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Enrique Zuazua - One of the best experts on this subject based on the ideXlab platform.

  • LACK OF COLLISION IN A SIMPLIFIED 1D MODEL FOR FLUID¿SOLID Interaction
    Mathematical Models and Methods in Applied Sciences, 2006
    Co-Authors: Juan Luis Vazquez, Enrique Zuazua
    Abstract:

    In this paper we consider a simplified model for fluid–solid Interaction in one space dimension. The fluid is assumed to be governed by the viscous Burgers equation. It is coupled with a finite number of solid masses in the form of point particles, which share the velocity of the fluid and are accelerated by the jump in velocity gradient of the fluid on both sides, which replaces here the standard pressure jump of Navier–Stokes models. We prove global existence and uniqueness of solutions. This requires proving that the solid particles never collide in finite time, a key fact that follows from suitable a priori estimates together with uniqueness results for ordinary differential equations. We also describe the asymptotic behavior of solutions as t → ∞, extending previous results established for a single solid mass. The evolution of the relative position of the particles is examined in terms of the strength of the convection term. The possible 2D analogues of these results in the context of Navier–Stokes equations are open problems.

  • lack of collision in a simplified 1d model for fluid solid Interaction
    Mathematical Models and Methods in Applied Sciences, 2006
    Co-Authors: Juan Luis Vazquez, Enrique Zuazua
    Abstract:

    In this paper we consider a simplified model for fluid–solid Interaction in one space dimension. The fluid is assumed to be governed by the viscous Burgers equation. It is coupled with a finite number of solid masses in the form of point particles, which share the velocity of the fluid and are accelerated by the jump in velocity gradient of the fluid on both sides, which replaces here the standard pressure jump of Navier–Stokes models. We prove global existence and uniqueness of solutions. This requires proving that the solid particles never collide in finite time, a key fact that follows from suitable a priori estimates together with uniqueness results for ordinary differential equations. We also describe the asymptotic behavior of solutions as t → ∞, extending previous results established for a single solid mass. The evolution of the relative position of the particles is examined in terms of the strength of the convection term. The possible 2D analogues of these results in the context of Navier–Stokes equations are open problems.

  • large time behavior for a simplified 1d model of fluid solid Interaction
    Pediatric Dermatology, 2003
    Co-Authors: Juan Luis Vazquez, Enrique Zuazua
    Abstract:

    Abstract In this article we consider a simple model in one space dimension for the Interaction between a fluid and a solid represented by a point mass. The fluid is governed by the viscous Burgers equation and the solid mass, which shares the velocity of the fluid, is accelerated by the difference of pressure at both sides of it. We describe the asymptotic behavior of solutions for integrable data using energy estimates and scaling techniques. We prove that the asymptotic profile of the fluid is a self-similar solution of the Burgers equation with an appropriate total mass, and we describe the parabolic trajectory of the point mass. We also prove that, asymptotically, the difference of pressure to both sides of the point mass vanishes. †Dedicated to C. Dafermos on his 60th birthday.

Juan Luis Vazquez - One of the best experts on this subject based on the ideXlab platform.

  • LACK OF COLLISION IN A SIMPLIFIED 1D MODEL FOR FLUID¿SOLID Interaction
    Mathematical Models and Methods in Applied Sciences, 2006
    Co-Authors: Juan Luis Vazquez, Enrique Zuazua
    Abstract:

    In this paper we consider a simplified model for fluid–solid Interaction in one space dimension. The fluid is assumed to be governed by the viscous Burgers equation. It is coupled with a finite number of solid masses in the form of point particles, which share the velocity of the fluid and are accelerated by the jump in velocity gradient of the fluid on both sides, which replaces here the standard pressure jump of Navier–Stokes models. We prove global existence and uniqueness of solutions. This requires proving that the solid particles never collide in finite time, a key fact that follows from suitable a priori estimates together with uniqueness results for ordinary differential equations. We also describe the asymptotic behavior of solutions as t → ∞, extending previous results established for a single solid mass. The evolution of the relative position of the particles is examined in terms of the strength of the convection term. The possible 2D analogues of these results in the context of Navier–Stokes equations are open problems.

