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Fourth-order multiple-relaxation-time lattice Boltzmann model and equivalent finite-difference scheme for one-dimensional convection-diffusion equations

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Physical Review E 2023年第5期107卷 055305-055305页

作者： Ying Chen Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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

In this paper, we first develop a fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is used. We also perform the Chapman-Enskog analysis to recover the CDE from the MRT-LB model. Then an explicit four-level finite-difference (FLFD) scheme is derived from the developed MRT-LB model for the CDE. Through the Taylor expansion, the truncation error of the FLFD scheme is obtained, and at the diffusive scaling, the FLFD scheme can achieve the fourth-order accuracy in space. After that, we present a stability analysis and derive the same stability condition for the MRT-LB model and FLFD scheme. Finally, we perform some numerical experiments to test the MRT-LB model and FLFD scheme, and the numerical results show that they have a fourth-order convergence rate in space, which is consistent with our theoretical analysis.

关键词： Lattice-Boltzmann methods

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Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows

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Physical Review E 2023年第3期107卷 035308-035308页

作者： Xi Liu Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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 work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

关键词： Multiphase flows Lattice-Boltzmann methods Two-fluid & multi-fluid model

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Diffuse-interface lattice Boltzmann modeling of charged particle transport in Poiseuille flow

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Physical Review E 2022年第1期106卷 015306-015306页

作者： Jiao Liu Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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

In this paper, we developed a coupled diffuse-interface lattice Boltzmann method (DI-LBM) to study the transport of a charged particle in the Poiseuille flow, which is governed by the Navier-Stokes equations for fluid field and the Poisson-Boltzmann equation for electric potential field. We first validated the present DI-LBM through some classical benchmark problems, and then investigated the effect of electric field on the lateral migration of the particle in the Poiseuille flow. The numerical results show that the electric field has a significant influence on the particle migration. When an electric field in the vertical direction is applied to the charged particle initially located above the centerline of the channel, the equilibrium position of the particle would drop suddenly as the electric field is larger than a critical value. This is caused by the wall repulsion due to lubrication, the inertial lift related to shear slip, the lift owing to particle rotation, the lift due to the curvature of the undisturbed velocity profile, and the electric force. On the other hand, when an electric field in the horizontal direction is adopted, the equilibrium position of the particle would move toward the centerline of the channel with the increase of the electric field.

关键词： Electrokinetic flows Fluid-particle interactions

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Auto-ejection of liquid from a nozzle

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Physical Review E 2024年第4期109卷 045302-045302页

作者： Fang Shan Zhenhua Chai Baochang Shi 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 Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan 430074 China

Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of meniscus at nozzle exit is first derived, which can be used to analyze the critical condition for auto-ejection of liquid. Then a consistent and conservative axisymmetric lattice Boltzmann (LB) method is proposed to study the auto-ejection process of liquid jet from a nozzle. We test the LB model by conducting some simulations, and find that the numerical results agree well with the theoretical and experimental data. We further consider the effects of contraction ratio, length ratio, contact angle, and nozzle structure on the auto-ejection, and observe some distinct phenomena during the ejection process, including the deformation of meniscus, capillary necking, and droplet pinch off. Finally, the results reported in the present work may play an instructive role on the design of droplet ejectors and the understanding of jetting dynamics in microgravity environment.

关键词： Lattice-Boltzmann methods

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Electromagnetic simulations of 2D optical microring resonators using the multidomain Legendre pseudospectral time-domain method

Electromagnetic simulations of 2D optical microring resonato...

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International Conference on Applications of Electromagnetism and Student Innovation Competition Awards (AEM2C)

作者： Shih-Yung Chung Chih-Yu Wang Chun-Hao Teng Chung-Ping Chen Hung-Chun Chang Graduate Institute of Electronics Engineering and Department of Electrical Engineering National Taiwan University Taipei Taiwan Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu Taiwan Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics and Graduate Institute of Communication Engineering National Taiwan University Taipei Taiwan

The high-accuracy pseudospectral time-domain (PSTD) method is utilized to simulate electromagnetic responses of two-dimensional (2D) optical microring resonators. Besides its inherent spectral convergence in accuracy, the PSTD method using multidomain approach with curvilinear-quadrilateral subdomain partitioning possesses superior advantage in fulfilling field continuity conditions across material interfaces. And it should provide better results than the FDTD method simulations for optical waveguide resonators involving circular rings since the stair-casing approximation as often employed in the latter is avoided.

关键词： Electromagnetic waveguides Time domain analysis Finite difference methods Optical resonators Mathematical model Waveguide discontinuities Resonant frequency

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A multidomain Legendre pseudospectral frequency-domain method with penalty scheme for solving maxwell's equations

A multidomain Legendre pseudospectral frequency-domain metho...

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International Conference on Applications of Electromagnetism and Student Innovation Competition Awards (AEM2C)

作者： Chih-Yu Wang Shih-Yung Chung Chun-Hao Teng Chung-Ping Chen Hung-chun Chang Graduate Institute of Electronics Engineering and Department of Electrical Engineering National Taiwan University Taipei Taiwan Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu Taiwan Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics and Graduate Institute of Communication Engineering National Taiwan University Taipei Taiwan

A new multidomain pseudospectral frequency-domain (PSFD) method based on Legendre polynomials with a penalty scheme for studying electromagnetic wave scattering is presented. Scattered field calculation with accuracy on the order of 10 -9 is obtained for a circular plasmonic cylinder. The method is further applied to demonstrate the scattering by a dielectric rectangular cylinder with sharp corners and by multiple circular plasmonic cylinders.

