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Ruxandra Stavre - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic analysis of a viscous fluid thin plate interaction Periodic Flow
    Mathematical Models and Methods in Applied Sciences, 2014
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid Flow–thin elastic plate" when the thickness of the plate, e, tends to zero, while the density and the Young's modulus of the plate material are of order e-1 and e-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when e tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

  • Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic Flow
    Mathematical Models and Methods in Applied Sciences, 2014
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid Flow–thin elastic plate" when the thickness of the plate, e, tends to zero, while the density and the Young's modulus of the plate material are of order e-1 and e-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when e tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

  • asymptotic analysis of a viscous fluid thin plate interaction Periodic Flow
    Comptes Rendus Mecanique, 2012
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    Abstract The interaction “viscous fluid–thin plate” is considered when the thickness of the plate, e, tends to zero, while the density and the Youngʼs modulus of the plate are of order e − 1 and e − 3 , respectively. The thickness of the fluid layer is of the order of one. An asymptotic expansion is constructed and the error estimates are proved. The leading term of the asymptotic expansion is the solution of the interaction problem “fluid-Kirchoff plate”. The method of asymptotic partial domain decomposition is discussed: the main part of the plate is described by a 1D model while a small part is simulated by the 2D elasticity equations, with appropriate junction conditions.

  • Asymptotic analysis of a non-Periodic Flow in a thin channel with visco-elastic wall
    Networks and Heterogeneous Media, 2008
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    Abstract. In this paper we continue the study of a fluid-structure interaction problem with the non Periodic case. We consider the non stationary Flow of a viscous fluid in a thin rectangle with an elastic membrane as the upper part of the boundary. The physical problem which corresponds to non homogeneous boundary conditions is stated. By using a boundary layer method, an asymp- totic solution is proposed. The properties of the boundary layer functions are established and an error estimate is obtained.

Grigory Panasenko - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic analysis of a viscous fluid thin plate interaction Periodic Flow
    Mathematical Models and Methods in Applied Sciences, 2014
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid Flow–thin elastic plate" when the thickness of the plate, e, tends to zero, while the density and the Young's modulus of the plate material are of order e-1 and e-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when e tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

  • Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic Flow
    Mathematical Models and Methods in Applied Sciences, 2014
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid Flow–thin elastic plate" when the thickness of the plate, e, tends to zero, while the density and the Young's modulus of the plate material are of order e-1 and e-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when e tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

  • Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic Flow
    Mathematical Models and Methods in Applied Sciences, 2014
    Co-Authors: Grigory Panasenko, R. Stavre
    Abstract:

    The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid Flow–thin elastic plate" when the thickness of the plate, ε, tends to zero, while the density and the Young's modulus of the plate material are of order ε-1and ε-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when ε tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

  • asymptotic analysis of a viscous fluid thin plate interaction Periodic Flow
    Comptes Rendus Mecanique, 2012
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    Abstract The interaction “viscous fluid–thin plate” is considered when the thickness of the plate, e, tends to zero, while the density and the Youngʼs modulus of the plate are of order e − 1 and e − 3 , respectively. The thickness of the fluid layer is of the order of one. An asymptotic expansion is constructed and the error estimates are proved. The leading term of the asymptotic expansion is the solution of the interaction problem “fluid-Kirchoff plate”. The method of asymptotic partial domain decomposition is discussed: the main part of the plate is described by a 1D model while a small part is simulated by the 2D elasticity equations, with appropriate junction conditions.

  • Asymptotic analysis of a non-Periodic Flow in a thin channel with visco-elastic wall
    Networks and Heterogeneous Media, 2008
    Co-Authors: Grigory Panasenko, Ruxandra Stavre
    Abstract:

    Abstract. In this paper we continue the study of a fluid-structure interaction problem with the non Periodic case. We consider the non stationary Flow of a viscous fluid in a thin rectangle with an elastic membrane as the upper part of the boundary. The physical problem which corresponds to non homogeneous boundary conditions is stated. By using a boundary layer method, an asymp- totic solution is proposed. The properties of the boundary layer functions are established and an error estimate is obtained.

Giovanni P. Galdi - One of the best experts on this subject based on the ideXlab platform.

  • Attainability of time-Periodic Flow of a viscous liquid past an oscillating body
    Journal of Evolution Equations, 2021
    Co-Authors: Giovanni P. Galdi, Toshiaki Hishida
    Abstract:

    A body $$\mathscr {B}$$ B is started from rest by a translational motion in an otherwise quiescent Navier–Stokes liquid filling the whole space. We show, for small data, that if after some time $$\mathscr {B}$$ B reaches a spinless oscillatory motion of period $$\mathcal T$$ T , the liquid will eventually execute also a time Periodic motion with the same period $$\mathcal T$$ T . This result is a suitable generalization of the famous Finn’s starting problem for steady states, to the case of time-Periodic motions.

