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A Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann model for the coupled Burgers' equations

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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 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 Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensional coupled Burgers’ equations is developed. We first adopt the Cole-Hopf transformation where an intermediate variable θ is introduced to eliminate the nonlinear convection terms in the Burgers’ equations on the velocity u = (u1, u2, . . ., ud). In this case, a diffusion equation on the variable θ can be obtained, and particularly, the velocity u in the coupled Burgers’ equations is determined by the variable θ and its gradient term ∇θ. Then we develop the MRT-LB model with the natural moments for the d-dimensional transformed diffusion equation and present the corresponding macroscopic finite-difference scheme. At the diffusive scaling, the fourth-order modified equation of the developed MRT-LB model is derived through the Maxwell iteration method. With the aid of the free parameters in the MRT-LB model, we find that not only the consistent fourth-order modified equation can be obtained, but also the gradient term ∇θ with a fourth-order accuracy can be determined by the non-equilibrium distribution function, this indicates that theoretically, the MRT-LB model for d-dimensional coupled Burgers’ equations can achieve the fourth-order accuracy in space. Finally, some simulations are conducted to test the MRT-LB model, and the numerical results show that the proposed MRT-LB model has a fourth-order convergence rate, which is consistent with our theoretical analysis. Copyright © 2023, The Authors. All rights reserved.

关键词： Distribution functions

Regularized lattice Boltzmann method based maximum principle and energy stability preserving finite-difference scheme for the Allen-Cahn equation

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arXiv 2023年

The Allen-Cahn equation (ACE) inherently possesses two crucial properties: the maximum principle and the energy dissipation law. Preserving these two properties at the discrete level is also necessary in the numerical methods for the ACE. In this paper, unlike the traditionally top-down macroscopic numerical schemes which discretize the ACE directly, we first propose a novel bottom-up mesoscopic regularized lattice Boltzmann method based macroscopic numerical scheme for d (=1, 2, 3)-dimensional ACE, where the DdQ(2d+1) [(2d+1) discrete velocities in d-dimensional space] lattice structure is adopted. In particular, the proposed macroscopic numerical scheme has a second-order accuracy in space, and can also be viewed as an implicit-explicit finite-difference scheme for the ACE, in which the nonlinear term is discretized semi-implicitly, the temporal derivative and dissipation term of the ACE are discretized by using the explicit Euler method and second-order central difference method, respectively. Then we demonstrate that the proposed scheme can preserve the maximum bound principle and the original energy dissipation law at the discrete level under some conditions. Finally, some numerical experiments are conducted to validate our theoretical analysis. Copyright © 2023, The Authors. All rights reserved.

关键词： Maximum principle

A thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows

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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, a thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows is proposed. In this model, a novel free energy for the gas-liquid-solid multiphase flows is established according to a ternary phase-field model, and it not only contains the standard bulk and interface free energies for two-phase flows, but also includes some additional terms to reflect the penalty in the solid phase and the wettability on the solid surface. Furthermore, a smooth indicator function of the solid phase is also introduced in the consistent Navier-Stokes equations to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface. Based on the proposed diffuse-interface model, the fluid interface dynamics, the fluid-structure interaction, and the wetting property of the solid surface can be described simply and efficiently. Additionally, the total energy is also proved to be dissipative for the two-phase flows in the stationary geometries. To test the present diffuse-interface model, we develop a consistent and conservative lattice Boltzmann method and conduct some simulations. The numerical results also confirm the energy dissipation and good capability of the proposed diffuse-interface model in the study of two-phase flows in complex geometries and gas-liquid-particle multiphase flows. © 2023, CC BY.

关键词： Energy dissipation

The Macroscopic Finite-Difference Scheme and Modified Equations of the General Propagation Multiple-Relaxation-Time Lattice Boltzmann Model

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SSRN

SSRN 2023年

作者： Chen, Ying Chai, Zhenhua Liu, Xi 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 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. © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

Saturated feedback stabilizability to trajectories for the Schlögl parabolic equation

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arXiv 2021年

作者： Azmi, Behzad Kunisch, Karl Rodrigues, Sérgio S. Johann Radon Institute for Computational and Applied Mathematics ÖAW Altenbergerstr. 69 Linz4040 Austria Institute for Mathematics and Scientific Computing 621 Heinrichstrasse 36 Graz8010 Austria

It is shown that there exist a finite number of indicator functions, which allow us to track an arbitrary given trajectory of the Schlögl model, by means of an explicit saturated feedback control input whose magnitude is bounded by a constant independent of the given targeted trajectory. Simulations are presented showing the stabilizing performance of the explicit feedback constrained control. Further, such performance is compared to that of a receding horizon constrained control minimizing the classical energy cost *** Codes 93C20, 93D15, 93B45, 35K58 Copyright © 2021, The Authors. All rights reserved.

