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linear stability of a fluid channel with a porous layer in the center

Acta Mechanica Sinica 2014年第1期30卷 28-36页

作者： Qi Li Hai-Yan Lei Chuan-Shan Dai School of Mechanical Engineering Tianjin University Key Laboratory of Efcient Utilization of Low and Medium Grade Energy MOETianjin University

We perform a Poiseuille flow in a channel linear stability analysis of a inserted with one porous layer in the centre, and focus mainly on the effect of porous filling ratio. The spectral collocation technique is adopted to solve the coupled linear stability problem. We investigate the effect of permeability, σ, with fixed porous filling ratio ψ = 1/3 and then the effect of change in porous filling ratio. As shown in the paper, with increasing σ, almost each eigenvalue on the upper left branch has two subbranches at ψ = 1/3. The channel flow with one porous layer inserted at its middle （ψ = 1/3） is more stable than the structure of two porous layers at upper and bottom walls with the same parameters. By decreasing the filling ratio ψ, the modes on the upper left branch are almost in pairs and move in opposite directions, especially one of the two unstable modes moves back to a stable mode, while the other becomes more instable. It is concluded that there are at most two unstable modes with decreasing filling ratio ψ. By analyzing the relation between ψ and the maximum imaginary part of the streamwise phase speed, Cimax, we find that increasing Re has a destabilizing effect and the effect is more obvious for small Re, where ψ a remarkable drop in Cimax can be observed. The most unstable mode is more sensitive at small filling ratio ψ, and decreasing ψ can not always increase the linear stability. There is a maximum value of Cimax which appears at a small porous filling ratio when Re is larger than 2 000. And the value of filling ratio 0 corresponding to the maximum value of Cimax in the most unstable state is increased with in- creasing Re. There is a critical value of porous filling ratio （= 0.24） for Re = 500; the structure will become stable as ψ grows to surpass the threshold of 0.24; When porous filling ratio ψ increases from 0.4 to 0.6, there is hardly any changes in the values of Cimax. We have also observed that the critical Reynolds number is especially sen

关键词： Porous layer linear stability Porous filling ratio Poiseuille flow Interface

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Exact solutions and linear stability analysis for two-dimensional Ablowitz Ladik equation

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Chinese Physics B 2014年第4期23卷 300-309页

作者：张金良王红县 School of Mathematics and Statistics Henan University of Science and Technology

The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the （GI/G）-expansion method, and the effects of the parameters （including the coupling constant and other parameters） on the linear stability of the exact solutions are analysed and numerically simulated.

关键词： two-dimensional Ablowitz-Ladik equation linear stability exact solution numerical simulation

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Ecological control strategy for cooperative autonomous vehicle in mixed traffic considering linear stability

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Journal of Intelligent and Connected Vehicles 2021年第3期4卷 115-124页

作者： Chaoru Lu Chenhui Liu Department of Civil Engineering and Energy Technology Oslo Metropolitan UniversityOsloNorway College of Civil Engineering Hunan UniversityChangshaChina

Purpose–This paper aims to present a cooperative adaptive cruise control,called stable smart driving model(SSDM),for connected and autonomous vehicles(CAVs)in mixed trafﬁc streams with human-driven ***/methodology/approach–Considering the linear stability,SSDM is able to provide smooth deceleration and acceleration in the vehicle platoons with or without ***,the calibrated Virginia tech microscopic energy and emission model is applied in this study to investigate the impact of CAVs on the fuel consumption of the vehicle platoon and trafﬁcﬂ*** the cut-in condition,the SSDM outperforms ecological SDM and SDM in terms of stability considering different desired time ***,single-lane vehicle dynamics are simulated for human-driven vehicles and ***–The result shows that CAVs can reduce platoon-level fuel *** can save the platoon-level fuel consumption up to 15%,outperforming other existing control *** the single-lane highway with merging,the higher market penetration of SSDM-equipped CAVs leads to less fuel ***/value–The proposed rule-based control method considered linear stability to generate smoother deceleration and acceleration *** research results can help to develop environmental-friendly control strategies and lay the foundation for the new methods.

关键词： Adaptive cruise control Connected and autonomous vehicle(CAV) linear stability

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Existence and linear stability of planar waves in the Oregonator model

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Chinese Physics B 2002年第12期11卷 1234-1239页

作者：周天寿何小兰 DepartmentofMathematicalSciences TsinghuaUniversityBeijing100084China DepartmentofInformationEngineering SchoolofEconomicsandManagementofGuandongGuanzhou510262China

In this paper, various waves in the Oregonator model are investigated in detail. The existence of planar waves (in particular, spiral waves) is rigorously proven and their linear stability is analysed. In addition, so... 详细信息

关键词： excitable media travelling wave spiral wave linear stability

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Effects of connected automated vehicle on stability and energy consumption of heterogeneous traffic flow system

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Chinese Physics B 2024年第3期33卷 291-301页

作者：申瑾赵建东刘华清姜锐余智鑫 School of Systems Science Beijing Jiaotong UniversityBeijing 100044China Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport Beijing Jiaotong UniversityBeijing 100044China School of Maritime and Transportation Ningbo UniversityNingbo 315000China