  • lack of collision in a simplified 1d model for fluid solid Interaction
    Mathematical Models and Methods in Applied Sciences, 2006
    Co-Authors: Juan Luis Vazquez, Enrique Zuazua
    Abstract:

    In this paper we consider a simplified model for fluid–solid Interaction in one space dimension. The fluid is assumed to be governed by the viscous Burgers equation. It is coupled with a finite number of solid masses in the form of point particles, which share the velocity of the fluid and are accelerated by the jump in velocity gradient of the fluid on both sides, which replaces here the standard pressure jump of Navier–Stokes models. We prove global existence and uniqueness of solutions. This requires proving that the solid particles never collide in finite time, a key fact that follows from suitable a priori estimates together with uniqueness results for ordinary differential equations. We also describe the asymptotic behavior of solutions as t → ∞, extending previous results established for a single solid mass. The evolution of the relative position of the particles is examined in terms of the strength of the convection term. The possible 2D analogues of these results in the context of Navier–Stokes equations are open problems.

  • large time behavior for a simplified 1d model of fluid solid Interaction
    Pediatric Dermatology, 2003
    Co-Authors: Juan Luis Vazquez, Enrique Zuazua
    Abstract:

    Abstract In this article we consider a simple model in one space dimension for the Interaction between a fluid and a solid represented by a point mass. The fluid is governed by the viscous Burgers equation and the solid mass, which shares the velocity of the fluid, is accelerated by the difference of pressure at both sides of it. We describe the asymptotic behavior of solutions for integrable data using energy estimates and scaling techniques. We prove that the asymptotic profile of the fluid is a self-similar solution of the Burgers equation with an appropriate total mass, and we describe the parabolic trajectory of the point mass. We also prove that, asymptotically, the difference of pressure to both sides of the point mass vanishes. †Dedicated to C. Dafermos on his 60th birthday.

Jing Tang Xing - One of the best experts on this subject based on the ideXlab platform.

  • Variational principles of linear fluid–solid Interaction systems
    Fluid-Solid Interaction Dynamics, 2020
    Co-Authors: Jing Tang Xing
    Abstract:

    Abstract In this chapter, we present the variational principles for linear fluid–solid Interaction (FSI) dynamic systems. Following a short introduction on the history of variational principles for linear FSI dynamics, we describe the mathematical equations and the corresponding boundary and FSI conditions for various FSI problems, which is a basis for investigating their variational formulations. After the detailed mathematical proofs of the two variational principles: the complementary and potential energy models, we further discuss some varieties of variational preinciples for FSI systems.

  • Application of incompressible smoothed particle hydrodynamics method for 3D fluid solid Interaction problem
    2013
    Co-Authors: Jing Tang Xing
    Abstract:

    A general method for fluid solid Interaction problem simulations has been developed in 3D algorithm using incompressible smoothed particle hydrodynamics (SPH) method. The solid is assumed to be rigid so it can be considered as moving boundaries for fluid. Using repulsive force has been proved to be an efficient boundary treatment for incompressible SPH method before with 2D examples. The advantage of this boundary treatment will be more obvious in 3D simulations of fluid-structure Interaction problems since that it requires the fewest particle numbers on the boundaries compared with other boundary treatments. The algorithm can be applied to fluid solid Interaction problems with deformable solid by using elastic or plastic solid theories. In this paper, 3D dam-breaking is used as an example to demonstrate the performance of this method and aircraft ditching is simulated.

  • A mixed finite-element finite-difference method for nonlinear fluid-structure Interaction dynamics . I . Fluid-rigid structure Interaction
    Proceeding Royal Society, 2003
    Co-Authors: Jing Tang Xing, W G Price
    Abstract:

    A mixed finite-element finite-difference numerical method is developed to calculate nonlinear Fluid-Solid Interaction problems. In this study, the structure is assumed to be rigid with large motion and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and Fluid-Solid Interaction interfaces. A moving coordinate system fixed at a point in the structure is used to describe the fluid flow, and for numerical analysis purposes, an arbitrary Lagrangian-Eulerian mesh system is constructed relative to this moving system. This provides a convenient method of overcoming the difficulties of matching fluid meshes with large solid motion. Nonlinear numerical equations describing nonlinear Fluid-Solid Interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. A selection of numerical examples illustrates the developed mathematical model and through numerical simulations it is shown that the proposed approach is practical and useful.

  • A numerical simulation of nonlinear fluid - Rigid structure Interaction problems
    ASME International Mechanical Engineering Congress and Exposition Proceedings, 2002
    Co-Authors: Jing Tang Xing, W G Price, Y.-g. Chen
    Abstract:

    A numerical method to simulate nonlinear fluid - rigid structure Interaction problems is developed herein. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid - solid Interaction interfaces. An Arbitrary-Lagrangian- Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block approach is adopted allowing relative motion between moving overset grids which are independent of one another. This provides a convenient method to overcome the difficulties of matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid - solid Interaction dynamics are derived through a numerical discretisation scheme of study. A coupling iteration process is used to solve these numerical equations. A numerical example is presented to demonstrate applications of the developed numerical model. Copyright ? 2002 by ASME.