  • attainability of time Periodic Flow of a viscous liquid past an oscillating body
    arXiv: Analysis of PDEs, 2020
    Co-Authors: Giovanni P. Galdi, Toshiaki Hishida
    Abstract:

    A body $\mathscr B$ is started from rest by translational motion in an otherwise quiescent Navier-Stokes liquid filling the whole space. We show, for small data, that if after some time $\mathscr B$ reaches a spinless oscillatory motion of period $\cal T$, the liquid will eventually execute also a time Periodic motion with same period $\cal T$. This problem is a suitable generalization of the famous Finn's starting problem for steady-states, to the case of time-Periodic motions

  • on bifurcating time Periodic Flow of a navier stokes liquid past a cylinder
    Archive for Rational Mechanics and Analysis, 2016
    Co-Authors: Giovanni P. Galdi
    Abstract:

    We provide general sufficient conditions for the existence and uniqueness of branching out of a time-Periodic family of solutions from steady-state solutions to the two-dimensional Navier-Stokes equations in the exterior of a cylinder. By separating the time-independent averaged component of the velocity field from its oscillatory one, we show that the problem can be formulated as a coupled elliptic-parabolic nonlinear system in appropriate and distinct function spaces, with the property that the relevant linearized operators become Fredholm of index 0. In this functional setting, the notorious difficulty of 0 being in the essential spectrum entirely disappears and, in fact, it is even meaningless. Our approach is different and, we believe, more natural and simpler than those proposed by previous authors discussing similar questions. Moreover, the latter all fail, when applied to the problem studied here.

  • on bifurcating time Periodic Flow of a navier stokes liquid past a cylinder
    arXiv: Analysis of PDEs, 2015
    Co-Authors: Giovanni P. Galdi
    Abstract:

    We provide general sufficient conditions for branching out of a time-Periodic family of solutions from steady-state solutions to the two-dimensional Navier-Stokes equations in the exterior of a cylinder. To this end, we first show that the problem can be formulated as a coupled elliptic-parabolic nonlinear system in appropriate function spaces. This is obtained by separating the time-independent averaged component of the velocity field from its "purely Periodic" one. We then prove that time-Periodic bifurcation occurs, provided the linearized time-independent operator of the parabolic problem possess a simple eigenvalue that crosses the imaginary axis when the Reynolds number passes through a (suitably defined) critical value. We also show that only supercritical or subcritical bifurcation may occur. Our approach is different and, we believe, more direct than those used by previous authors in similar, but distinct, context.

  • On Time-Periodic Flow of a Viscous Liquid past a Moving Cylinder
    Archive for Rational Mechanics and Analysis, 2013
    Co-Authors: Giovanni P. Galdi
    Abstract:

    We show existence, uniqueness and spatial asymptotic behavior of a two-dimensional time-Periodic Flow around a cylinder that moves orthogonal to its axis, with a time-Periodic velocity, v. The result is proved if the size of the data is sufficiently small, and the average of v over a period is not zero.

R. Stavre - One of the best experts on this subject based on the ideXlab platform.

  • Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic Flow
    Mathematical Models and Methods in Applied Sciences, 2014
    Co-Authors: Grigory Panasenko, R. Stavre
    Abstract:

    The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid Flow–thin elastic plate" when the thickness of the plate, ε, tends to zero, while the density and the Young's modulus of the plate material are of order ε-1and ε-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when ε tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a Periodic Flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

Chinhsiang Cheng - One of the best experts on this subject based on the ideXlab platform.

  • numerical simulation of Periodic mixed convective heat transfer in a rectangular cavity with a vibrating lid
    Applied Thermal Engineering, 2009
    Co-Authors: Chin Lung Chen, Chinhsiang Cheng
    Abstract:

    Abstract Periodic behavior of the mixed convective Flow in a rectangular cavity with a vibrating lid is investigated numerically in this study. The Periodic Flow patterns and heat transfer characteristics found are discussed with attention being focused on the interaction between the frequency of the lid velocity vibration and the frequency of the natural Periodic Flow. Several practical cases are investigated to evaluate the effects of the frequency of vibration of lid velocity (W) at Re = 100 and Gr = 5 × 105. The frequency of the natural Periodic Flow can be most clearly seen when the lid is moved at a constant-velocity (without vibration). As the vibration is imposed on the lid with the dimensionless frequency of the lid velocity varied between 0.1 and 0.3, the combined effects of the natural frequency and the lid vibration frequency on the transient variations in the Flow and the thermal characteristics have been observed. When the dimensionless frequency of lid velocity vibration is increased to be equal to or higher than 0.4, the natural Periodic Flow frequency disappears, and the lid vibration frequency dominates the Flow field, which means that the Periodic Flow field has locked-on to the lid vibration.

