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Martina Bukac - One of the best experts on this subject based on the ideXlab platform.
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stability and convergence analysis of the extensions of the kinematically Coupled Scheme for the fluid structure interaction
SIAM Journal on Numerical Analysis, 2016Co-Authors: Martina Bukac, Boris MuhaAbstract:In this work we analyze the stability and convergence properties of a loosely-Coupled Scheme, called the kinematically Coupled Scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic structure. We consider a benchmark problem where the structure is modeled using a general thin structure model, and the coupling between the fluid and structure is linear. We derive the energy estimates associated with the unconditional stability of an extension of the kinematically Coupled Scheme, called the $\beta$-Scheme. Furthermore, for the first time we present a priori estimates showing optimal, first-order in time convergence in the case where $\beta=1$. We further discuss the extensions of our results to other fluid-structure interaction problems, in particular the fluid-thick structure interaction problem. The theoretical stability and convergence results are supported with numerical examples.
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partitioning strategies for the interaction of a fluid with a poroelastic material based on a nitsche s coupling approach
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Martina Bukac, Ivan Yotov, Rana Zakerzadeh, Paolo ZuninoAbstract:Abstract We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand, it shares common traits with fluid–structure interaction. On the other hand it resembles the Stokes–Darcy coupling. For these reasons, the numerical simulation of the Stokes–Biot Coupled system is a challenging task. The need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners for the equations at hand are typical shortcomings of classical discretization methods applied to this problem, such as the finite element method for spatial discretization and finite differences for time stepping. The application of loosely Coupled time advancing Schemes mitigates these issues, because it allows to solve each equation of the system independently with respect to the others, at each time step. In this work, we develop and thoroughly analyze a loosely Coupled Scheme for Stokes–Biot equations. The Scheme is based on Nitsche’s method for enforcing interface conditions. Once the interface operators corresponding to the interface conditions have been defined, time lagging allows us to build up a loosely Coupled Scheme with good stability properties. The stability of the Scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem. The error of the resulting method is also analyzed, showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization Schemes. In order to restore good approximation properties, while maintaining the computational efficiency of the loosely Coupled approach, we consider the application of the loosely Coupled Scheme as a preconditioner for the monolithic approach. Both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand.
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partitioning strategies for the interaction of a fluid with a poroelastic material based on a nitsche s coupling approach
arXiv: Numerical Analysis, 2014Co-Authors: Martina Bukac, Ivan Yotov, Rana Zakerzadeh, Paolo ZuninoAbstract:We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it shares common traits with fluid-structure interaction. On the other hand it resembles the Stokes-Darcy coupling. For these reasons, the numerical simulation of the Stokes-Biot Coupled system is a challenging task. The need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners are typical shortcomings of classical discretization methods applied to this problem. The application of loosely Coupled time advancing Schemes mitigates these issues because it allows to solve each equation of the system independently with respect to the others. In this work we develop and thoroughly analyze a loosely Coupled Scheme for Stokes-Biot equations. The Scheme is based on Nitsche's method for enforcing interface conditions. Once the interface operators corresponding to the interface conditions have been defined, time lagging allows us to build up a loosely Coupled Scheme with good stability properties. The stability of the Scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem. The error of the resulting method is also analyzed, showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization Schemes. In order to restore good approximation properties, while maintaining the computational efficiency of the loosely Coupled approach, we consider the application of the loosely Coupled Scheme as a preconditioner for the monolithic approach. Both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand.
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fluid structure interaction in blood flow capturing non zero longitudinal structure displacement
Journal of Computational Physics, 2013Co-Authors: Martina Bukac, Suncica Canic, Roland Glowinski, Josip Tambaca, Annalisa QuainiAbstract:We present a new model and a novel loosely Coupled partitioned numerical Scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement. Fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid. The two are fully Coupled via kinematic and dynamic coupling conditions. Our numerical Scheme is based on a new modified Lie operator splitting that decouples the fluid and structure sub-problems in a way that leads to a loosely Coupled Scheme which is unconditionally stable. This was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub-problems, leading to an implicit coupling between the fluid and structure velocities. The proposed Scheme is a modification of the recently introduced ''kinematically Coupled Scheme'' for which the newly proposed modified Lie splitting significantly increases the accuracy. The performance and accuracy of the Scheme were studied on a couple of instructive examples including a comparison with a monolithic Scheme. It was shown that the accuracy of our Scheme was comparable to that of the monolithic Scheme, while our Scheme retains all the main advantages of partitioned Schemes, such as modularity, simple implementation, and low computational costs.
