The Experts below are selected from a list of 22926 Experts worldwide ranked by ideXlab platform
Johnny Guzman - One of the best experts on this subject based on the ideXlab platform.
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well posedness and h div conforming finite element approximation of a linearised model for Inviscid incompressible Flow
Mathematical Models and Methods in Applied Sciences, 2020Co-Authors: Gabriel R Barrenechea, Erik Burman, Johnny GuzmanAbstract:We consider a linearised model of incompressible Inviscid Flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model...
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well posedness and h div conforming finite element approximation of a linearised model for Inviscid incompressible Flow
arXiv: Numerical Analysis, 2019Co-Authors: Gabriel R Barrenechea, Erik Burman, Johnny GuzmanAbstract:We consider a linearised model of incompressible Inviscid Flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using H(div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the $L^2$-norm of order $O(h^{k+\frac12})$. We also prove error estimates for the pressure error in the $L^2$-norm.
Silas Alben - One of the best experts on this subject based on the ideXlab platform.
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eigenmode analysis of membrane stability in Inviscid Flow
Physical Review Fluids, 2021Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the stability of a thin membrane (of zero bending rigidity) with a vortex sheet as a nonlinear eigenvalue problem in the parameter space of membrane mass (${R}_{1}$) and pretension (${T}_{0}$). With both ends fixed light membranes become unstable by a divergence instability and heavy membranes lose stability by flutter and divergence for a ${T}_{0}$ that increases with ${R}_{1}$. With the leading edge fixed and trailing edge free, or both edges free, membrane eigenmodes transition in shape across the stability boundary. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.
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eigenmode analysis of membrane stability in Inviscid Flow
arXiv: Fluid Dynamics, 2020Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an Inviscid fluid Flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem iteratively with large ensembles of initial guesses, for three canonical boundary conditions---both ends fixed, one end fixed and one free, and both free. Over several orders of magnitude of membrane mass density, we find instability by divergence or flutter (particularly at large mass density, or with one or both ends free). The most unstable eigenmodes generally become "wavier" at smaller mass density and smaller tension, but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.
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large amplitude membrane flutter in Inviscid Flow
Journal of Fluid Mechanics, 2020Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional Inviscid fluid Flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming Flow.
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large amplitude membrane flutter in Inviscid Flow
arXiv: Fluid Dynamics, 2019Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in 2D Inviscid fluid Flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free, the membranes flutter with very small amplitudes and high spatial and temporal frequencies at small mass density. As mass density increases, the membranes transition to periodic and then increasingly aperiodic motions, and the amplitudes increase and spatial and temporal frequencies decrease. With both edges free, the membranes flutter similarly to the fixed-free case but also translate vertically with steady, periodic, or aperiodic trajectories, and with nonzero slopes that lead to small angles of attack with respect to the oncoming Flow.
Gabriel R Barrenechea - One of the best experts on this subject based on the ideXlab platform.
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well posedness and h div conforming finite element approximation of a linearised model for Inviscid incompressible Flow
Mathematical Models and Methods in Applied Sciences, 2020Co-Authors: Gabriel R Barrenechea, Erik Burman, Johnny GuzmanAbstract:We consider a linearised model of incompressible Inviscid Flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model...
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well posedness and h div conforming finite element approximation of a linearised model for Inviscid incompressible Flow
arXiv: Numerical Analysis, 2019Co-Authors: Gabriel R Barrenechea, Erik Burman, Johnny GuzmanAbstract:We consider a linearised model of incompressible Inviscid Flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using H(div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the $L^2$-norm of order $O(h^{k+\frac12})$. We also prove error estimates for the pressure error in the $L^2$-norm.
Christiana Mavroyiakoumou - One of the best experts on this subject based on the ideXlab platform.
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eigenmode analysis of membrane stability in Inviscid Flow
Physical Review Fluids, 2021Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the stability of a thin membrane (of zero bending rigidity) with a vortex sheet as a nonlinear eigenvalue problem in the parameter space of membrane mass (${R}_{1}$) and pretension (${T}_{0}$). With both ends fixed light membranes become unstable by a divergence instability and heavy membranes lose stability by flutter and divergence for a ${T}_{0}$ that increases with ${R}_{1}$. With the leading edge fixed and trailing edge free, or both edges free, membrane eigenmodes transition in shape across the stability boundary. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.
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eigenmode analysis of membrane stability in Inviscid Flow
arXiv: Fluid Dynamics, 2020Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an Inviscid fluid Flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem iteratively with large ensembles of initial guesses, for three canonical boundary conditions---both ends fixed, one end fixed and one free, and both free. Over several orders of magnitude of membrane mass density, we find instability by divergence or flutter (particularly at large mass density, or with one or both ends free). The most unstable eigenmodes generally become "wavier" at smaller mass density and smaller tension, but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.
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large amplitude membrane flutter in Inviscid Flow
Journal of Fluid Mechanics, 2020Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional Inviscid fluid Flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming Flow.
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large amplitude membrane flutter in Inviscid Flow
arXiv: Fluid Dynamics, 2019Co-Authors: Christiana Mavroyiakoumou, Silas AlbenAbstract:We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in 2D Inviscid fluid Flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free, the membranes flutter with very small amplitudes and high spatial and temporal frequencies at small mass density. As mass density increases, the membranes transition to periodic and then increasingly aperiodic motions, and the amplitudes increase and spatial and temporal frequencies decrease. With both edges free, the membranes flutter similarly to the fixed-free case but also translate vertically with steady, periodic, or aperiodic trajectories, and with nonzero slopes that lead to small angles of attack with respect to the oncoming Flow.
Andrey Morgulis - One of the best experts on this subject based on the ideXlab platform.
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instability of an Inviscid Flow between porous cylinders with radial Flow
Journal of Fluid Mechanics, 2013Co-Authors: Konstantin Ilin, Andrey MorgulisAbstract:The stability of a two-dimensional Inviscid Flow in an annulus between two permeable cylinders is examined. The basic Flow is irrotational, and both radial and azimuthal components of the velocity are non-zero. The direction of the radial Flow can be from the inner cylinder to the outer one (the diverging Flow) or from the outer cylinder to the inner one (the converging Flow). It is shown that, independent of the direction of the radial Flow, the basic Flow is unstable to small two-dimensional perturbations provided that the ratio of the azimuthal component of the velocity to the radial one is sufficiently large. The instability is oscillatory and persists if the viscosity of the fluid is taken into consideration.
