建立一维格子Boltzmann模型的演化方程,运用Taylor展开和Chapman-Enskog多尺度分析技术,推导出能够恢复一类非线性耦合的NLS-KDV方程的平衡态分布函数和修正函数。最后,数值算例验证出该方法的计算结果与给出的精确解有很好的一致性。Th...建立一维格子Boltzmann模型的演化方程,运用Taylor展开和Chapman-Enskog多尺度分析技术,推导出能够恢复一类非线性耦合的NLS-KDV方程的平衡态分布函数和修正函数。最后,数值算例验证出该方法的计算结果与给出的精确解有很好的一致性。The evolution equations of the one-dimensional lattice Boltzmann model are established, and the equilibrium distribution function and the correction function that can recover a class of nonlinearly coupled NLS-KDV equations are derived by using Taylor expansion and Chapman-Enskog multiscale analysis techniques. Finally, numerical examples verify that the computational results of the method are in good agreement with the given exact solutions.展开更多
To address the limitations of traditional finite element methods,particularly the continuum assumption and difficulties in tracking the solid-liquid interface,this study introduces a lattice Boltzmann-based mathematic...To address the limitations of traditional finite element methods,particularly the continuum assumption and difficulties in tracking the solid-liquid interface,this study introduces a lattice Boltzmann-based mathematical and physical model to simulate flow and heat transfer in the laser welding molten pool of tin-coated copper used in solar panel busbars(a thin strip or wire of conductive metal embedded on the surface of a solar cell to collect and conduct the electricity generated by the photovoltaic cell).The model incorporates key external forces,including surface tension,solid-liquid interface tension,and recoil pressure.A moving and rotating Gaussian-body heat source is adopted,with temperature treated as an implicit function of enthalpy.Coupled iterative schemes for the temperature and velocity fields are constructed using a dual-distribution function approach with a D3Q15 lattice structure.The model is implemented in Python,utilizing libraries such as NumPy,SciPy,Mayavi,and Matplotlib for computation and visualization.Simulation results reveal that the heat transfer mechanism in the molten pool transitions from pure conduction to conduction-convection due to surface tension effects,leading to the formation of multiple counter-rotating vortex structures.The peak temperature at the pool center reaches 3200 K,with maximum melt depth and width measured at 0.5 and 1.2 mm,respectively.Over time,both penetration depth and melt width increase,though the width exhibits a more pronounced growth.Comparison with experimental thermal cycling data from laser weld joints shows strong agreement,with a maximum error of less than 1%,validating the accuracy of the proposed method.展开更多
In this paper,the liquid–vapor phase separation under viscous shear is investigated by using a pseudopotential central moment lattice Boltzmann method.Physically,the multiphase shear flow is governed by two competing...In this paper,the liquid–vapor phase separation under viscous shear is investigated by using a pseudopotential central moment lattice Boltzmann method.Physically,the multiphase shear flow is governed by two competing mechanisms:surface tension and shear force.It is interesting to find that the liquid tends to form a droplet when the surface tension dominates under conditions of low temperature,shear velocity,and viscosity,and in larger domain size.Otherwise,the liquid tends to form a band if shear force dominates.Moreover,the average density gradient is used as a physical criterion to distinguish the spinodal decomposition and domain growth.Both spatial and temporal changes of density are studied during the phase separation under shear.展开更多
The Richtmyer–Meshkov(RM)instability plays an important role in various natural and engineering fields such as inertial confinement fusion.In this study,the effect of relaxation time on the RM instability under resho...The Richtmyer–Meshkov(RM)instability plays an important role in various natural and engineering fields such as inertial confinement fusion.In this study,the effect of relaxation time on the RM instability under reshock impact is investigated using a two-component discrete Boltzmann method.The hydrodynamic and thermodynamic characteristics of the fluid system are comprehensively analyzed from the perspectives of the density gradient,vorticity,kinetic energy,mixing degree,mixing width and non-equilibrium intensity.Simulation results indicate that for longer relaxation time,the diffusion and dissipation are enhanced,the physical gradients decrease,and the growth of the interface is suppressed.Furthermore,the non-equilibrium manifestations show complex patterns,driven by the competitive physical mechanisms of the diffusion,dissipation,shock wave,rarefaction wave,transverse wave and fluid instabilities.These findings provide valuable insight into the fundamental mechanism of compressible fluid flows.展开更多
文摘建立一维格子Boltzmann模型的演化方程,运用Taylor展开和Chapman-Enskog多尺度分析技术,推导出能够恢复一类非线性耦合的NLS-KDV方程的平衡态分布函数和修正函数。最后,数值算例验证出该方法的计算结果与给出的精确解有很好的一致性。The evolution equations of the one-dimensional lattice Boltzmann model are established, and the equilibrium distribution function and the correction function that can recover a class of nonlinearly coupled NLS-KDV equations are derived by using Taylor expansion and Chapman-Enskog multiscale analysis techniques. Finally, numerical examples verify that the computational results of the method are in good agreement with the given exact solutions.