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Stability of the kinematically Coupled \beta-Scheme for fluid-structure interaction problems in hemodynamics
arXiv: Numerical Analysis, 2012Co-Authors: Sunčica Čanić, Boris Muha, Martina BukacAbstract:It is well-known that classical Dirichlet-Neumann loosely Coupled partitioned Schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in \cite{causin2005added} on a simple test problem, that these instabilities are associated with the so called ``added-mass effect''. By considering the same test problem as in \cite{causin2005added}, the present work shows that a novel, partitioned, loosely Coupled Scheme, recently introduced in \cite{MarSun}, called the kinematically Coupled $\beta$-Scheme, does not suffer from the added mass effect for any $\beta \in [0,1]$, and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly Coupled benchmark FSI problem, first considered in \cite{formaggia2001coupling}.
Suncica Canic - One of the best experts on this subject based on the ideXlab platform.
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existence of a solution to a fluid multi layered structure interaction problem
arXiv: Analysis of PDEs, 2013Co-Authors: Boris Muha, Suncica CanicAbstract:We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the fluid, and a thick layer which sits on top of the thin structural layer. The fluid flow, which is driven by the time-dependent dynamic pressure data, is governed by the 2D Navier-Stokes equations for an incompressible, viscous fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. The fluid and the structure, as well as the two structural layers, are fully Coupled via the kinematic and dynamic coupling conditions describing continuity of velocity and balance of contact forces. The thin structural layer acts as a fluid-structure interface with mass. The resulting FSI problem is a nonlinear moving boundary problem of parabolic-hyperbolic type. This problem is motivated by the flow of blood in elastic arteries whose walls are composed of several layers, each with different mechanical characteristics and thickness. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical Scheme, known as the kinematically Coupled Scheme. We effectively prove convergence of that numerical Scheme to a solution of the nonlinear fluid-multi-layered-structure interaction problem. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin fluid-structure interface with mass regularizes solutions of the Coupled problem.
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fluid structure interaction in blood flow capturing non zero longitudinal structure displacement
Journal of Computational Physics, 2013Co-Authors: Martina Bukac, Suncica Canic, Roland Glowinski, Josip Tambaca, Annalisa QuainiAbstract:We present a new model and a novel loosely Coupled partitioned numerical Scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement. Fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid. The two are fully Coupled via kinematic and dynamic coupling conditions. Our numerical Scheme is based on a new modified Lie operator splitting that decouples the fluid and structure sub-problems in a way that leads to a loosely Coupled Scheme which is unconditionally stable. This was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub-problems, leading to an implicit coupling between the fluid and structure velocities. The proposed Scheme is a modification of the recently introduced ''kinematically Coupled Scheme'' for which the newly proposed modified Lie splitting significantly increases the accuracy. The performance and accuracy of the Scheme were studied on a couple of instructive examples including a comparison with a monolithic Scheme. It was shown that the accuracy of our Scheme was comparable to that of the monolithic Scheme, while our Scheme retains all the main advantages of partitioned Schemes, such as modularity, simple implementation, and low computational costs.
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existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Boris Muha, Suncica CanicAbstract:We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully Coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical Scheme, known as the kinematically Coupled Scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically Coupled Scheme is the well-known Marchuk–Yanenko Scheme, also known as the Lie splitting Scheme. We effectively prove convergence of that numerical Scheme to a solution of the corresponding FSI problem.
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existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls
arXiv: Analysis of PDEs, 2012Co-Authors: Boris Muha, Suncica CanicAbstract:We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by 2D incompressible Navier-Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the 1D cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully Coupled (2-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and balance of contact forces at the fluid-structure interface. We prove existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical Scheme, known as the kinematically Coupled Scheme, introduced in \cite{GioSun} to solve the underlying FSI problems. The backbone of the kinematically Coupled Scheme is the well-known Marchuk-Yanenko Scheme, also known as the Lie splitting Scheme. We effectively prove convergence of that numerical Scheme to a solution of the corresponding FSI problem.
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stability of the kinematically Coupled beta Scheme for fluid structure interaction problems in hemodynamics
International Journal of Numerical Analysis and Modeling, 2012Co-Authors: Suncica Canic, Boris Muha, Martina BukacAbstract:It is known that classical Dirichlet-Neumann loosely Coupled partitioned Schemes for uid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown by Causin, Gerbeau, and Nobile [17] that these instabilities are associated with the \added-mass eect". The \added mass eect" was studied in [17] by considering the simplest FSI problem which captures the main features responsible for the instabilities of classical Dirichlet-Neumann loosely Coupled Schemes. By considering the same test problem, the present work shows that a novel, partitioned, loosely Coupled Scheme, recently introduced in [11], called the kinematically Coupled -Scheme, does not suer from the added mass eect for any 2 [0; 1], and is unconditionally stable for all the parameter values in the problem. Numerical results are presented for a fully nonlinear benchmark FSI problem in hemodynamics of Formaggia et al. [30]. The results show that the Scheme is stable for this benchmark problem even for the parameter values well within the parameter range for which the classical Dirichlet-Neumann Schemes are unconditionally unstable. The main contribution of this work is in explicitly showing how the implicit enforcement of the kinematic coupling condition and the inclusion of the structure inertia into the uid sub-problem avoid the presence of the added mass eect in the kinematically-Coupled -Scheme.
