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Simulation of Phase Transition with Lattice Boltzmann Method ZHAO Kai, LI Qiang, XUAN Yimin CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2008, 25 (2): 151-156.   Abstract （292）      PDF （428KB）（2108）       Knowledge map    A lattice Bohzmann model is established to describe liquid-vapor phase transitions using a model proposed by Shan instead of the R-K model. Evaporation from a higher density phase to a lower density phase is simulated. The model improves calculation efficiency and obtains good results. The model is also used to simulate phase transitions in porous media with a pore scale to demonstrate feasibility of the model for complicate phase transition problems. Related Articles | Metrics

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AI for Accelerating Scientific Simulation, Design, Control, and Discovery Tailin WU Chinese Journal of Computational Physics    2025, 42 (2): 127-145.   DOI: 10.19596/j.cnki.1001-246x.9020 Abstract （348）   HTML （26）    PDF （22676KB）（284）       Knowledge map    With the vigorous development of AI for Science in recent years, the integration of artificial intelligence and various scientific disciplines has become a major trend. However, AI for Science covers a wide range and involves many disciplines. Therefore, organizing it into a unified framework will enable better navigation for newcomers to the field. In this article, we posit that although the objects and methods of scientific research seem to be vastly different, AI can provide a universal paradigm and methods for scientific research in the following three aspects: scientific simulation, design and control, and discovery, solving problems in the field. This article will specifically elaborate on the task setting and current representative work. Through specific examples, we will explain how AI can concretely assist scientific research, facilitating researchers to better apply existing methods or develop novel methods. Table and Figures | Reference | Related Articles | Metrics

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Gas-kinetic Scheme Based on Cahn-Hilliard Phase-field Equation Hao ZHONG, Lianhua ZHU, Jin BAO, Zhaoli GUO Chinese Journal of Computational Physics    2025, 42 (2): 171-181.   DOI: 10.19596/j.cnki.1001-246x.8862 Abstract （39）   HTML （0）    PDF （5287KB）（190）       Knowledge map    The gas kinetic scheme based on Cahn-Hilliard phase field equation with interfacial fluxes determined by the Chapman-Enskog first-order approximation is constructed in the framework of finite volume. It is further demonstrated that the proposed model can be accurately recovered to Cahn-Hilliard equation. The method is tested through several cases and compared with the corresponding lattice Boltzmann method. The results show that the method in this paper has excellent accuracy and numerical stability for interface trapping. The study extends application of the gas-kinetic scheme to phase-field theory and provides a new solution for the simulation of two-phase fluid systems. Table and Figures | Reference | Related Articles | Metrics

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Computing fractal dimension and the kolmogorov entropy from chaotic time series Zhao Guibing, Shi Yanfu, Duan Wenfeng, Yu Huarui CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    1999, 16 (3): 309-315.   Abstract （516）      PDF （279KB）（2426）       Knowledge map    On the basis of the G-P algorithm it proposes an optimal algorithm for computing simultaneously the correlation dimension and the Kolmogorov entropy from time series.The correlation dimension obtained from this method is optimal and the stable estimation of the Kolmogorov entropy is also obtained.The applicability of the method is illustrated with two examples,viz.,the Lorenz attractor and Rossler attractor. Related Articles | Metrics

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SMOOTHED PARTICLE HYDRODYNAMICS (SPH) METHOD (A REVIEW) Zhang Suochun CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    1996, 13 (4): 385-397.   Abstract （582）      PDF （435KB）（3024）       Knowledge map    This paper describes a new and pure Lagrangian method——called "Smoothed Particle Hy drodynamics" (SPH) method. The method is to actually evaluate spatial gradients without the use of any grid. Thus it does not suffer form the severe problems always associated with mesh tangling and distortion. Therefore it can be applied to multidimensional hydrodynamics which could effectively model three-dimensional systems which lack symmetry and possess large voids. At first, the paper gives an introduction to theoretical basis to SPH. Emphasis is given to a proper derivation of the SPH equations from the hydrodynamical conservation equations. Discussion covers some relative problems such as artifical viscosity, thermal conduction, self-gravity and sink and magnetic fields, choosing the smoothing kernels, and implementation of SPH code, etc. Related Articles | Metrics

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Progress in Numerical Methods for Radiation Diffusion Equations YUAN Guangwei, HANG Xudeng, SHENG Zhiqiang, YUE Jingyan CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2009, 26 (4): 475-500.   Abstract （581）      PDF （1809KB）（3806）       Knowledge map    Radiative transfer in fluid flow of radiation hydrodynamics is studied.Kinetic laws under radiation condition are investigated.Practical radiation hydrodynamics process is complicated,and numerical simulation is one of primary research means.Splitting methods are often used in numerical simulation,in which fluid motion and radiation are computed separately.We discuss computational problems in radiation diffusion calculations.Diffusion schemes and nonlinear iterative methods on severely distorted meshes are studied.A brief introduction on research progress is given. Related Articles | Metrics

