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Clustering solver for displacement-based numerical homogenization

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Theoretical & Applied Mechanics Letters 2022年第3期12卷 207-212页

作者： Shaoqiang Tang Xi Zhu hedps CAPT and LTCSCollege of EngineeringPeking UniversityBeijing 100871China

Based on strain-clustering via k-means,we decompose computational domain into clusters of possibly disjoint *** cells in each cluster take the same strain,we reconstruct displacement *** further propose a new way to condensate the governing equations of displacement-based finite element method to reduce the complexity while maintain the *** examples are presented to illustrate the efficiency of the clustering *** convergence studies are performed for the *** complexities which is common in existing clustering analysis methods,the proposed clustering solver is easy to implement,particularly for numerical homogenization using commercial softwares.

关键词： Clustering Finite element method Numerical homogenization

Numerical comparison of three stochastic methods for nonlinear PN junction problems

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Frontiers of Mathematics in China 2014年第3期9卷 659-698页

作者： Wenqi YAO Tiao LU School of Mathematical Sciences Peking University Beijing 100871 China hedps CAPT and LMAM Peking University Beijing 100871 China

We apply the Monte Carlo, stochastic Galerkin, and stochastic collocation methods to solving the drift-diffusion equations coupled with the Poisson equation arising in semiconductor devices with random rough surfaces. Instead of dividing the rough surface into slices, we use stochastic mapping to transform the original deterministic equations in a random domain into stochastic equations in the corresponding deterministic domain. A finite element discretization with the help of AFEPack is applied to the physical space, and the equations obtained are solved by the approximate Newton iterative method. Comparison of the three stochastic methods through numerical experiment on different PN junctions are given. The numerical results show that, for such a complicated nonlinear problem, the stochastic Galerkin method has no obvious advantages on efficiency except accuracy over the other two methods, and the stochastic collocation method combines the accuracy of the stochastic Galerkin method and the easy implementation of the Monte Carlo method.

关键词： Stochastic partial differential equation stochastic Galerkin method stochastic collocation method Monte Carlo method

AnAdaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

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Communications in Computational Physics 2012年第1期11卷 114-146页

作者： Peng He Huazhong Tang hedps CAPT&LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871China

This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)*** algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration *** the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing *** second part is an iterative *** each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative *** numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

关键词： Adaptive moving mesh method finite volume method conservative interpolation relativistic hydrodynamics

ARobust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 212-250页

作者： Ruo Li Yanli Wang Chengbao Yao hedps&capt LMAM&School of Mathematical SciencesPeking UniversityBeijingChina College of Engineering Peking UniversityBeijingChina School of Mathematical Sciences Peking UniversityBeijingChina and Northwest Institute of Nuclear TechnologyXi’anShaanxi 710024China

We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between the fluid and solid in the case of phase *** hydrostatic components of the solid is described by a family of general Mie-Gruneisen equation of state(EOS),while the deviatoric component includes the elastic phase,linearly hardened plastic phase and fluid *** approximate solver provides the interface stress and normal velocity by an iterative *** well-posedness and convergence of our solver are proved with mild assumptions on the equations of *** proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian *** numerical examples,including Riemann problems,shock-bubble interactions,implosions and high speed impact applications,are presented to validate the approximate solver.

关键词： Riemann solver Mie-Gruneisen hydro-elastoplastic solid multi-medium flow

Surface-charge-governed electrolyte transport in carbon nanotubes

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Chinese Physics B 2015年第8期24卷 480-486页

作者：薛建明郭鹏盛倩 State Key Laboratory of Nuclear Physics and Technology School of Physics Peking University capt HEDPS and IFSA Collaborative Innovation Center of Mo E Peking University

The transport behavior of pressure-driven aqueous electrolyte solution through charged carbon nanotubes(CNTs) is studied by using molecular dynamics simulations. The results reveal that the presence of charges around the nanotube can remarkably reduce the flow velocity as well as the slip length of the aqueous solution, and the decreasing of magnitude depends on the number of surface charges and distribution. With 1-M KCl solution inside the carbon nanotube, the slip length decreases from 110 nm to only 14 nm when the number of surface charges increases from 0 to 12 e. This phenomenon is attributed to the increase of the solid–liquid friction force due to the electrostatic interaction between the charges and the electrolyte particles, which can impede the transports of water molecules and electrolyte ions. With the simulation results,we estimate the energy conversion efficiency of nanofluidic battery based on CNTs, and find that the highest efficiency is only around 30% but not 60% as expected in previous work.

