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Frontiers of physics 2012年第4期7卷 481-490页

作者： yan-biao gan Ai-Guo Xu Guang-Cai Zhang Ying-Jun Li North China Institute of Aerospace Engineering Langfang 065000 China National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26 Beijing 100088 China State Key Laboratory for GeoMechanics and Deep Underground Engineering SMCEChina University of Mining and Technology (Beijing) Beijing 100083 China

The aims of the present paper are threefold. First, we further study the fast Fourier transform thermal lattice Boltzmann （FFT-TLB） model for van der Waals （VDW） fluids proposed in Phys. Rev. E, 2011, 84（4）： 046715. We analyze the merits of the FFT approach over the traditional finite difference scheme and investigate the effects of smoothing factors on accuracy and stability in detail. Second, we incorporate the VDW equation of state with flexible parameters into the FFT- TLB model. As a result, the revised model may be used to handle multiphase flows with various critical densities and temperatures. Third, we design appropriate boundary conditions for systems with solid walls. These improvements, from the views of numerics and physics, significantly extend the application scope of the model in science and engineering.

关键词： van der Waals fluids lattice Boltzmann method FFT equation of state

Thermodynamic Nonequilibrium Features in Binary Diffusion

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Communications in Theoretical Physics 2018年第6期69卷 722-726页

作者： Chuan-Dong Lin Kai Hong Luo yan-biao gan Hui-Lin Lai Center for Combustion Energy Key Laboratory for Thermal Science and Power Engineering of Ministry of Education Department of Energy and Power EngineeringTsinghua UniversityBeijing 100084China College of Mathematics and Informatics ＆ FJKLMAA Fujian Normal UniversityPuzhou 350007China Department of Mechanical Engineering University College LondonTorrington PlaceLondon WC1E 7JEUK North China Institute of Aerospace Engineering Langfang 065000China

Diffusion is a ubiquitous physical phenomenon where thermodynamic nonequilibrium effects(TNEs) are outstanding issues. In this work, we employ the discrete Boltzmann method to investigate the TNEs in the dynamic process of binary diffusion. The main features of the distribution function in velocity space are recovered and *** is found that, with the decreasing gradients of macroscopic quantities(such as density, concentration, velocity, etc.),both the local and global TNEs decrease with the time but increase with the relaxation time in a power law, respectively.

关键词： thermodynamic nonequilibrium binary diffusion discrete Boltzmann

Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows

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Frontiers of physics 2019年第4期14卷 83-99页

作者： yan-biao gan Ai-Guo Xu Guang-Cai Zhang Chuan-Dong Lin Hui-Lin Lai Zhi-Peng Liu North China Institute of Aerospace Engineering Langfang 065000 China College of Mathematics and Informatics & FJKLMAA Fujian Normal University Fuzhou 350007 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26 Beijing 100088 China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China Center for Applied Physics and Technology MOE Key Center for High Energy Density Physics Simulations College of Engineering Peking University Beijing 100871 China Center for Combustion Energy Key Laboratory for Thermal Science and Power Engineering of Ministry of Education Department of Energy and Power Engineering Tsinghua University Beijing 100084 China Department of Physics School of Science Tianjin Chengjian University Tianjin 300384 China

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann ***,two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic *** is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures;the other is to evaluate the growth rate of KHI from the slopes of morphological ***,it is found that the time histories of width of mixing layer,TNE intensity,and boundary length show high correlation and attain their maxima *** viscosity effects are twofold,stabilize the KHI,and enhance both the local and global TNE *** to the monotonically inhibiting effects of viscosity,the heat conduction effects firstly refrain then enhance the evolution *** physical reasons are analyzed and presented.

关键词： Kelvin-Helmholtz instability discrete Boltzmann method thermodynamic nonequilibrium effect morphological characterization

Lattice Boltzmann modeling and simulation of compressible flows

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Frontiers in Biology 2012年第5期7卷 582-600页

作者： Ai-Guo Xu Guang-Cai Zhang yan-biao gan Feng Chen Xi-Jun Yu National Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China North China Institute of Aerospace Engineering Langfang 065000China School of Science Linyi UniversityLinyi 276005China

In this mini-review we summarize the progress of Lattice Boltzmann （LB） modeling and simulating compressible flows in our group in recent years. Main contents include （i） Single-Relaxation-Time （SRT） LB model supplemented by additional viscosity, （ii） Multiple-Relaxation-Time （MRT） LB model, and （iii） LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model sup- plemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross Krook （LBGK）. So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a com- pletely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.

