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25 July 2024, Volume 41 Issue 4 Previous Issue    Next Issue

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Analysis of Parallel Scalability Bottleneck for Algebraic Multigrid in Typical Real Applications Runzhang MAO, Hao DU, Hongyun TIAN, Silu HUANG, Peng ZHANG, Xiaowen XU 2024, 41(4): 403-417.  DOI: 10.19596/j.cnki.1001-246x.8737 Abstract ( )   HTML ( )   PDF (26445KB) ( )   Algebraic multigrid (AMG) is an optimal algorithm for solving large-scale sparse linear systems. However, its complexity makes it challenging to achieve ideal parallel scalability and identify parallel scalability bottlenecks. In this paper, we analyze the performance skeletons and communication patterns of the AMG algorithm to identify three categories of scalability bottlenecks. Additionally, we introduce the concept of the sparse matrix communication domain to characterize the influence of sparse patterns on parallel communication performance. We examine six typical examples with varying sparse pattern features in practical applications such as radiation fluid dynamics, structural mechanics, and aero-engines. Through our analysis, we identify and analyze multi-granularity parallel scalability bottlenecks and provide insights into future directions for improving AMG parallel performance.

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Two-level Grad-div Stabilized Finite Element Methods for Steady Incompressible Navier-Stokes Equations Yali WANG, Bo ZHENG, Yueqiang SHANG 2024, 41(4): 418-425.  DOI: 10.19596/j.cnki.1001-246x.8731 Abstract ( )   HTML ( )   PDF (5605KB) ( )   Accuracy of the approximate velocity of the steady incompressible Navier-Stokes equations computed by the standard mixed finite element methods is often affected by the pressure. In order to circumvent or weaken the influence of pressure on the accuracy of the computed velocity, by combining grad-div stabilized method with two-level finite element method, this paper presents a kind of two-level grad-div stabilized finite element methods for solving the steady incompressible Navier-Stokes equations numerically. The basic idea of the methods is to first solve a grad-div stabilized nonlinear Navier-Stokes problems on a coarse grid, and then solve, respectively, Stokes-linearized, Newton-linearized and Oseen-linearized Navier-Stokes problem with grad-div stabilization on a fine grid. Numerical examples are given to verify the high efficiency of the two-level grad-div stabilized finite element methods.

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High Accuracy Numerical Solution of Wave Equation Hongwang YUAN, Xiyin WANG, Jin LI 2024, 41(4): 426-439.  DOI: 10.19596/j.cnki.1001-246x.8732 Abstract ( )   HTML ( )   PDF (11078KB) ( )   A barycentric Lagrange interpolation collocation method is proposed to solve the three-dimensional and four-dimensional wave equations. Firstly, the barycentric Lagrange interpolation method is introduced and the matrix format of the collocation method is given. Secondly, the solution function and initial boundary conditions of the wave equation are approximated by Lagrange interpolation. The discrete equation is obtained by collocation method, and the matrix expression of the wave equation is obtained. Finally, the initial and boundary conditions of the wave equation are imposed by the addition method and the replacement method respectively. Numerical examples show that the barycentric Lagrange interpolation collocation method has high computational accuracy and efficiency.

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PML Implementation of WLP-FDTD Algorithm Based on "Decomposition" Ideology in Cylindrical Coordinate System Dawei ZHU, Hailin CHEN, Jiachen XU, Xiaoxiao ZHOU, Boao XU 2024, 41(4): 440-452.  DOI: 10.19596/j.cnki.1001-246x.8728 Abstract ( )   HTML ( )   PDF (7777KB) ( )   Based on the basic equations of conventional finite-difference-time-domian(FDTD) algorithm in cylindrical coordinate system, in order to solve the problems of large memory consumption and low computational efficiency in computation of conventional weighted-Laguerre-polynomial(WLP)-FDTD algorithm. The idea of "Decomposition" in this paper is divided into two parts. Firstly, the electromagnetic field equation is decomposed for the first time in the frequency domain, and PML parameters are substituted, and the decomposed time-domain equation is converted to the Laguerre domain, so that the original three-dimensional bidirectional solution problem is converted into two-dimensional one-way scale to solve, reducing the memory consumption of calculation. Secondly, LU decomposition is used to decompose the coefficient matrix of Laguerre domain after solution scale reduction, which realizes the first step of avoiding large sparse matrix, and then the chase after method is used to solve the conventional electromagnetic field equation, so as to improve the computational efficiency and reduce memory consumption. Numerical examples show that comparing with conventional WLP-FDTD, the proposed scheme can reduce the memory consumption by 57% and increase the computing efficiency by 49%, without losing the accuracy, the proposed method has a good electromagnetic wave absorption effect, and the reflection error can reach -70 dB.