Boris Muha - One of the best experts on this subject based on the ideXlab platform.
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stability and convergence analysis of the extensions of the kinematically Coupled Scheme for the fluid structure interaction
SIAM Journal on Numerical Analysis, 2016Co-Authors: Martina Bukac, Boris MuhaAbstract:In this work we analyze the stability and convergence properties of a loosely-Coupled Scheme, called the kinematically Coupled Scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic structure. We consider a benchmark problem where the structure is modeled using a general thin structure model, and the coupling between the fluid and structure is linear. We derive the energy estimates associated with the unconditional stability of an extension of the kinematically Coupled Scheme, called the $\beta$-Scheme. Furthermore, for the first time we present a priori estimates showing optimal, first-order in time convergence in the case where $\beta=1$. We further discuss the extensions of our results to other fluid-structure interaction problems, in particular the fluid-thick structure interaction problem. The theoretical stability and convergence results are supported with numerical examples.
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existence of a solution to a fluid multi layered structure interaction problem
arXiv: Analysis of PDEs, 2013Co-Authors: Boris Muha, Suncica CanicAbstract:We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the fluid, and a thick layer which sits on top of the thin structural layer. The fluid flow, which is driven by the time-dependent dynamic pressure data, is governed by the 2D Navier-Stokes equations for an incompressible, viscous fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. The fluid and the structure, as well as the two structural layers, are fully Coupled via the kinematic and dynamic coupling conditions describing continuity of velocity and balance of contact forces. The thin structural layer acts as a fluid-structure interface with mass. The resulting FSI problem is a nonlinear moving boundary problem of parabolic-hyperbolic type. This problem is motivated by the flow of blood in elastic arteries whose walls are composed of several layers, each with different mechanical characteristics and thickness. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical Scheme, known as the kinematically Coupled Scheme. We effectively prove convergence of that numerical Scheme to a solution of the nonlinear fluid-multi-layered-structure interaction problem. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin fluid-structure interface with mass regularizes solutions of the Coupled problem.
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existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Boris Muha, Suncica CanicAbstract:We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully Coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical Scheme, known as the kinematically Coupled Scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically Coupled Scheme is the well-known Marchuk–Yanenko Scheme, also known as the Lie splitting Scheme. We effectively prove convergence of that numerical Scheme to a solution of the corresponding FSI problem.
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existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls
arXiv: Analysis of PDEs, 2012Co-Authors: Boris Muha, Suncica CanicAbstract:We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by 2D incompressible Navier-Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the 1D cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully Coupled (2-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and balance of contact forces at the fluid-structure interface. We prove existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical Scheme, known as the kinematically Coupled Scheme, introduced in \cite{GioSun} to solve the underlying FSI problems. The backbone of the kinematically Coupled Scheme is the well-known Marchuk-Yanenko Scheme, also known as the Lie splitting Scheme. We effectively prove convergence of that numerical Scheme to a solution of the corresponding FSI problem.
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Stability of the kinematically Coupled \beta-Scheme for fluid-structure interaction problems in hemodynamics
arXiv: Numerical Analysis, 2012Co-Authors: Sunčica Čanić, Boris Muha, Martina BukacAbstract:It is well-known that classical Dirichlet-Neumann loosely Coupled partitioned Schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in \cite{causin2005added} on a simple test problem, that these instabilities are associated with the so called ``added-mass effect''. By considering the same test problem as in \cite{causin2005added}, the present work shows that a novel, partitioned, loosely Coupled Scheme, recently introduced in \cite{MarSun}, called the kinematically Coupled $\beta$-Scheme, does not suffer from the added mass effect for any $\beta \in [0,1]$, and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly Coupled benchmark FSI problem, first considered in \cite{formaggia2001coupling}.
Eleanor Blyth - One of the best experts on this subject based on the ideXlab platform.