  • Numerical study of the effects of lid oscillation on the Periodic Flow pattern and convection heat transfer in a triangular cavity
    International Communications in Heat and Mass Transfer, 2009
    Co-Authors: Chin Lung Chen, Chinhsiang Cheng
    Abstract:

    Abstract This study is concerned with a Periodic Flow pattern with mixed convection in a triangular cavity caused by the effects of lid oscillation and buoyancy. The dimensionless stream function–vorticity formulation is adopted, and a curvilinear grid method for solving the stream function–vorticity equations in irregular geometries is used. Attention is in particular focused on the Flow behaviour under the interaction between the frequency of the oscillation of the lid velocity and the frequency of the natural Periodic Flow. Meanwhile, numerical predictions of the thermal characteristics represented by local and average Nusselt numbers on the walls as well as the transient Flow patterns are also provided. Results show that the frequency of oscillation of lid velocity and the natural Periodic Flow frequency both appear to be major frequencies in the frequency spectrum of the cavity Flow, for cases with a dimensionless lid oscillation frequency less than 0.5. When the dimensionless frequency of the oscillation of the lid velocity is equal to or higher than 0.5, the Flow and thermal fields are completely locked-on to the lid oscillation, and the natural Periodic Flow frequency is no longer visible in the spectrum.

  • Periodic Flow Pattern and Convection Heat Transfer in an Arc-Shaped Cavity with Oscillating Lid
    Numerical Heat Transfer Part A: Applications, 2006
    Co-Authors: Chin Lung Chen, Chinhsiang Cheng
    Abstract:

    The present study is concerned with Periodic behavior of mixed-convective Flow in an arc-shaped cavity with a vibrating lid. Numerical predictions of the effects of frequency of the vibration of the lid on the cavity Flow and heat transfer are presented. In this study, the dimensionless frequency of the lid velocity ranges between 0 and 1.0 in order to investigate the lid vibration effects extensively. The interaction between the frequency of vibration of lid velocity and the frequency of the natural Periodic Flow is of major concerns. Results show that the frequency of vibration of lid velocity and the natural Periodic Flow frequency both appear to be major frequencies in the frequency spectrum of the cavity Flow, for cases with dimensionless lid vibration frequency less than 0.4. When the dimensionless frequency of vibration of lid velocity is equal to or greater than 0.4, the Flow and thermal fields are completely “locked on” by the lid vibration, and the natural Periodic Flow frequency is no longer vi...

  • Buoyancy-induced Periodic Flow and heat transfer in lid-driven cavities with different cross-sectional shapes
    International Communications in Heat and Mass Transfer, 2005
    Co-Authors: Chinhsiang Cheng, Chin Lung Chen
    Abstract:

    Abstract This report is concerned with transient behavior of a buoyancy-induced Periodic Flow in different lid-driven cavities with different cross-sectional shapes. Periodic Flow patterns and heat transfer characteristics for various geometries are predicted. Governing equations are discretized based on the finite volume method with a curvilinear grid system generated numerically by the body-fitted coordinate transformation. Attentions are focused at nine cases of cross-sectional shape. For all the cases considered, Reynolds number and Grashof number are fixed at 100 and 5×10 5 , respectively. Results show that among the nine cases, cases 1/5C, 1/4C, 1/4T, and 1/5R tend to produce the Periodic Flow pattern and, case 1/5T exhibits the highest heat transfer performance.

  • NUMERICAL PREDICTION OF BUOYANCY-INDUCED Periodic Flow PATTERN AND HEAT TRANSFER IN A LID-DRIVEN ARC-SHAPE CAVITY
    Numerical Heat Transfer Part A: Applications, 2003
    Co-Authors: Chin Lung Chen, Chinhsiang Cheng
    Abstract:

    Numerical simulation has been carried out to study the unsteady phenomenon of a buoyancy-induced Periodic Flow and convection heat transfer in a lid-driven arc-shape cavity. The governing equations in terms of the stream function-vorticity formulation are solved by the finite-volume method coupled with a body-fitted coordinate transformation scheme. In the range of the Reynolds number (Re) from 100 to 2,000 and Grashof number (Gr) up to 5 2 10 7 , the heat transfer characteristics and Flow pattern have been predicted. Attention has been focused on the combined effects of the inertial and buoyant forces exerted on the fluid. Results show that only when the inertial and buoyant forces are of approximately equal strength that can the Periodic Flow pattern be observed. For an inertia-dominant or buoyancy-dominant situation, the Periodic Flow pattern is not visible.