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Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations Shasha LIU, Supei ZHENG, Chengzhi ZHANG, Jianhu FENG 2024, 41(4): 453-462.  DOI: 10.19596/j.cnki.1001-246x.8744 Abstract ( )   HTML ( )   PDF (1947KB) ( )   The shallow water equations with source term have steady-state solution. The numerical scheme for solving this kind of equations must have well-balanced property, otherwise it will cause oscillation. For the bottom-non-flat shallow water with source term, this paper studies the well-balanced property of the high order compact central weighted essentially non-oscillatory (CCWENO) entropy stable scheme, and proves its well-balanced property. The theory is verified by one- and two-dimensional numerical examples. The numerical results show that the high order CCWENO scheme has the well-balanced property and can accurately capture the small perturbation of the solution even based on the coarse grid.

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Finite Element Analysis of Inertial Migration of Double Vesicles in Microtubular Flow Yelin LIU, Peng HAO, Mingming DING 2024, 41(4): 463-471.  DOI: 10.19596/j.cnki.1001-246x.8755 Abstract ( )   HTML ( )   PDF (6103KB) ( )   The finite element method based on fluid-structure interaction is used to systematically study the inertial migration of double vesicles in microtubule flow with a two-dimensional model. The results show that the equilibrium position of inertial migration of two circular vesicles with initial symmetry is always symmetric about the center of the channel, and with the increase of Reynolds number, the equilibrium position will be closer and closer to the center of the channel. Secondly, for the double vesicle system composed of circular vesicles and elliptic vesicles, when the initial positions of circular vesicles and elliptic vesicles are located on both sides of the channel, the equilibrium position of circular vesicle inertial migration is almost constant with the increase of Reynolds number, but the elliptic vesicles shift to the center of the channel and across the center to the other side of the channel, and finally move slowly to the wall with the increase of Reynolds number, and at Re≥500, the radial displacement of elliptic vesicle reaches the maximum value. When the circular and elliptical vesicles are located on the same side of the channel, the final equilibrium position is closer to the wall of the channel with the increase of Reynolds number, regardless of whether the elliptic vesicles are anterior or posterior. The present study elucidates the physical mechanism behind the vesicles based on their forces, and the related results can facilitate the application of inertial microfluidics in the precise separation and manipulation of vesicles.

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Discharge Characteristics of Low Pressure Capacitively Coupled Ar/CH4 Plasma Guiqin YIN, Yongbo JIANG, Yutian HUANG 2024, 41(4): 472-479.  DOI: 10.19596/j.cnki.1001-246x.8734 Abstract ( )   HTML ( )   PDF (9627KB) ( )   To further understand the discharge mechanism and the particle states incident to the pole plate during the capacitively coupled plasma discharge, the discharge of argon and methane gas mixture is simulated by PIC/MCC program, and the electron density, CH4+ and CH3+ group particle concentrations, electron energy probability distribution, as well as the energy angle distribution and particle species of the particles reaching the pole plate boundary are simulated and calculated under different Ar/CH4 ratios and different pole plate gap conditions. The simulation results show that the electron density, Ar+, CH2- and H- ion density in the discharge center decrease and then increase with the increase of the pole plate spacing at a fixed Ar/CH4 of 9∶1, and the CH4+ and CH3+ ion density change in the opposite trend; the electron energy probability function (EEPF) from double Maxwell distribution to single Maxwell distribution when the pole plate spacing increases; the percentage of electrons arriving at the pole plate is larger and changes less with the pole plate spacing, the probability of Ar+ arriving at the pole plate first decreases and then increases, and the percentage of CH4+, CH3+ and CH2+ ions arriving at the pole plate increases with the increase of the pole plate spacing. At fixed pole plate spacing, the electron density and Ar+ density in the discharge center show a decreasing trend with increasing CH4 content, and the densities of CH4+, CH3+, CH2- and H- ions show an increasing trend; the effect of the change in pole plate spacing on the EEPF distribution is more obvious than the effect of the change in CH4 ratio on the EEPF distribution; with the increase in CH4 content, the change in the percentage of electrons arriving at the pole plate is not obvious, and the percentage of Ar+ ions decreases significantly, while the percentage of CH4+, CH3+, CH2+ and the rest of ions arriving at the pole-plate increase.