关键词： Scattering Polynomials Silver Mathematical model Frequency domain analysis Dielectrics

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Rfmnet: Robust Deep Functional Maps for Unsupervised Non-Rigid Shape Correspondence

SSRN

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SSRN 2023年

作者： Hu, Ling Li, Qinsong Liu, Shengjun Yan, Dong-Ming Xu, Haojun Liu, Xinru School of Mathematics and Statistics Hunan First Normal University China Institute of Engineering Modeling and Scientific Computing Central South University China Big Data Institute Central South University China National Laboratory of Pattern Recognition Chinese Academy of Sciences China

We introduce a novel strategy to compute the functional map in the deep functional map framework, which jointly considers training stability and more geometric shape features than previous works. We directly first produce a pointwise map by resorting to optimal transport and then convert it to an initial functional map. Such a mechanism mitigates the requirements for the descriptor and avoids the training instabilities resulting from the least square solver. Then, we successfully integrate a state-of-the-art geometric regularization for further optimizing the functional map. We show our novel computing functional map module brings more stable training even under encoding the functional map with high-frequency information and faster convergence speed. Finally, an unsupervised loss is presented for penalizing the correspondence distortion of Delta functions between shapes. Experimental results demonstrate our apparent superiority in correspondence quality and generalization across various shape discretizations and different datasets compared to the state-of-the-art learning methods. © 2023, The Authors. All rights reserved.

关键词： Delta functions

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Numerical investigation of light scattering by coupled plasmonic nanospheres using a high-accuracy multidomain Legendre pseudospectral time-domain method

Numerical investigation of light scattering by coupled plasm...

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General Assembly and scientific Symposium, URSI

作者： Shih-Yung Chung Chih-Yu Wang Chun-Hao Teng Chung-Ping Chen Hung-chun Chang Graduate Institute of Electronics Engineering National Taiwan University Taipei Taiwan Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing Tung University Hsinchu Taiwan Graduate Institute of Electronics Engineering and Department of Electrical Engineering National Taiwan University Taipei Taiwan Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics and Graduate Institute of Communication Engineering National Taiwan University Taipei Taiwan

A high-numerical-accuracy multidomain Legendre pseudospectral time-domain (PSTD) method is utilized to study the three-dimensional problem of light scattering by coupled metallic nanospheres and associated plasmonic resonances. With the multidomain technique, the simulation environment is partitioned into curvilinear hexahedral subdomains that well match the geometrical profile and material interfaces, which is an essential treatment to assure numerical accuracy, in particular, in near-field calculations. Cross sections are accurately calculated for studying the effects of different sphere radii and spacings. Interactions between two silver spheres are investigated for different incident wave propagation directions and polarizations. Electric near fields at plasmon resonances are examined.

关键词： Plasmons Silver Electronic mail Scattering Educational institutions Electric fields

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Electron-phonon interaction contribution to the total energy of group IV semiconductor polymorphs: Evaluation and implications

arXiv

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arXiv 2022年

作者： Varma, Arjun Varma Ramasimha Paul, Shilpa Itale, Anup Pable, Pranav Tibrewala, Radhika Dodal, Samruddhi Yerunkar, Harshal Bhaumik, Saurav Shah, Vaishali Gururajan, Mogadalai Pandurangan Prasanna, Tiramkudlu R.S. Department of Metallurgical Engineering and Materials Science Indian Institute of Technology Bombay Mumbai400076 India Department of Mathematics Indian Institute of Technology Bombay Mumbai400076 India Department of Scientific Computing Modeling and Simulation Savitribai Phule Pune University Pune411007 India

In density functional theory (DFT) based total energy studies, the van der Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are included to obtain energy differences between polymorphs. We propose and compute a new correction term to the total energy, due to electron-phonon interactions (EPI). We rely on Allen's general formalism, which goes beyond the Quasi-Harmonic Approximation (QHA), to include the free energy contributions due to quasiparticle interactions. We show that, for semiconductors and insulators, the EPI contributions to the free energies of electrons and phonons are the corresponding zero-point energy contributions. Using an approximate version of Allen's formalism in combination with the Allen-Heine theory for EPI corrections, we calculate the zero-point EPI corrections to the total energy for cubic and hexagonal polytypes of Carbon, Silicon and Silicon Carbide. The EPI corrections alter the energy differences between polytypes. In SiC polytypes, the EPI correction term is more sensitive to crystal structure than the vdW and ZPVE terms and is thus essential in determining their energy differences. It clearly establishes that the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our results are consistent with the experimental results of Kleykamp. Our study enables the inclusion of EPI corrections as a separate term in the free energy expression. This opens the way to go beyond the QHA by including the contribution of EPI on all thermodynamic properties. © 2022, CC BY.

关键词： Silicon carbide

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The Onsager-Machlup Function as Lagrangian for the Most Probable Path of a Jump-Diffusion Process

arXiv

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arXiv 2018年

作者： Chao, Ying Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences 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

This work is devoted to deriving the Onsager-Machlup function for a class of stochastic dynamical systems under (non-Gaussian) Lévy noise as well as (Gaussian) Brownian noise, and examining the corresponding most probable paths. This Onsager-Machlup function is the Lagrangian giving the most probable path connecting metastable states for jump-diffusion processes. This is done by applying the Girsanov transformation for measures induced by jump-diffusion processes. Moreover, we have found this Lagrangian function is consistent with the result in the special case of diffusion processes. Finally, we apply this new Onsager-Machlup function to investigate dynamical behaviors analytically and numerically in several examples. These include the transitions from one metastable state to another metastable state in a double-well system, with numerical experiments illustrating most probable transition paths for various noise parameters. Copyright © 2018, The Authors. All rights reserved.

关键词： Lagrange multipliers

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