基金Science and Technology Research Key Competitive Project of Quzhou Science and Technology Bureau(Nos.2023K266,2024K010)General Project for Cultivating Outstanding Young Teachers in Anhui Province’s Universities(2025).
文摘To address the limitations of traditional finite element methods,particularly the continuum assumption and difficulties in tracking the solid-liquid interface,this study introduces a lattice Boltzmann-based mathematical and physical model to simulate flow and heat transfer in the laser welding molten pool of tin-coated copper used in solar panel busbars(a thin strip or wire of conductive metal embedded on the surface of a solar cell to collect and conduct the electricity generated by the photovoltaic cell).The model incorporates key external forces,including surface tension,solid-liquid interface tension,and recoil pressure.A moving and rotating Gaussian-body heat source is adopted,with temperature treated as an implicit function of enthalpy.Coupled iterative schemes for the temperature and velocity fields are constructed using a dual-distribution function approach with a D3Q15 lattice structure.The model is implemented in Python,utilizing libraries such as NumPy,SciPy,Mayavi,and Matplotlib for computation and visualization.Simulation results reveal that the heat transfer mechanism in the molten pool transitions from pure conduction to conduction-convection due to surface tension effects,leading to the formation of multiple counter-rotating vortex structures.The peak temperature at the pool center reaches 3200 K,with maximum melt depth and width measured at 0.5 and 1.2 mm,respectively.Over time,both penetration depth and melt width increase,though the width exhibits a more pronounced growth.Comparison with experimental thermal cycling data from laser weld joints shows strong agreement,with a maximum error of less than 1%,validating the accuracy of the proposed method.
基金supported by National Natural Science Foundation of China under Grant No.51806116Guangdong Basic and Applied Basic Research Foundation under Grant No.2024A1515010927+2 种基金China Scholarship Council under Grant No.202306380288Humanities and Social Science Foundation of the Ministry of Education in China under Grant No.24YJCZH163Fundamental Research Funds for the Central Universities,Sun Yat-sen University under Grant No.24qnpy044。
文摘In this paper,the liquid–vapor phase separation under viscous shear is investigated by using a pseudopotential central moment lattice Boltzmann method.Physically,the multiphase shear flow is governed by two competing mechanisms:surface tension and shear force.It is interesting to find that the liquid tends to form a droplet when the surface tension dominates under conditions of low temperature,shear velocity,and viscosity,and in larger domain size.Otherwise,the liquid tends to form a band if shear force dominates.Moreover,the average density gradient is used as a physical criterion to distinguish the spinodal decomposition and domain growth.Both spatial and temporal changes of density are studied during the phase separation under shear.
基金supported by the National Natural Science Foundation of China(Grant No.U2242214)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2024A1515010927)+3 种基金the Humanities and Social Science Foundation of the Ministry of Education in China(Grant No.24YJCZH163)the Fujian Provincial Units Special Funds for Education and Research(Grant No.2022639)Fundamental Research Funds for the Central Universities,Sun Yatsen University(Grant No.24qnpy044)partly supported by the Open Research Fund of Key Laboratory of Analytical Mathematics and Applications(Fujian Normal University),Ministry of Education,P.R.China(Grant No.JAM2405)。
文摘The Richtmyer–Meshkov(RM)instability plays an important role in various natural and engineering fields such as inertial confinement fusion.In this study,the effect of relaxation time on the RM instability under reshock impact is investigated using a two-component discrete Boltzmann method.The hydrodynamic and thermodynamic characteristics of the fluid system are comprehensively analyzed from the perspectives of the density gradient,vorticity,kinetic energy,mixing degree,mixing width and non-equilibrium intensity.Simulation results indicate that for longer relaxation time,the diffusion and dissipation are enhanced,the physical gradients decrease,and the growth of the interface is suppressed.Furthermore,the non-equilibrium manifestations show complex patterns,driven by the competitive physical mechanisms of the diffusion,dissipation,shock wave,rarefaction wave,transverse wave and fluid instabilities.These findings provide valuable insight into the fundamental mechanism of compressible fluid flows.
