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A finite-difference lattice Boltzmann model with second-order accuracy of time and space for incompressible flow

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arXiv 2019年

作者： Chen, Xinmeng Chai, Zhenhua Wang, Huili Shi, Baochang 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 School of Mathematics and Computer Science Wuhan Textile University Wuhan430073 China

In this paper, a kind of finite-difference lattice Boltzmann method with the second-order accuracy of time and space (T2S2-FDLBM) is proposed. In this method, a new simplified two-stage fourth order time-accurate discretization approach is applied to construct time marching scheme, and the spatial gradient operator is discretized by a mixed difference scheme to maintain a second-order accuracy both in time and space. It is shown that the previous finite-difference lattice Boltzmann method (FDLBM) proposed by Guo [1] is a special case of the T2S2-FDLBM. Through the von Neumann analysis, the stability of the method is analyzed and two specific T2S2-FDLBMs are discussed. The two T2S2-FDLBMs are applied to simulate some incompressible flows with the nonuniform grids. Compared with the previous FDLBM and SLBM, the T2S2-FDLBM is more accurate and more stable. The value of the Courant-Friedrichs-Lewy condition number in our method can be up to 0.9, which also significantly improves the computational efficiency. Copyright © 2019, The Authors. All rights reserved.

关键词： Incompressible flow

Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations

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arXiv 2019年

作者： Shang, Jinlong Chai, Zhenhua Wang, Huili Shi, Baochang 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 School of Mathematics and Computer Science Wuhan Textile University Wuhan430073 China

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and find that the numerical results are in good agreement with analytical solutions and the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, DUGKS can also adopt the nonuniform mesh. Besides, we performed some comparisons among the DUGKS, finite-volume lattice Boltzmann model (FV-LBM), single-relaxation-time lattice Boltzmann model (SLBM) and multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the DUGKS model is more accurate than FV-LBM, more stable than SLBM, and almost has the same accuracy as the MRT-LBM. Besides, the using of non-uniform mesh may make DUGKS model more flexible. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite volume method

Computationally efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

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Physical Review E 2021年第4期103卷 043303-043303页

作者： Yuemin Ding Jin-Long Liu Xiaohui Li Yu-Chu Tian Zu-Guo Yu Department of Energy and Process Engineering Norwegian University of Science and Technology 7049 Trondheim Norway School of Computer Science Queensland University of Technology Brisbane QLD 4000 Australia Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China School of Information Science and Engineering Wuhan University of Science and Technology Wuhan Hubei 430081 China

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

关键词： Network formation & growth Fractals Fractal dimension characterization

A diffuse-interface lattice Boltzmann method for fluid-particle interaction problems

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arXiv 2021年

作者： Liu, Jiao Huang, Changsheng Chaia, Zhenhua Shia, 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 Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this paper, a diffuse-interface lattice Boltzmann method (DI-LBM) is developed for fluid-particle interaction problems. In this method, the sharp interface between the fluid and solid is replaced by a thin but nonzero thickness transition region named diffuse interface, where the physical variables varies continuously. In order to describe the diffuse interface, we introduce a smooth function, which is similar to the order parameter in phase-field model or the volume fraction of solid phase in the partially saturated lattice Boltzmann method (PS-LBM). In addition, to depict the fluid-particle interaction more accurately, a modified force term is also proposed and included in the evolution equation of the DI-LBM. Some classical problems are used to test the DI-LBM, and the results are in good agreement with some available theoretical and numerical works. Finally, it is also found that the DI-LBM is more efficient and accurate than the PS-LBM with the superposition model. © 2021, CC BY.

关键词： Kinetic theory

A multiple-relaxation-time lattice boltzmann model based four-level finite-difference scheme for one-dimensional diffusion equation

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arXiv 2020年

作者： Lin, Yuxin Hong, Ning Shi, Baochang Chai, Zhenhua School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China School of General Education Wuchang University of Technology Wuhan430223 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient ω0 and the relaxation parameters s1 and s2 corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations, and find that the numerical results are consistent with our theoretical analysis. © 2020, CC BY.

