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A novel spatial-temporal radial Trefftz collocation method for the backward heat conduction analysis with time-dependent source term

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International Journal of Heat and Mass Transfer 2023年 201卷

作者： Li, Mingjuan Fu, Zhuojia Xu, Wenzhi Fan, Chia-Ming Key Laboratory of Ministry of Education for Coastal Disaster and Protection Hohai University Nanjing210098 China Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing211100 China Department of Harbor and River Engineering & Computation and Simulation Center National Taiwan Ocean University Keelung20224 Taiwan

In this paper, a novel spatial-temporal radial Trefftz collocation method (STRTCM) is proposed to solve 2D and 3D backward heat conduction equations with time-dependent source term. Unlike the traditional time-domain discretization strategies (Laplace/Fourier transformation and time-stepping methods), the proposed spatial-temporal meshless collocation method employs the derived semi-analytical spatial-temporal radial Trefftz basis function as basis function, which naturally satisfies the governing equation with zero source term in advance. Due to this property, only the final conditions and boundary conditions need to be discretized. For non-zero source term, the extended multiple reciprocity method (E-MRM) is introduced to transform the original governing equation with several specific source terms to the high-order governing equation without the source term. By deriving the high-order semi-analytical spatial-temporal radial Trefftz basis function, the STRTCM can also avoid the node discretization of governing equation. For solving the backward heat conduction equations, the present numerical scheme uses the final temperature distribution and the related boundary conditions to obtain the unknown initial temperature field. Finally, the accuracy and efficiency of the proposed method is numerically verified by four benchmark examples about backward heat conduction equations with time-dependent source term. © 2022 Elsevier Ltd

关键词： Boundary conditions

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Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces

arXiv

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arXiv 2023年

作者： Hu, Wen Fu, Zhuojia Ling, Leevan Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing211100 China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

This paper introduces the first attempt to employ a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is used as a localized meshless technique to discretize the surface gradient and Laplace-Beltrami operators defined extrinsically in the governing equations. An absorbing boundary condition is introduced to reduce reflections from boundaries and accurately simulate wave propagation on unclosed surfaces with periodic inclusions. Several benchmark examples demonstrate the efficiency and accuracy of the proposed method in simulating acoustic wave propagation on surfaces with diverse geometries, including complex shapes and periodic holes or *** Codes 35J05, 65N35, 74J05 © 2023, CC BY-NC-ND.

关键词： Acoustic wave propagation

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Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

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Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1520-1534页

作者： Yan Gu Chia-Ming Fan Zhuojia Fu School of Mathematics and Statistics Qingdao UniversityQingdaoShandong 266071China Department of Civil Engineering University of SiegenPaul-Bonatz-Str.9-11D-57076 SiegenGermany Department of Harbor and River Engineering&Computation and Simulation Center Taiwan Ocean UniversityKeelung 20224Taiwan Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and MaterialsHohai UniversityNanjingJiangsu 211100China

A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity *** present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS *** a combination will be an important improvement to the classical MFS for complicated and large-scale engineering *** examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed *** advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.

关键词： Method of fundamental solutions meshless method large-scale simulations elasticity problems.

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Dynamic Interactions of Large-Scale Tandem Bubbles with a Rigid Wall

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International Journal of Mechanical sciences 2025年 297-298卷

作者： Liu, Rui Zhao, Zitong Rong, Jili School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China CAEP Software Center for High Performance Numerical Simulation Beijing 100088 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