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Nonradiative Recombination for Mn and Sn Doped in Inorganic Perovskite CsPbI3 by First-principles Renjie ZHANG, Hongshuai TAO 2024, 41(4): 480-486.  DOI: 10.19596/j.cnki.1001-246x.8738 Abstract ( )   HTML ( )   PDF (3564KB) ( )   The defect forming energy, transition level and carrier nonradiative recombination coefficient of Mn and Sn doped α-CsPbI3 system are investigated by first-principles based on density functional theory. It is found that the lattice constant of Mn doped CsPbI3 decreases obviously, while the lattice constant of Sn doped system decreases slightly, which improves the stability of the material. The deep level defects of both systems are close to conduction band and mainly capture electrons from conduction band. The doping of Mn and Sn elements improves the phonon energy distribution of the perfect system and enhances the heat transport capacity of the material. The nonradiative recombination coefficient of the holes in Sn doping system is much higher than that in Mn doping system and the nonradiative recombination coefficient of the two doping systems is higher than that of CsPbI3 containing intrinsic defects Ii and ICs, so the impurity may introduce the nonradiative recombination center. These results provide data support for the experiment of Mn and Sn doped CsPbI3 system, and provide a theoretical basis for the CsPbI3 doping perovskite in experiments.

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First-principles Study on State Equation and Thermodynamic Properties of Energetic Ionic Salt TKX-50 Meng ZHOU, Yingqi TAO, Xiaoyun ZHOU, Yulong ZHANG, Cai CHENG 2024, 41(4): 487-493.  DOI: 10.19596/j.cnki.1001-246x.8740 Abstract ( )   HTML ( )   PDF (3363KB) ( )   By employing first-principles based on density functional theory, combined with the Debye model and lattice dynamics theory, the themodynamic properties and state equation of TKX-50 under high temperture and pressure are calculated. It is shown that, the calculated lattice constants of TKX-50 agree well with the available experimental and other theoretical data. And then we calculate the lattice structure and relate thermodynamic properties under different temperature and pressure. The results show that the lattice of TKX-50 is the most difficult to compress along the a-axis; the thermal capacity is influenced by temperature and pressure strongly; the Debye temperature, Gruneison constant, and the thermal expansion coefficient changes rapidly with temperature. The results of this paper not only reveal how the thermodynamic properties of TKX-50 change with temperature and pressure, a guide to predict and explain its temperature pressure performance, but also provide necessary theoretical support, for the engineering application and risk assessment of TKX-50.

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Heredity and Evolution of Cluster in Rapid Solidification of Liquid Ni50Zr50 Alloy under Different Cooling Rates Qinghua QI, Dadong WEN, Bei CHEN, Ming GAO, Zhou YI, Yonghe DENG, Ke DENG, Ping PENG 2024, 41(4): 494-502.  DOI: 10.19596/j.cnki.1001-246x.8742 Abstract ( )   HTML ( )   PDF (10257KB) ( )   Amorphous alloys have been severely restricted to widespread commercial application by their limited glass-forming ability (GFA). Since it is essentially a "freezing liquid" to some extent, studying the correlation of the atomic structures in solid with those in liquid during the rapid solidification of liquid alloys is expected to provide new insights for GFA. Therefore, the rapid solidification processes of liquid Ni50Zr50 alloy under six different cooling rates are simulated using molecular dynamics (MD) methods. The microstructure as well as its evolution of the rapidly solidified Ni50Zr50 alloys are characterized and analyzed with pair distribution function (PDF), cluster-type-index method (CTIM), and reverse atomic trajectory tracking method. The results show that the most numerous atomic configurations in Ni50Zr50 metallic glass is (11 2/1441 8/1551 1/1661), i.e., Z11 Kasper cluster, rather than icosahedra. The characteristic clusters in rapidly solidified Ni50Zr50 alloys tended to aggregate to form medium-range orders (MROs), and their numbers increase with the decrease of cooling rate. The configurational heredity of basic clusters emerges in the supercooled liquid region of Tm-Tg. Among the typical clusters, Z11 Kasper cluster possesses the highest fraction f of staged heredity in a wide temperature range above Tg. Raising cooling rate is beneficial for increasing f of basic clusters in the supercooled liquid region and increasing onset temperature of configuration heredity. The GFA of Ni50Zr50 alloy induced by raising cooling rate can be attributed to the enhanced hereditary ability of characteristic clusters such as Z11 Kasper cluster.