关键词： lattice Boltzmann modeling compressible flows shock waves hydrodynamic instability

A new procedure for exploring chaotic attractors in nonlinear dynamical systems under random excitations

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Acta Mechanica Sinica 2011年第4期27卷 593-601页

作者： Chun-biao gan Hua Lei Department of Mechanical Engineering Zhejiang University310027 Hangzhou China Institute of Applied Mechanics SAAZhejiang University310027 Hangzhou China

Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixing with each other, so it is very difficult to identify irregular signals evolving from arbitrary initial states. Here, periodic attractors from the simple cell mapping method are further iterated by a specific Poincare map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations. The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure. From the positions and the variations of attractors in the phase space, the action mechanism of bounded noise excitation is studied in detail. Several numerical examples are employed to illustrate the present procedure. It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.

关键词： Dynamical system Bounded noise excitationPoincare map Chaotic attractor. Bifurcation

A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

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Acta Mechanica Sinica 2012年第5期28卷 1416-1423页

作者： Chun-biao gan Shi-Xi yang Hua Lei Department of Mechanical Engineering Zhejiang University Department of Engineering Mechanics Zhejiang University

We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.

关键词： Stochastic excitation - Dynamical system - Specific Poincare map Noise-induced transition to chaos

Dynamical analysis and performance evaluation of a biped robot under multi-source random disturbances

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Acta Mechanica Sinica 2014年第6期30卷 983-994页

作者： Chun-biao gan Chang-Tao Ding Shi-Xi yang The State Key Laboratory of Fluid Power Transmission and Control Department of Mechanical EngineeringZhejiang University

During bipedal walking,it is critical to detect and adjust the robot postures by feedback control to maintain its normal state amidst multi-source random disturbances arising from some unavoidable uncertain *** radical basis function（RBF）neural network model of a five-link biped robot is established,and two certain disturbances and a randomly uncertain disturbance are then mixed with the optimal torques in the network model to study the performance of the biped robot by several evaluation indices and a specific Poincar′e *** contrast with the simulations,the response varies as desired under optimal inputting while the output is fluctuating in the situation of disturbance *** results from noise inputting also show that the dynamics of the robot is less sensitive to the disturbance of knee joint input of the swing leg than those of the other three joints,the response errors of the biped will be increasing with higher disturbance levels,and especially there are larger output fluctuations in the knee and hip joints of the swing leg.

关键词： Biped robot Multi-source random disturbances Sensitive parameters RBF neural network Taguchi method Performance evaluation

Input torque sensitivity to uncertain parameters in biped robot

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Acta Mechanica Sinica 2013年第3期29卷 452-461页

作者： Chang-Tao Ding Shi-Xi yang Chun-biao gan Department of Mechanical Engineering Zhejiang University

Input torque is the main power to maintain bipedal walking of robot, and can be calculated from trajectory planning and dynamic modeling on biped robot. During bipedal walking, the input torque is usually required to be adjusted due to some uncertain parameters arising from objective or subjective factors in the dynamical model to maintain the pre-planned stable trajectory. Here, a planar 5-link biped robot is used as an illustrating example to investigate the effects of uncertain parameters on the input torques. Kine-matic equations of the biped robot are firstly established by the third-order spline curves based on the trajectory planning method, and the dynamic modeling is accomplished by taking both the certain and uncertain parameters into account. Next, several evaluation indices on input torques are intro-duced to perform sensitivity analysis of the input torque with respect to the uncertain parameters. Finally, based on the Monte Carlo simulation, the values of evaluation indices on input torques are presented, from which all the robot param-eters are classified into three categories, i.e., strongly sensi-tive, sensitive and almost insensitive parameters.

关键词： Biped robot · Uncertain parameter · Trajectory planning · Input torque · Sensitivity

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow:Two-Dimensional Case

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Communications in Theoretical Physics 2008年第7期50卷 201-210页

作者： gan yan-biao XU Ai-Guo ZHANG Guang-Cai ZHANG Ping ZHANG Lei LI Ying-Jun China University of Mining and Technology （Beijing） Beijing 100083 China State Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P.O. Box 8009-26 Beijing 100088 China Fundamental Science Department North China Institute of Aerospace Engineering Langfang 065000 China

Lattice Boltzmann （LB） modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 （2007） 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests： shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

关键词： lattice Boltzmann method high-speed compressible flow von Neumann analysis

Highly Efficient Lattice Boltzmann Model for Compressible Fluids:Two-Dimensional Case

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Communications in Theoretical Physics 2009年第10期52卷 681-693页

作者： CHEN Feng XU Ai-Guo ZHANG Guang-Cai gan yan-biao CHENG Tao LI Ying-Jun China University of Mining and Technology （Beijing） Beijing 100083 China National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P.O. Box 8009-26 Beijing 100088 China North China Institute of Aerospace Engineering Langfang 065000 China

We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 （2004） 035701（R）] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the yon Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include （i） Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, （ii） Regular and Mach shock reflections, and （iii） Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.

关键词： lattice Boltzmann method compressible flows specific-heat-ratio von Neumann stability analysis