In natural phenomena and industrial applications, bubble evolution is often governed by complex inter-bubble interactions and boundary effects. However, the evolution of tandem bubbles near boundaries has not been thoroughly investigated in existing studies. The interface-sharpening six-equation multiphase model is capable of accurately capturing rapid topology evolution at gas–liquid interfaces, enabling the prediction of complex phenomena such as bubble coalescence and collapse. In this study, the accuracy of the numerical model is validated through free-field experiment and the unified bubble theory. The numerical model simulates the evolution of single bubbles, tandem bubbles, and out-of-phase tandem bubbles near a rigid wall. The effects of inter-bubble distance (γbb ∈ [0.5, 1.6]) and out-of-phase parameter (τ ∈ [0, 1]) on bubble dynamics and wall impact are investigated, with particular attention to their influence on bubble penetration. The impact load on the wall is primarily composed of bubble collapse pressure, water-jet impact pressure, and bubble pulsation pressure. As γbb increases, the collapse mechanism of upper bubble transitions from water-jet induced mechanism to a local high-pressure induced mechanism, reaching the highest impact intensity at γbb = 1.2. As τ increases, the collapse mechanism of upper bubble gradually shifts from low-pressure bubble suppression mechanism to a local high-pressure induced mechanism. When γbb ≤ 0.9, the impact enhancement effect on the wall can be induced by adjusting the parameter τ, with the optimal impact enhancement occurring at τ = 0.833. These transitions in collapse mechanisms are further explained by the Kelvin impulse theory. The analytical conclusions provide valuable insights into the complex evolution of tandem bubbles near boundaries. © 2025 Elsevier Ltd

关键词： Multiphase flow

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Three-Dimensional numerical Study on the Effect of Radius of the Equal-Area Mixing Chamber on Auxiliary Entraining of the Two-Stage Ejector

SSRN

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SSRN 2023年

作者： Yan, Jia Gao, Haiping Wang, Zheng School of Civil Engineering and Architecture Southwest University of Science and Technology Mianyang City621010 China Tianfu Engineering Numerical Simulation and Software Innovation Center School of Computer Sciences Sichuan University Chengdu City610041 China

In this study, for the two-stage ejector under three inlet conditions of air-conditioning, refrigerating and freezing, a three-dimensional simulation is used to study the impact of the mixing chamber radius of the first and second stage on the minimum pressure in the ejector without auxiliary entraining first, and then, the impact of real auxiliary entraining effects on ejector performance for two-stage ejector with varied equal-area mixing chamber radius is evaluated accordingly. Results show that: (1) as the second stage equal-area mixing chamber radius (Ram2) increases, the minimum first stage ejector pressure (Pmin1) decreases and the minimum second stage ejector pressure (Pmin2) increases;(2) with the increase of radius of the first-stage equal-area mixing chamber (Ram1), the decreasing effect of Pmin1 and the increasing effect of Pmin2 are both weakened as Ram2 increases from 3.0 mm to 4.6 mm;(3) the minimum pressures of the two-stage have a great influence on the auxiliary entraining effect. © 2023, The Authors. All rights reserved.

关键词： Ejectors (pumps)

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Two-Level preconditioning method for solving saddle point systems in contact computation

arXiv

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arXiv 2024年

作者： Duan, Xiaoyu An, Hengbin Institute of Applied Physics and Computational Mathematics Beijing100094 China Graduate School of China Academy of Engineering Physics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China

In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. Given that the saddle point matrix is indefinite, solving these systems presents significant challenges. For a two-dimensional tied contact problem, an efficient two-level preconditioning method is developed. This method utilizes physical quantities for coarsening, introducing two types of interpolation operators and corresponding smoothing algorithms. Additionally, the constructed coarse grid operator exhibits symmetry and positive definiteness, adequately reflecting the contact constraints. numerical results show the effectiveness of the method. Copyright © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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Stochastic dynamic analysis of multi-layer functionally graded material cylinders using direct probability integral method with improved smoothing technique

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Probabilistic engineering Mechanics 2025年 80卷

作者： Lu, Wen Wu, Zhigen Yang, Dixiong Meng, Zeng Chen, Hanshu School of Civil Engineering Hefei University of Technology Hefei230009 China State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics Dalian University of Technology Dalian116024 China Jianghuai Advance Technology Center Hefei230000 China Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Engineering Science Hohai University Nanjing211100 China

Uncertainties are inherently inevitable in the application of functionally graded materials (FGMs) structures. Existing analysis methods face challenges in terms of accuracy and efficiency when addressing these uncertainties, especially for dynamic problems. To this end, this paper proposes a direct probability integral method with improved smoothing technique (DPIM-IST) for the stochastic dynamic analysis of FGM cylinders. Subsequently, an adaptive framework is constructed based on the maximum entropy principle to determine the variable smoothing parameters at each representative point. To search for the proper smoothing parameter vector, a hybrid grey wolf optimizer is employed, which combines the grey wolf optimizer and BFGS method. Moreover, the dynamic responses at each representative point are evaluated by utilizing the differential quadrature method and Newmark algorithm. Several numerical and multiphase and multi-layer FGM hollow cylinder examples, involving nonlinear performance functions with Gaussian and non-Gaussian parameters, are investigated to validate the accuracy of the proposed DPIM-IST. © 2025 Elsevier Ltd