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Quantum Monte Carlo and Its Applications in Condensed and Warm Dense Matters Tianxing MA, Ting GUO, Zhongbing HUANG, Haiqing LIN Chinese Journal of Computational Physics    2024, 41 (6): 701-716.   DOI: 10.19596/j.cnki.1001-246x.8974 Abstract （209）   HTML （13）    PDF （908KB）（529）       Knowledge map    This paper firstly introduces the development of quantum Monte Carlo and several types of typical quantum Monte Carlo methods in detail, and then summarizes the recent researches of condensed and warm dense matter systems, including transport, magnetism, superconductivity and thermodynamic properties. Finally, the development prospect of quantum Monte Carlo methods is discussed. Reference | Related Articles | Metrics

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Global Sensitivity Analysis Based on Polynomial Chaos HU Jun, ZHANG Shudao CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2016, 33 (1): 1-14.   Abstract （360）   HTML （14）    PDF （658KB）（2194）       Knowledge map    Global sensitivity analysis method based on polynomial chaos and variance decomposition is reviewed comprehensively. In order to alleviate "curse of dimensionality" coming from high-dimensional random spaces or high-order polynomial chaos expansions, several approaches such as least square regression, sparse grid quadrature and sparse recovery based on l1 minimization (i. e. compressive sensing) are used to reduce sample size of collocation points that needed by non-intrusive polynomial chaos method. With computation of Sobol global sensitivity indices for several benchmark response models including Ishigami function, Sobol function, Corner peak function and Morris function, effective implementations of polynomial chaos method for variance-based global sensitivity analysis are exhibited. Reference | Related Articles | Metrics

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Key Technologies of Coupling for Multiphysics in Numerical Reactor DENG Li, SHI Dunfu, LI Gang CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2016, 33 (6): 631-638.   Abstract （1066）   HTML （116）    PDF （1623KB）（3454）       Knowledge map    With rapid development of computer and super computation, coupling for multi-physics,multi-scale and multi-process has become possible. Some lone process are integrated together. Some approximates from experience will be removed after all of the processes to be considered. This work is based on a virtual reactor. The goal is to improve precision by improvement of modeling and high fidelity computation. At present, study measures are changed from experiment and engineer dependent to theory analysis and numerical simulation. Numerical simulation will become more and more important. In this paper, CASL and NURESAFE are introduced. Then, several challenges, which include key technologies of software, are put forward in development of nuclear energy. Finally, suggestions are given for numerical reactor. It is only for reference and discussion. Reference | Related Articles | Metrics

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Unified Modeling and Optimization of UPML Absorbing Boundary Conditions CHAI Yanjie, SUN Jiyin, LI Linlin, SUN Dongyang CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2011, 28 (3): 413-419.   Abstract （452）      PDF （505KB）（1470）       Knowledge map    Transformation of dielectric properties in uniaxial anisotropic perfectly matched layer(UPML) regions is explored and unified modeling of UPML is proposed.Two condensing optimized algorithms for auxiliary variables,six regions' intersected method and parameter-compressed method,are proposed.In three cycles all initialization of medium parameters and iterative coefficients in three directions are completed with unified modeling method.Though the six regions' intersected method saves a lot of memory,it is the slowest.The parameter-compressed method saves space,which is programmed easily and runs the fastest. Related Articles | Metrics

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MULTIGRID SOLUTIONS FOR THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN ARTIFICIAL COMPRESSIBILITY FORMULATION YUAN Li CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2002, 19 (1): 23-29.   Abstract （297）      PDF （289KB）（1388）       Knowledge map    The full approximation storage (FAS) multigrid algorithm is applied in conjunction with the artificial compressibility method to accelerate steady solutions of the 3D incompressible Navier Stokes equations. Neumann boundary conditions in terms of the solution correction are implemented on the coarse grid when solving the coarse grid equations. The basic scheme used is the diagonalized approximate factorization scheme, and the spatial difference for inviscid fluxes adopts both MUSCL scheme and symmetric TVD scheme respectively for comparing. The performance of the present method is studied for the entry flow through a 90° bent square duct and the flow past an inclined prolate spheroid with an axes ratio of 4:1. It is found that the proposed multigrid method can save the computing time by at least half, and that MUSCL scheme is slightly better than TVD scheme in resolving the flow structures. Related Articles | Metrics