关键词： Feedback control

A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraints

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arXiv 2024年

作者： Wang, Lei Xiao, Nachuan Liu, Xin Department of Statistics Pennsylvania State University University ParkPA United States Institute of Operational 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 Beijing China

In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit ubiquitous in practical applications, remain unsolvable by existing algorithms in the presence of distributed constraints. To address this issue, we convert the original problem into an unconstrained penalty model by resorting to the recently proposed constraint-dissolving operator. However, this transformation compromises the essential property of separability in the resulting penalty function, rendering it impossible to employ existing algorithms to solve. We overcome this difficulty by introducing a novel algorithm that tracks the gradient of the objective function and the Jacobian of the constraint mapping simultaneously. The global convergence guarantee is rigorously established with an iteration complexity. To substantiate the effectiveness and efficiency of our proposed algorithm, we present numerical results on both synthetic and real-world datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： Optimization algorithms

Initial 24-h perfusion index of ICU admission is associated with acutekidney injury in perioperative critically ill patients: A retrospective cohortanalysis

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Journal of Intensive Medicine 2023年第3期3卷 261-267页

作者： Shengjun Liu Longxiang Su Changjing Zhuge Huaiwu He Yun Long Department of Critical Care Medicine State Key Laboratory of Complex Severe and Rare DiseasesPeking Union Medical College HospitalPeking Union MedicalCollegeChinese Academy of Medical SciencesBeijing 100730China Beijing Institute for Scientific and Engineering Computing Department of MathematicsFaculty of ScienceBeijing University of TechnologyBeijing 100124China

Background:The relationship between perfusion index(PI)and organ dysfunction in patients in the intensivecare unit(ICU)is not *** study aimed to explore the relationship between PI and renal function in theperioperative critical care setting and evaluate the predictive efficiency of PI on patients with acute kidney injury(AKI)in the ***:This retrospective analysis involved 12,979 patients who had undergone an operation and were admitted to the ICU in Peking Union Medical College Hospital from January 2014 to December *** distributionof average PI in the first 24 h after ICU admission and its correlation with AKI was calculated by Cox *** operating characteristic(ROC)curves were generated to compare the ability of PI,mean arterial pressure(MAP),creatinine,blood urea nitrogen(BUN),and central venous pressure(CVP)to discriminate AKI in thefirst 48 h in all perioperative critically ill ***:Average PI in the first 24 h served as an independent protective factor of AKI(Odds ratio[OR]=0.786,95%confidence interval[CI]:0.704–0.873,P<0.0001).With a decrease in PI by one unit,the incidence of AKIincreased 1.74 *** the variables explored for the prediction of AKI(PI,MAP,creatine,BUN,and CVP),PI yielded the highest area under the ROC curve,with a sensitivity of 64.34%and specificity of 70.14%.A cut-offvalue of PI≤2.12 could be used to predict AKI according to the Youden ***,patients in the low PIgroup(PI≤2.12)exhibited a marked creatine elevation at 24–48 h with a slower decrease compared with thosein the high PI group(PI>2.12).Conclusions:As a local blood flow indicator,the initial 24-h average PI for perioperative critically ill patients canpredict AKI during their first 120 h in the ICU.

关键词： Perfusion index Acute kidney injury Perioperative

Meson spectroscopy from spectral densities in lattice gauge theories

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Physical Review D 2024年第7期110卷 074509页

作者： Ed Bennett Luigi Del Debbio Niccolò Forzano Ryan C. Hill Deog Ki Hong Ho Hsiao Jong-Wan Lee C.-J. David Lin Biagio Lucini Alessandro Lupo Maurizio Piai Davide Vadacchino Fabian Zierler Swansea Academy of Advanced Computing Higgs Centre for Theoretical Physics School of Physics and Astronomy Department of Physics Faculty of Science and Engineering School of Physics and Astronomy Department of Physics Extreme Physics Institute Institute of Physics Particle Theory and Cosmology Group Center for Theoretical Physics of the Universe Centre for High Energy Physics Centre for Theoretical and Computational Physics Department of Mathematics Faculty of Science and Engineering Université de Toulon CNRS CPT Marseille France Centre for Mathematical Sciences

Spectral densities encode nonperturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics, observable at current colliders, as well as correlation functions characterizing new physics proposals, testable in future experiments. By making use of numerical data produced in a Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group, we perform a systematic study to demonstrate the effectiveness of recent technological progress in the reconstruction of spectral *** this purpose, we write and test new software packages that use energy-smeared spectral densities to analyze the mass spectrum of mesons. We assess the effectiveness of different smearing kernels and optimize the smearing parameters to the characteristics of available lattice ensembles. For concreteness, we analyze the Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group. We generate new ensembles for the theory in consideration, with lattices that have a longer extent in the time direction with respect to the spatial ones. We run our tests on these ensembles, obtaining new results about the spectrum of light mesons and their excitations. We make available our algorithm and software for the extraction of spectral densities, that can be applied to theories with other gauge groups, including the theory of strong interactions (QCD) governing hadronic physics in the standard model.

关键词： Hybrid Monte Carlo algorithm Lattice field theory

Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise

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arXiv 2021年

作者： Hong, Jialin Hou, Baohui Sun, Liying Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the interior penalty discontinuous Galerkin finite element method to discretize space variable and present two semi-discrete schemes, respectively. Then we make use of the discrete gradient method and the Pad'e approximation to propose efficient fully-discrete schemes. These semi-discrete and fully-discrete schemes are proved to preserve the discrete averaged energy evolution law. In particular, we also prove that the proposed fully-discrete schemes exactly inherit the averaged energy evolution law almost surely if the considered model is driven by additive noise. Numerical experiments are given to confirm theoretical findings. © 2021, CC BY.

关键词： Finite difference method