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the joint uk land environment simulator jules model description part 2 carbon fluxes and vegetation dynamics
Geoscientific Model Development, 2011Co-Authors: Douglas B Clark, Lina M Mercado, Stephen Sitch, Chris D Jones, N Gedney, Martin Best, M Pryor, G G Rooney, Richard Essery, Eleanor BlythAbstract:Abstract. The Joint UK Land Environment Simulator (JULES) is a process-based model that simulates the fluxes of carbon, water, energy and momentum between the land surface and the atmosphere. Many studies have demonstrated the important role of the land surface in the functioning of the Earth System. Different versions of JULES have been employed to quantify the effects on the land carbon sink of climate change, increasing atmospheric carbon dioxide concentrations, changing atmospheric aerosols and tropospheric ozone, and the response of methane emissions from wetlands to climate change. This paper describes the consolidation of these advances in the modelling of carbon fluxes and stores, in both the vegetation and soil, in version 2.2 of JULES. Features include a multi-layer canopy Scheme for light interception, including a sunfleck penetration Scheme, a Coupled Scheme of leaf photosynthesis and stomatal conductance, representation of the effects of ozone on leaf physiology, and a description of methane emissions from wetlands. JULES represents the carbon allocation, growth and population dynamics of five plant functional types. The turnover of carbon from living plant tissues is fed into a 4-pool soil carbon model. The process-based descriptions of key ecological processes and trace gas fluxes in JULES mean that this community model is well-suited for use in carbon cycle, climate change and impacts studies, either in standalone mode or as the land component of a Coupled Earth system model.
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The Joint UK Land Environment Simulator (JULES), model description – Part 2: Carbon fluxes and vegetation dynamics
Copernicus Publications, 2011Co-Authors: Douglas B Clark, Lina M Mercado, Stephen Sitch, Chris D Jones, N Gedney, M Pryor, G G Rooney, Richard Essery, M. J. Best, Eleanor BlythAbstract:The Joint UK Land Environment Simulator (JULES) is a process-based model that simulates the fluxes of carbon, water, energy and momentum between the land surface and the atmosphere. Many studies have demonstrated the important role of the land surface in the functioning of the Earth System. Different versions of JULES have been employed to quantify the effects on the land carbon sink of climate change, increasing atmospheric carbon dioxide concentrations, changing atmospheric aerosols and tropospheric ozone, and the response of methane emissions from wetlands to climate change. <br><br> This paper describes the consolidation of these advances in the modelling of carbon fluxes and stores, in both the vegetation and soil, in version 2.2 of JULES. Features include a multi-layer canopy Scheme for light interception, including a sunfleck penetration Scheme, a Coupled Scheme of leaf photosynthesis and stomatal conductance, representation of the effects of ozone on leaf physiology, and a description of methane emissions from wetlands. JULES represents the carbon allocation, growth and population dynamics of five plant functional types. The turnover of carbon from living plant tissues is fed into a 4-pool soil carbon model. <br><br> The process-based descriptions of key ecological processes and trace gas fluxes in JULES mean that this community model is well-suited for use in carbon cycle, climate change and impacts studies, either in standalone mode or as the land component of a Coupled Earth system model
Sunčica Čanić - One of the best experts on this subject based on the ideXlab platform.
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Stability of the kinematically Coupled \beta-Scheme for fluid-structure interaction problems in hemodynamics
arXiv: Numerical Analysis, 2012Co-Authors: Sunčica Čanić, Boris Muha, Martina BukacAbstract:It is well-known that classical Dirichlet-Neumann loosely Coupled partitioned Schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in \cite{causin2005added} on a simple test problem, that these instabilities are associated with the so called ``added-mass effect''. By considering the same test problem as in \cite{causin2005added}, the present work shows that a novel, partitioned, loosely Coupled Scheme, recently introduced in \cite{MarSun}, called the kinematically Coupled $\beta$-Scheme, does not suffer from the added mass effect for any $\beta \in [0,1]$, and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly Coupled benchmark FSI problem, first considered in \cite{formaggia2001coupling}.
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Stable loosely-Coupled-type algorithm for fluid-structure interaction in blood flow
Journal of Computational Physics, 2009Co-Authors: Giovanna Guidoboni, Roland Glowinski, Nicola Cavallini, Sunčica ČanićAbstract:We introduce a novel loosely Coupled-type algorithm for fluid-structure interaction between blood flow and thin vascular walls. This algorithm successfully deals with the difficulties associated with the ''added mass effect'', which is known to be the cause of numerical instabilities in fluid-structure interaction problems involving fluid and structure of comparable densities. Our algorithm is based on a time-discretization via operator splitting which is applied, in a novel way, to separate the fluid sub-problem from the structure elastodynamics sub-problem. In contrast with traditional loosely-Coupled Schemes, no iterations are necessary between the fluid and structure sub-problems; this is due to the fact that our novel splitting strategy uses the ''added mass effect'' to stabilize rather than to destabilize the numerical algorithm. This stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub-problem. The stability of the Scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed Scheme is unconditionally stable. Due to the crucial role played by the kinematic lateral boundary condition, the proposed algorithm is named the ''kinematically Coupled Scheme''.