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A Production Prediction Model for Fractured Horizontal Wells with Irregular Fracture Network in Low Permeability Reservoirs Siyu LIU, Kun WANG, Mingying XIE, Shasha FENG, Li LI, Yang GAO 2024, 41(4): 503-514.  DOI: 10.19596/j.cnki.1001-246x.8745 Abstract ( )   HTML ( )   PDF (6840KB) ( )   A non-uniform complex fracture network structure formed by fracturing is considered with introducing the fractal theory and combining the stress sensitivity of fracture system to demonstrate the change of fluid flow capacity, and a production prediction model for three-zone compound seepage flow in fractured horizontal wells in low permeability reservoirs is established successfully in this paper. Laplace transform, perturbation theory, and numerical inversion are applied to obtain the analytical solution of the proposed production model, and the productivity formulas for single well under two situations of uniform and non-uniform distribution of fractures in horizontal wells are derived. The reliability of the production prediction model is verified with the real production data and basic parameters of a fractured horizontal well in Bohai oilfield, and the effects of related influential parameters on production of horizontal well are analyzed. The research results show that smaller the stress sensitivity coefficient and threshold pressure gradient results in larger the oil production. Larger the fractal dimension contributes to larger the horizontal well production. Additionally, the oil production increases with the increase of the number of fractures and fracture half-length, but the growth rate slows down, which means these parameters have optimal values.

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Study on Grid Access of Distributed Power Stations Based on Power Supply Efficiency of Source-load Node Pair Kexiang WU, Yanli ZOU 2024, 41(4): 515-522.  DOI: 10.19596/j.cnki.1001-246x.8736 Abstract ( )   HTML ( )   PDF (7030KB) ( )   The optimal site selection of distributed power stations on a weighted network is studied by combining the topology and electrical characteristics of the network. Firstly, the second-order Kuramoto-like phase oscillator model is used to model the power grid, and the network power flow value under equal coupling strength is used to weight the power grid lines to construct a weighted network model of the power grid; by calculating the transmission efficiency from each load node to each generator node and the power absorbed by each load node from each generator node, which defines the power supply efficiency index of source-load node pair. Then, according to the power supply efficiency value of the source-load nodes of each load node, three grid access methods are defined. The influence of three different grid access methods of distributed power stations on the synchronizability of the grid is studied on the coupling weighted network. Study shows that the access mode of distributed power stations is the best in order to arrange the power supply efficiency value from small to large, followed by the way of randomly selects load nodes, and the way in which the power supply efficiency value is arranged in descending order is the worst. Therefore, the power grid can achieve better synchronizability when the distributed power stations connect to the power grid on the load node with the lower power supply efficiency index of the source-load node pair.

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Dynamics and Implementation of Memristive System Exhibiting Extreme Multistability Ji CHEN, Yi XU, Jinfu LIU, Tao LIU 2024, 41(4): 523-534.  DOI: 10.19596/j.cnki.1001-246x.8760 Abstract ( )   HTML ( )   PDF (16860KB) ( )   Based on a class of parameter-adjustable chaotic systems, an improved four-dimensional memristive chaotic system is established by replacing the gain resistor of the original system circuit with a memristor. Theoretical analysis demonstrates that the new system possesses two line equilibrium points and can generate self-excited attractors. The dynamics of the new system are analyzed through numerical simulation such as bifurcation diagrams, Lyapunov exponents, phase diagrams, etc. With the variation of initial conditions, the memristive system with fixed parameters exhibits not only the extreme multistability phenomenon of coexisting infinitely many attractors but also complex transient behaviors. Finally, to validate the theoretical and numerical simulation results, an equivalent circuit of the memristive chaotic system is designed, and hardware circuit experiments as well as PSIM circuit simulations confirm the correctness of the MATLAB numerical simulations.

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Mass Exchange Network Mass Transfer Load Infeasibility Treatment and Dynamic Regulation Strategy Siheng XIONG, Huanhuan DUAN, Guomin CUI, Yuan XIAO, Zhikang YI 2024, 41(4): 535-546.  DOI: 10.19596/j.cnki.1001-246x.8733 Abstract ( )   HTML ( )   PDF (6962KB) ( )   In the optimization of mass exchange networks with mass transfer load as the optimization variable, using the penalty function method to deal with infeasible solutions that violate the feasible constraints on mass transfer will limit the generation of mass transfer units, and at the same time bring negative effects on the optimization algorithm's optimization path. In view of this, the negative impact of the penalty function method to deal with mass transfer constraints on optimization is analyzed, based on which a dynamic regulation strategy of mass transfer load is proposed to deal with the units mass transfer constraints by using different regulation methods, attenuating the mass transfer load of the units that violate the mass transfer constraints or eliminating the unit to ensure that the mass transfer units in the structure not violate the constraints. The validation is carried out by two mass exchange network arithmetic examples, and the obtained results demonstrate the effectiveness of the strategy by decreasing 2 943 ＄·a-1 and 1 697 ＄·a-1, respectively, compared with the optimal results in the literature, and increasing the number of mass transfer units in the structure.