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Deep Learning Method for Solving Inverse Problem of Diffusion Coefficients for Diffusion Equation Yanqing ZHANG, Tongxiang GU Chinese Journal of Computational Physics    2025, 42 (2): 146-159.   DOI: 10.19596/j.cnki.1001-246x.8892 Abstract （60）   HTML （4）    PDF （7789KB）（119）       Knowledge map    Physics-Informed Neural Networks (PINN) have provided a new way of numerically solving forward and inverse problems of partial differential equations with promising applications. This paper focuses on the diffusion coefficient inverse problem of the diffusion equation. A systematic study is carried out for the problems of fixed coefficients, anisotropic coefficients, spatial dependence coefficients, spatio-temporal dependence coefficients, and nonlinear diffusion coefficients, and the neural network structure and solution method required for solving each type of problem are proposed. Numerical experiments show that the PINN method can reconstruct the unknown coefficients accurately with less data and is robust under a certain noise level. Table and Figures | Reference | Related Articles | Metrics

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Radial Basis Function Interpolation in Moving Mesh Technique LIN Yanzhong, CHEN Bing, XU Xu CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2012, 29 (2): 191-197.   Abstract （488）      PDF （6186KB）（3217）       Knowledge map    A spring stream method used for unstructured grid and a transfinite interpolation method used for structured grid are discussed.A method using radial basis function is proposed,which resolves moving mesh problem without any grid-connectivity information.Corresponding mesh numerical program is developed.Rotation of a two-dimensional rhombic aerofoil and deformation of a three-dimensional F104 aerofoil are taken as examples to show effects of function and radius on mesh quality and numerical efficiency.Results are compared with mesh-deformation using lineal spring method.It validats availability of the RBF method.We concluded that the RBF method is remarked with simple data structure,high numerical efficiency and strong adapting ability for large mesh deformation.It could be applied to CFD dynamic mesh problems. Related Articles | Metrics

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Development and Application of Multi-dimensional Particle-in-cell Codes for Investigation of Laser Plasma Interactions CHEN Min, SHENG Zhengming, ZHENG Jun, MA Yanyun, ZHANG Jie CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2008, 25 (1): 43-50.   Abstract （563）      PDF （637KB）（2268）       Knowledge map    A multi-dimensional particle-in-cell code KLAP is introduced. Field ionization, impact ionization and two body collision are considered in a one-dimensional code. Moving window technology is used in a three-dimensional code to study laser wakefield acceleration in GeV region. Terahertz radiation, laser propagation in neutral gas medium, surface electron acceleration as well as GeV electron generation in laser wakefield acceleration are studied. Related Articles | Metrics

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Application of KDF-SPH Method in Numerical Solution of Fractional Convection-diffusion Equation Xiuxia ZHANG, Imin RAHMATJAN Chinese Journal of Computational Physics    2025, 42 (1): 18-27.   DOI: 10.19596/j.cnki.1001-246x.8820 Abstract （46）   HTML （2）    PDF （4528KB）（183）       Knowledge map    Based on the smoothed particle hydrodynamics (SPH) method, the SPH method without kernel function derivative (KDF-SPH) is applied to the numerical solution of the time fractional convection-diffusion equation. In the simulation process of the time fractional convection-diffusion equation, the finite difference method (FDM) is used for the Caputo time fractional derivative, and the KDF-SPH method and SPH method are used for the spatial derivative respectively. The results show that the error of KDF-SPH method is much smaller than that of SPH method. Compared with the SPH method, KDF-SPH retains all the advantages of SPH (meshless, Lagrangian and particle properties). This method plays a great role in reducing errors and maintaining stability, and numerical approximation can be carried out regardless of whether the kernel gradient exists or not. It avoids the calculation of the derivative of the kernel function, reduces the requirement for the derivability of the kernel function, improves the calculation efficiency and is easy to be programmed. It is easy to expand the calculation of high-dimensional problems and has good practical application value. Table and Figures | Reference | Related Articles | Metrics

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Boundary Conditions in Lattice Boltzmann Method NIE De-ming, LIN Jian-zhong CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2004, 21 (1): 21-26.   Abstract （819）      PDF （250KB）（3775）       Knowledge map    Comparison and discussion of several boundary conditions in lattice Boltzmann method are presented. To achieve improved accuracy, a new method based on the idea of standard bounce-back scheme is proposed. Numerical simulations for two-dimensional Poiseuille flow and unsteady Couette flow are carried out using d2q9 model, and the results are identical to the analytical solutions. The convergence for different boundary treatments is discussed by changing single relaxation time τ and Re number. The results show that LBM can recover Navier-Stokes equation at low Mach number. It is also indicated that the errors for large τ are much bigger than those for τ close to 1. Related Articles | Metrics