关键词： efficiency surface charge slip

Generation and regulation of electromagnetic pulses generated by femtosecond lasers interacting with multitargets

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Nuclear Science and Techniques 2024年第1期35卷 96-107页

作者： Ya-Dong Xia De-Feng Kong Qiang-You He Zhen Guo Dong-Jun Zhang Tong Yang Hao Cheng Yu-Ze Li Yang Yan Xiao Liang Ping Zhu Xing-Long Xie Jian-Qiang Zhu Ting-Shuai Li Chen Lin Wen-Jun Ma Xue-Qing Yan State Key Laboratory of Nuclear Physics and Technology and Key Laboratory of HEDP of the Ministry of EducationCAPTPeking UniversityBeijing 100871China Beijing Laser Acceleration Innovation Center Beijing 101407China Institute of Guangdong Laser Plasma Technology Guangzhou 510540China National Laboratory on High Power Laser and Physics Shanghai Institute of Optics and FineChinese Academy of SciencesShanghai 201800China School of Materials and Energy University of Electronic Science and Technology of ChinaChengdu 611731China

Ultrashort and powerful laser interactions with a target generate intense wideband electromagnetic pulses(EMPs).In this study,we report EMPs generated by the interactions between petawatt(30 fs,1.4×10^(20) W/cm^(2))femtosecond(fs)lasers with metal flat,plastic flat,and plastic nanowire-array(NWA)*** analyses are conducted on the EMPs in terms of their spatial distribution,time and frequency domains,radiation energy,and *** results indicate that EMPs from metal targets exhibit larger amplitudes at varying angles than those generated by other types of targets and are enhanced significantly for NWA *** a plastic target holder and increasing the laser focal spot can significantly decrease the radiation energy of the ***,the composite shielding materials indicate an effective shielding effect against *** simulation results show that the NWA targets exert a collimating effect on thermal electrons,which directly affects the distribution of *** study provides guidance for regulating EMPs by controlling the laser focal spot,target parameters,and target rod material and is beneficial for electromagnetic-shielding design.

关键词： Electromagnetic pulses Laser plasma interaction Electromagnetic shielding Electron distribution

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

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Applied Mathematics and Mechanics(English Edition) 2016年第11期37卷 1441-1466页

作者： Kailiang WU Huazhong TANG LMAM School of Mathematical Sciences Peking University hedps CAPT & LMAM School of Mathematical SciencesPeking University School of Mathematics and Computational Science Xiangtan University

A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.

关键词： Newton method multigrid block symmetric Gauss-Seidel shallow waterequation (SWE) steady-state solution

A High-Order Accurate Gas-Kinetic Scheme for One-and Two-Dimensional Flow Simulation

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Communications in Computational Physics 2014年第4期15卷 911-943页

作者： Na Liu Huazhong Tang hedps CAPT&LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871P.R.China

This paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one-and two-dimensional flow simulations,which is an extension of the third-order accurate gas-kinetic scheme[***,***,and ***,***.,229(2010),6715-6731]and the second-order accurate gas-kinetic scheme[***,***.,171(2001),289-335].It is formed by two parts:quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux *** first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the“initial”cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell *** is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic *** generalized moment limiter is employed there to suppress the possible numerical *** the second part,the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level,*** transport and the Bhatnagar-Gross-Krook(BGK)*** other words,the fourth-order flux evolution is based on the solution(*** particle velocity distribution function)of the BGK model for the Boltzmann *** 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic *** comparing with the exact solutions or the numerical solutions obtained the secondorder or third-order accurate gas-kinetic scheme,the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows,and the accuracy of the high-order GKS depends on the choice of the(numerical)collision time.

关键词： Gas-kinetic scheme initial reconstruction BGK model Boltzmann equation velocity distribution function

Robust a Simulation for Shallow Flows with Friction on Rough Topography

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Numerical Mathematics(Theory,Methods and Applications) 2013年第2期6卷 384-407页

作者： Jian Deng Ruo Li Tao Sun Shuonan Wu School of Mathematical Sciences Peking UniversityBeijing 100871China hedps&capt LMAM&School of Mathematical SciencesPeking UniversityBeijing 100871China Reservoir Characterization Division ExxonMobil Upstream Research Company P.O.Box 2189 HoustonTexas 77252USA

In this paper,we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough *** major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface *** analytical integration method is presented for the friction force term to remove the *** the vicinity of wet/dry interface,the numerical stability can be attained by introducing an empirical parameter,the water depth tolerance,as extensively adopted in *** propose a problem independent formulation for this parameter,which provides a stable scheme and preserves the overall truncation error of δ(Δx^(3)).The method is applied to solve problems with complex rough topography,coupled with h-adaptive mesh techniques to demonstrate its robustness and efficiency.

关键词： Shallow water free interface Manning force