关键词： Finite difference method

A ternary phase-field model for two-phase flows in complex geometries

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arXiv 2023年

作者： Zhan, Chengjie 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

In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn-Hilliard model is considered as the solid phase, and only one Cahn-Hilliard equation with degenerate mobility needs to be solved due to the condition of volume conservation, which is consistent with the standard phase-field model with a single-scalar variable for two-phase flows. To depict different wetting properties at the complex fluid-solid boundaries, the spreading parameters in ternary phase-field model are determined based on the Young's law, in which the liquid-solid surface tension coefficient is assumed to be a linear function of gas-liquid surface tension coefficient and related to the contact angle and the minimum curvature of the solid surface. In addition, to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface, the phase-field variable of the solid phase is also used to derive the modified Navier-Stokes equations. To test the present model, we further develop a consistent and conservative Hermite-moment based lattice Boltzmann method where an adjustable scale factor is introduced to improve the numerical stability, and conduct the numerical simulations of several benchmark problems. The results illustrate that present model has the good capability in the study of the two-phase flows in complex geometries. © 2023, CC BY.

关键词： Two phase flow

The optimal displacement of immiscible two-phase fluids in a pore doublet

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arXiv 2022年

作者： Shan, Fang Chai, Zhenhua Shi, Baochang Zhao, Meng 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

The displacement of multiphase fluid flow in a pore doublet is a fundamental problem, and is also of importance in understanding of the transport mechanisms of multiphase flows in the porous media. During the displacement of immiscible two-phase fluids in the pore doublet, the transport process is not only influenced by the capillary and viscous forces, but also affected by the channel geometry. In this paper, we first present a mathematical model to describe the two-phase fluid displacement in the pore doublet where the effects of capillary force, viscous force and the geometric structure are included. Then we derive an analytical solution of the model for the first time, and find that the displacement process is dominated by the capillary number, the viscosity ratio and the radius ratio. Furthermore, we define the optimal displacement that the wetting fluids in two daughter channels break through the branches simultaneously (both of them have the same breakthrough time), and also obtain the critical capillary number corresponding to the optimal displacement, which is related to the radius ratio of two daughter channels and viscosity ratio of two immiscible fluids. Finally, it is worthy noting that the present analytical results on the displacement in the pore doublet can be used to explain and understand the phenomenon of preferential imbibition or preferential flow in porous media. © 2022, CC BY.

关键词： Porous materials

A unified fourth-order Bhatnagar-Gross-Krook lattice Boltzmann model for high-dimensional linear hyperbolic equations

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arXiv 2024年

作者： Chen, Ying 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

In this work, we first develop a unified Bhatnagar-Gross-Krook lattice Boltzmann (BGK-LB) model for the d(d ≥ 1)-dimensional linear hyperbolic equation (L-HE), where the natural moments and the DdQ(2d2 + 1) [(2d2 + 1) discrete velocities in d-dimensional space] lattice structure are considered. Subsequently, at the acoustic scaling, we conduct an accuracy analysis on the developed BGK-LB model by the direct Taylor expansion (DTE) method, and present the second- and third-order moments of the equilibrium distribution functions (EDFs) to ensure that the BGK-LB model can be fourth-order consistent with the L-HE. And on this basis, when considering the Dirichlet boundary condition, the fourth-order full-way and half-way boundary schemes are proposed to approximate the unknown distribution functions to ensure that the BGK-LB model can be overall fourth-order accurate. Thereafter, based on the kinetic entropy theory, we derive the conditions that the fourth-order moments of the EDFs should satisfy to ensure the microscopic entropy stability of the BGK-LB model. In addition, with the aid of the von Neumann stability analysis, we also discuss the L2 stability of the BGK-LB model and numerically plot the stability regions. In particular, from a numerical perspective, we find that the region of microscopic entropy stability is identical to that of L2 stability. Finally, we carry out some numerical experiments to test the accuracy and stability of the BGK-LB model, and the numerical results are in agreement with our theoretical analysis. In addition, we compare the developed full-way and half-way boundary schemes for the Dirichlet boundary condition, which shows that the full-way boundary scheme is more stable. Copyright © 2024, The Authors. All rights reserved.

关键词： Entropy

A comparative study of two Allen-Cahn models for immiscible N-phase flows by using a consistent and conservative lattice Boltzmann method

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arXiv 2023年

作者： Zhan, Chengjie Liu, Xi 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

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [Model A: Zheng et al., Phys. Rev. E 101, 0433202 (2020) and Model B: Mirjalili and Mani, (2023)] for the immiscible N-phase flows. Mathematically, these two AC equations can be proved to be equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considered numerically. To this end, we propose a consistent and conservative lattice Boltzmann method for the AC models for N-phase flows, and present some numerical comparisons of accuracy and stability between these two AC models. The results show that both two AC models have good performances in accuracy, but the Model B is more stable for the realistic complex N-phase flows, although there is an adjustable parameter in the Model A. © 2023, CC BY-NC-ND.

关键词： Kinetic theory