D group equivariant convolutional neural network layers, significantly improving the training stability and data efficiency of conventional CNN layers (at 0.05 significance level). The code is available at https://***/ZhaoWenzhao/WMCSFB. Copyright © 2024, The Authors. All rights reserved.

关键词： Spheres

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

SSRN

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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

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A Consistent and Conservative Axisymmetric Lattice Boltzmann Method for Multiphase Electro-Hydrodynamic Flows

SSRN

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SSRN 2023年

作者： Liu, Xi Chai, Zhenhua Shi, Baochang Yuan, Xiaolei School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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, a consistent and conservative mathematical model is first developed for multiphase electro-hydrodynamic (EHD) flows, which has some distinct features in the volume conservation, the consistency of reduction, and the consistency of mass-momentum transport. Then a two-relaxation-time axisymmetric lattice Boltzmann (LB) method is proposed for multiphase EHD flows, and the present LB method consists of three LB models, which are used to solve the axisymmetric reduction-consistent and conservative Allen-Cahn equation for the multiphase field, the axisymmetric Poisson equation for the electric potential, and the axisymmetric consistent and conservative Navier-Stokes equations for the flow field. Owing to the reduction-consistent property, the present LB method can be used to handle a set of M (1≤M≤N) EHD fluids in N-phase system. To test the capacity of the LB method, the deformations of a single two-phase droplet and a ternary-phase compound droplet under a uniform electric field are considered. It is found that different from a single droplet with two deformation modes, the compound droplet has four deformation modes, and additionally, the effects of the electric strength, the conductivity ratio and the permittivity ratio on the compound droplet are also investigated. Finally, the compound droplet in the quaternary-phase system is also explored, and there are eight deformation modes that have not been reported in the available literature. © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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A Consistent and Conservative Axisymmetric Lattice Boltzmann Method for Multiphase Electro-Hydrodynamic Flows

SSRN

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SSRN 2024年

关键词： Navier Stokes equations

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Phase-field based lattice Boltzmann method for containerless freezing

arXiv

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arXiv 2024年

作者： Huang, Jiangxu Wang, Lei Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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, a phase-field based lattice Boltzmann (LB) method is proposed to simulate solid-liquid phase change phenomena in multiphase systems. The method couples the thermal properties of the solidification front with the dynamics of the droplet interface, which enables the description of the complex interfacial changes during solid-liquid phase change process. The volume expansion or shrinkage of the droplet caused by the change of density during phase change is represented by adding a mass source term to the continuum equation. We first test the developed LB method by the three-phase Stefan problem and the droplet solidification on a cold surface, and the numerical results are in good agreement with the analytical and experimental solutions. Then the LB method is used to study the solidification problem with bubbles. The results show that the model can accurately capture the effect of bubbles on the solidification process, which is in good agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle. Copyright © 2024, The Authors. All rights reserved.

关键词： Freezing

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Most Probable Transition Pathways and Maximal Likely Trajectories in a Genetic Regulatory System

arXiv

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arXiv 2018年

作者： Cheng, Xiujun Wang, Hui Wang, Xiao Duan, Jinqiao Li, Xiaofan Center for Mathematical Sciences School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Statistics Henan University Kaifeng475000 China Department of Applied Mathematics Illinois Institute of Technology Chicago60616 United States School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 China

We study the most probable transition pathways and maximal likely trajectories in a genetic regulation model of the transcription factor activator’s concentration evolution, with Gaussian noise and non-Gaussian stable Lévy noise in the synthesis reaction rate taking into account, respectively. We compute the most probable transition pathways by the Onsager-Machlup least action principle, and calculate the maximal likely trajectories by spatially maximizing the probability density of the system path, i.e., the solution of the associated nonlocal Fokker-Planck equation. We have observed the rare most probable transition pathways in the case of Gaussian noise, for certain noise intensity, evolution time scale and system parameters. We have especially studied the maximal likely trajectories starting at the low concentration metastable state, and examined whether they evolve to or near the high concentration metastable state (i.e., the likely transcription regime) for certain parameters, in order to gain insights into the transcription processes and the tipping time for the transcription likely to occur. This enables us: (i) to visualize the progress of concentration evolution (i.e., observe whether the system enters the transcription regime within a given time period);(ii) to predict or avoid certain transcriptions via selecting specific noise parameters in particular regions in the parameter space. Moreover, we have found some peculiar or counter-intuitive phenomena in this gene model system, including: (a) A smaller noise intensity may trigger the transcription process, while a larger noise intensity can not, under the same asymmetric Lévy noise. This phenomenon does not occur in the case of symmetric Lévy noise;(b) The symmetric Lévy motion always induces transition to high concentration, but certain asymmetric Lévy motions do not trigger the switch to transcription. These findings provide insights for further experimental research, in order to achieve or to avoid sp

关键词： Trajectories

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The Exponential Transformation Based Lattice Boltzmann Model for Convection-Diffusion Equation

SSRN

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SSRN 2022年

作者： Zhang, Ting Cui, Shuqi Hong, Ning Shi, Baochang College of Sciences Wuhan University of Science and Technology Wuhan430081 China School of General Education Wuchang University of Technology Wuhan430223 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

In this paper, an exponential transformation based lattice Boltzmann (LB) model for solving the n -dimensional ( n D) convection-diffusion equation(CDE) is developed. Firstly, a class of exponential transformation is proposed to convert the n D CDE into a diffusion equation. Then, the converted diffusion equation is solved by the LB model. So, compared to the available LB models for CDE, the present LB model can eliminate the difficulty in treating the convection term. With the direct Taylor expansion method, it is shown that the CDE can be exactly derived from the exponential transformation based LB model. Finally, a variety of numerical tests have been conducted to validate the present LB model. It can be found that the numerical results agree well with the analytical solutions. Moreover, we also find that the present LB model has a second-order convergence rate in space, and it is more effective and more stable than the previous LB model for the CDE. © 2022, The Authors. All rights reserved.

关键词： Boltzmann equation

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Multiple-distribution-function finite-difference lattice Boltzmann method for incompressible Navier-Stokes equation

arXiv

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arXiv 2023年

作者： Chen, Xinmeng Chai, Zhenhua Zhao, Yong Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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 School of Mathematics and Statistics Changsha University of Science and Technology Hunan Changsha410114 China

In this paper, a multiple-distribution-function finite-difference lattice Boltzmann method (MDF-FDLBM) is proposed for the convection-diffusion system based incompressible Navier-Stokes equations (NSEs). By Chapman Enskog analysis, the convection-diffusion system based incompressible NSEs can be recovered from MDF-FDLBM. Some quantities, including the velocity gradient, velocity divergence, strain rate tensor, shear stress and vorticity, can be computed locally by the first-order moment of the non-equilibrium distribution function. Through the von Neumann analysis, we conduct the stability analysis for the MDF-FDLBM and incompressible finite-difference lattice Boltzmann method (IFDLBM). It is found that the IFDLBM will be more stable than that of MDF-FDLBM with small kinematic viscosity, and the MDF-FDLBM will be more stable than that of IFDLBM with large Courant-Friedrichs-Lewy condition number. Finally, some simulations are conducted to validate the MDF-FDLBM. The results agree well with the analytical solutions and previous results. Through the numerical testing, we find that the MDF-FDLBM has a second-order convergence rate in space and time. The MDF-FDLBMcombined with non-uniform grid also works well. Meanwhile, compared with IFDLBM, it can be found that MDF-FDLBM offers higher accuracy and computational efficiency, reducing computation time by more than 36%. © 2023, CC BY.

关键词： Distribution functions

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