With the development of intelligent and interconnected traffic system,a convergence of traffic stream is anticipated in the foreseeable future,where both connected automated vehicle(CAV)and human driven vehicle(HDV)will *** order to examine the effect of CAV on the overall stability and energy consumption of such a heterogeneous traffic system,we first take into account the interrelated perception of distance and speed by CAV to establish a macroscopic dynamic model through utilizing the full velocity difference(FVD)***,adopting the linear stability theory,we propose the linear stability condition for the model through using the small perturbation method,and the validity of the heterogeneous model is verified by comparing with the FVD *** nonlinear theoretical analysis,we further derive the KdV-Burgers equation,which captures the propagation characteristics of traffic density ***,by numerical simulation experiments through utilizing a macroscopic model of heterogeneous traffic flow,the effect of CAV permeability on the stability of density wave in heterogeneous traffic flow and the energy consumption of the traffic system is *** analysis reveals emergent traffic *** experimental findings demonstrate that as CAV permeability increases,the ability to dampen the propagation of fluctuations in heterogeneous traffic flow gradually intensifies when giving system perturbation,leading to enhanced stability of the traffic ***,higher initial traffic density renders the traffic system more susceptible to congestion,resulting in local clustering effect and stop-and-go traffic ***,the total energy consumption of the heterogeneous traffic system exhibits a gradual decline with CAV permeability *** evidence has demonstrated the positive influence of CAV on heterogeneous traffic *** research contributes to providing theoretical guidance for future CAV applic

关键词： heterogeneous traffic flow CAV linear stability nonlinear stability energy consumption

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Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

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Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 563-580页

作者： N.HUMNEKAR D.SRINIVASACHARYA Department of Mathematics National Institute of TechnologyWarangal 506004TelanganaIndia

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is *** DarcyBrinkman model is used to characterize the fluid flow dynamics in porous *** analytical solutions are obtained for the unidirectional and completely developed *** on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is *** eigenvalue problem is then solved by the spectral ***,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing *** results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the ***,the flow is the most unstable when the channel is vertically oriented.

关键词： nanofluid inclined channel variable viscosity linear stability double dif-fusion porous medium

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stability of Three-Dimensional Interfacial Waves Under Subharmonic Disturbances

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中国海洋工程:英文版 2023年第4期37卷 558-567页

作者： Nabil ALLALOU Mohammed DEBIANE Christian KHARIF Facultéde Physique Universitédes Sciences et de la Technologie Houari Boumediene(USTHB)Algiers 16123Algeria Technopole de Chateau-Gombert Institut de Recherche sur les Phénomènes Hors Equilibre(IRPHE)Marseille 13384France

This study examines the stability regimes of three-dimensional interfacial gravity *** numerical results of the linear stability analysis extend the three-dimensional surface waves results of Ioualalen and Kharif(1994)to three-dimensional interfacial *** approach of the collocation type has been developed for this *** equations of motion are reduced to an eigenvalue problem where the perturbations are spectrally decomposed into normal *** results obtained showed that the density ratio plays a stabilizing *** addition,the dominant instability is of three-dimensional structure,and it belongs to class I for all values of density ratio.

关键词： short-crested interfacial waves linear stability collocation method Padéapproximant

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A High-Order Semi-Lagrangian Finite Difference Method for Nonlinear Vlasov and BGK Models

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Communications on Applied Mathematics and Computation 2023年第1期5卷 170-198页

作者： Linjin Li Jingmei Qiu Giovanni Russo Department of Mathematical Sciences University of DelawareNewarkDE 19717USA Department of Mathematics and Computer Science University of CataniaCataniaItaly

In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK *** finite difference scheme has better computational flexibility by working with point values,especially when working with high-dimensional problems in an operator splitting *** reconstruction procedure in the proposed SLFD scheme is motivated from the SL finite volume *** particular,we define a new sliding average function,whose cell averages agree with point values of the underlying *** developing the SL finite volume scheme for the sliding average function,we derive the proposed SLFD scheme,which is high-order accurate,mass conservative and unconditionally stable for linear *** performance of the scheme is showcased by linear transport applications,as well as the nonlinear Vlasov-Poisson and BGK ***,we apply the Fourier stability analysis to a fully discrete SLFD scheme coupled with diagonally implicit Runge-Kutta(DIRK)method when applied to a stiff two-velocity hyperbolic relaxation *** stability and asymptotic accuracy properties of DIRK methods are discussed in theoretical and computational aspects.

关键词： Semi-Lagrangian WENO Finite difference Vlasov-Poisson BGK equation linear stability

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ON INstability OF DILUTE FIBER SUSPENSIONS IN AN AXISYMMETRIC TAYLOR-COUETTE FLOW

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Journal of Hydrodynamics 2005年第4期17卷 398-403页

作者： WAN Zhan-hong LIN Jian-zhong LI Bing-ru Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

A stability analysis of flow between two coaxial rotating cylinders in the presence of fibers was performed. Based on the axisymmetric normal mode for the disturbances, a modified stability equation was derived. Then the numerical solution of the eigenvalue problem about the equation was obrained using the fourth order finite difference scheme. The marginal curves that determine the instability property were drawn. The results show that the flow instability of the dilute fiber suspensions is governed by the aspect ratio of fiber H, the inerement of H causes an increase of critical inner Reynohts number. The fiber additives effectively attenuate the instability of the flow. which is in agreement with those of related experiments.

关键词： linear stability fiber suspensions Taylor-Couette flow numerical simulation

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An accurate model for the thin film flow

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Acta Mechanica Sinica 2008年第4期24卷 375-380页

作者： Hamid Ait Abderahmane Georgios H.Vatistas Department of Mechanical and Industrial Engineering Concordia University 1455 de Maisonneuve Blvd West Montreal OC H3G 1M8 Canada

This paper deals with the linear stability of a liquid film flowing down an inclined plane. The Navier-Stokes equations were reduced into four evolution equations that describe the development of the film depth, the flow rate, the free surface velocity, and the wall shear stress, using the Karman-Polhausen boundary layer integral method. Thus, we were able to determine the stability threshold and approach well the critical wave number for long waves. The obtained results were found to be in good agreement with the experiments of Liu et al.

关键词： Liquid film linear stability Flow model

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