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Application of High-dimensional Multi-objective Differential Evolution Algorithm Based on Global Ordering in Resistance Identification of Heating Pipe Network Junli YU, Enze ZHOU, Zhuangkuo LIU, Wenxiao XU, Yingshuai YANG, Mingyu XIANG Chinese Journal of Computational Physics    2025, 42 (1): 118-126.   DOI: 10.19596/j.cnki.1001-246x.8825 Abstract （47）   HTML （1）    PDF （4868KB）（178）       Knowledge map    A high-dimensional multi-objective differential evolution algorithm based on global ranking is developed to identify the resistance coefficient of heat supply network, and the multi-objective algorithm is applied to the resistance identification of heat supply network, and the calculation process of resistance identification is improved. The fuzzy mathematics method is applied to the process of resistance identification, a set of optimal solution is generated by identifying each pipe segment, and the optimal solution is selected from the optimal solution set according to the fuzzy membership degree. The results show that compared with the single objective algorithm, the optimal solution set generated by the high-dimensional multi-objective differential evolution algorithm based on global ranking is uniformly distributed and concentrated, and the optimal solution obtained is more accurate. Table and Figures | Reference | Related Articles | Metrics

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A Design of 3D Spot-size Converter Based on a Rib Waveguide Structure ZHANG Xi-fei, XIAO Jin-biao, CAI Chun, ZHANG Ming-de, SUN Xiao-han CHINESE JOURNAL OF COMPUTATIONAL PHYSICS    2005, 22 (2): 171-178.   Abstract （425）      PDF （403KB）（1586）       Knowledge map    A 3D trapered spot-size converter (3D-SSC) on a rib cross-sectional optical waveguide, one of the key components in photonic devices connecting with single mode optical fibers,is investigated through simulating lightwave transmission in this component based on 3D-FD beam propagation method.Geometry parameters,such as laterally boundaries,length,width of the large section,thickness and those of the transitional optical waveguide for connecting SMOF to 3D-SSC are discussed and analyzed.The simulation shows that the insert loss of 3D-SSC can be lower than 2 dB as the width in the area of 11.5 μm~13.5 μm and the thickness in the area of 4.5 μm~6.5 μm at the large end of the taper when the taper length is in the region of 200 μm~500 μm.The capability and the alignment tolerance of the 3D-SSC is better than those of the planar SSC,and the 3D-SSC with a nonlinear lateral boundary acquires lower insertion loss than that with a linear lateral boundary.It is found that the 3D-SSC converts gradually the guided modes from multi-mode to single mode finally. Related Articles | Metrics

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Progress in Study of Equation of State of Warm Dense Matter with Path-integral Monte Carlo Method Zixiang YAN, Wei KANG, Weiyan ZHANG, Xiantu HE Chinese Journal of Computational Physics    2023, 40 (2): 258-274.   DOI: 10.19596/j.cnki.1001-246x.8599 Abstract （60）   HTML （12）    PDF （4085KB）（1193）       Knowledge map    In this paper, the basic framework of PIMC method is firstly described in detail. In particular, four techniques developed for PIMC simulations to deal with the Fermi sign problem are reviewed. EOS data of various WDM systems obtained with PIMC simulations are then summarized, with which the advantages and disadvantages of PIMC method are illustrated. Finally, some future prospects of PIMC method are discussed. Table and Figures | Reference | Related Articles | Metrics

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Study on Instability of Viscoelastic Liquid Jet in Homogeneous Wind Field Tengfei ZHAO, Hua ZHANG Chinese Journal of Computational Physics    2025, 42 (1): 1-9.   DOI: 10.19596/j.cnki.1001-246x.8835 Abstract （106）   HTML （7）    PDF （1818KB）（192）       Knowledge map    The present study aims to establish a mathematical model for the stability analysis of a viscous compressible liquid jet in a homogeneous wind field, utilizing linear stability theory. Furthermore, the validity of the proposed mathematical model and its solution method are subsequently verified. The findings indicate that the homogeneous wind field exerts an equal influence on both the axisymmetric disturbance and the non-axisymmetric disturbance, with the latter being the predominant form of disturbance. The compressibility of the gas phase has a detrimental effect on the stability of jet flow, while the compressibility of the liquid phase has negligible impact on the stability of jet flow. The impact of a homogeneous wind field on jet stability is primarily manifested in two key dimensions. The presence of a tailwind field has the potential to enhance the stability of jets and impede the likelihood of splitting and atomization. The presence of the deadwind field has the potential to diminish the stability of the jet flow and facilitate the occurrence of splitting and atomization. Table and Figures | Reference | Related Articles | Metrics