关键词： Integral equations

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A DOFs condensation based algorithm for solving saddle point systems in contact computation

arXiv

引用

arXiv 2024年

作者： Duan, Xiaoyu An, Hengbin Mo, Zeyao Institute of Applied Physics and Computational Mathematics Beijing100094 China Graduate School of China Academy of Engineering Physics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China

In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. The mortar finite element method is usually employed to discretize the variational form on the meshed contact surfaces, leading to a large-scale discretized saddle point system. Due to the indefiniteness of the discretized system, it is a challenge to solve the saddle point algebraic system. For two-dimensional tied contact problem, an efficient DOFs condensation technique is developed. The essential of the proposed method is to carry out the DOFs elimination by using the tridiagonal characteristic of the mortar matrix. The scale of the linear system obtained after DOFs elimination is smaller, and the matrix is symmetric positive definite. By using the preconditioned conjugate gradient (PCG) method, the linear system can be solved efficiently. numerical results show the effectiveness of the method. Copyright © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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Effect of leading-edge and trailing-edge camber morphing on gust load for an elastic wing

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Chinese Journal of Aeronautics 2025年第4期 208-224页

作者： Yuting DAI Yating HU You WU Chen SONG Chao YANG School of Aeronautic Science and Engineering Beihang University Tianmushan Laboratory CAEP Software Center for High-Performance Numerical Simulation Institute of Applied Physics and Computational Mathematics

This paper investigates the influence of the spanwise-distributed trailing-edge camber morphing on the dynamic stall characteristics of a finite-span wing at Re=2×10～*** mathematical model of the spanwise-distributed trailing-edge camber morphing is established based on Chebyshev polynomials,and the deformed wing surface is modeled by a spline surface according to the rib's morphing in the chordwise *** Computational Fluid Dynamics(CFD)method is adopted to obtain flow-field results and aerodynamic *** SST-γ model is introduced and the overset mesh technique is *** numerical results show that the spanwisedistributed trailing-edge morphing obviously changes the aerodynamic and energy transfer characteristics of the dynamic *** when the phase difference between the trailing-edge motion and the wing pitch is-π/2,the interaction between the three-dimensional(3-D) Leading-Edge Vortex(LEV) and Trailing-Edge Vortex(TEV) is strengthened,and the work done by the aerodynamic force turns *** indicates that the trailing-edge deformation has the potential to suppress the oscillation amplitude of stall *** also found that as the trailing-edge camber morphing varies more complexly along the spanwise direction,the suppression effect decreases accordingly.

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Multi-phase-field simulation of austenite peritectic solidification based on a ferrite grain

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Chinese Physics B 2021年第1期30卷 572-577页

作者： Chao Yang Jing Wang Junsheng Wang Yu Liu Guomin Han Haifeng Song Houbing Huang School of Materials Science and Engineering Beijing Institute of TechnologyBeijing 100081China Advanced Research Institute of Multidisciplinary Science Beijing Institute of TechnologyBeijing 100081China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Software Center for High Performance Numerical Simulation China Academy of Engineering PhysicsBeijing 100088China

A multi-phase-field model is implemented to investigate the peritectic solidification of Fe-C alloy. The nucleation mode of austenite is based on the local driving force, and two different thicknesses of the primary austenite on the surface of the ferrite equiaxed crystal grain are used as the initial conditions. The simulation shows the multiple interactions of ferrite, austenite, and liquid phases, and the effects of carbon diffusion, which presents the non-equilibrium dynamic process during Fe-C peritectic solidification at the mesoscopic scale. This work not only reveals the influence of the austenite nucleation position, but also clarifies the formation mechanism of liquid phase channels and molten pools. Therefore, the present study contributes to the understanding of the micro-morphology and micro-segregation evolution mechanisms of Fe-C alloy during peritectic solidification.

关键词： multi-phase-field simulation morphology evolution peritectic solidification carbon diffusion Fe-C alloy

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