  • Variational principles of nonlinear dynamical Fluid-Solid Interaction systems
    Philosophical transactions - Royal Society. Mathematical physical and engineering sciences, 1997
    Co-Authors: Jing Tang Xing, W G Price
    Abstract:

    Based on the fundamental equations of continuum mechanics, the concept of Hamilton's principle and the adoption of Eulerian and Lagrangian descriptions of fluid and solid, respectively,variational principles admitting variable boundary conditions are developed to model mathematically the nonlinear dynamical behaviour of the responses and Interactions between fluid and solid. The nonlinearity of the fluid is introduced through nonlinear field equations and nonlinear boundary conditions on the free surface and fluid–solid Interaction interface. The structure is treated as a nonlinear elastic body. This model assumes the fluid inviscid, incompressible or compressible and the fluid motion irrotational or rotational but isentropic along the flow path of each fluid particle. The stationary conditions of the variational principles include the governing equations of nonlinear elastic dynamics, fluid dynamics and those relating to the fluid-structure Interaction interface as well as the imposed boundary conditions. A family of variational principles are obtained depending on the assumptions introduced into the mathematical model (i.e. fluid incompressible, motion irrotational, etc.) and these provide a foundation to construct numerical schemes of study to assess the dynamical behaviour of nonlinear fluid–solid Interaction systems. Two simple illustrative examples are presented demonstrating the applicability of the proposed theoretical approach.

Dunja Perić - One of the best experts on this subject based on the ideXlab platform.

  • On the coupling between fluid flow and mesh motion in the modelling of fluid-structure Interaction
    Computational Mechanics, 2008
    Co-Authors: Wulf G Wg Wulf G Dettmer, Dunja Perić
    Abstract:

    Partitioned Newton type solution strategies for the strongly coupled system of equations arising in the computational modelling of Fluid-Solid Interaction require the evaluation of various coupling terms. An essential part of all ALE type solution strategies is the fluid mesh motion. In this paper, we investigate the effect of the terms which couple the fluid flow with the fluid mesh motion on the convergence behaviour of the overall solution procedure. We show that the computational efficiency of the simulation of many Fluid-Solid Interaction processes, including fluid flow through flexible pipes, can be increased significantly if some of these coupling terms are calculated exactly. © 2008 Springer-Verlag.

  • A Fully Implicit Computational Strategy for Strongly Coupled Fluid–Solid Interaction
    Archives of Computational Methods in Engineering, 2007
    Co-Authors: Wulf G Wg Wulf G Dettmer, Dunja Perić
    Abstract:

    This article summarises the authors’ research work in the area of computational modelling of Interaction of fluid flow with solid structures. Our approach relies on a fully implicit iterative solution strategy which resolves the strong coupling and allows for optimal rate of convergence of the residuals. Therefore, the methodology is a viable competitor for the solution of the highly nonlinear Interaction of fluid flow with solid structures that experience large displacements and deformations. The key ingredients of our strategy include the following: Stabilised low order velocity–pressure finite elements are used for the modelling of the fluid flow combined with an arbitrary Lagrangian–Eulerian (ALE) strategy. For the temporal discretisation of both fluid and solid bodies, the discrete implicit generalised- α method is employed. An important aspect of the present work is the introduction of the independent interface discretisation, which allows an efficient, modular and expandable implementation of the solution strategy. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface. The resulting strongly coupled set of nonlinear equations is solved by means of a partitioned solution procedure, which is based on the Newton–Raphson methodology and incorporates the full linearisation of the overall incremental problem. Thus, asymptotically quadratic convergence of the residuals is achieved. Numerical examples are presented to demonstrate the robustness and efficiency of the methodology. Finally, we present the results obtained by combining the presented methodology with a remeshing procedure.

Y. Yan - One of the best experts on this subject based on the ideXlab platform.

  • Strongly coupling of partitioned Fluid-Solid Interaction solvers using reduced-order models
    Applied Mathematical Modelling, 2010
    Co-Authors: W. Q. Wang, Y. Yan
    Abstract:

    In this work a powerful technique is described which allows the implicit coupling of partitioned solvers in fluid-structure Interaction (FSI) problems. The flow under consideration is governed by the Navier-Stokes equations for incompressible viscous fluids and modeled with the finite volume method. The structure is represented by a finite element formulation. The method allows the use of a black box fluid and structural solver because it builds up a reduced order model of the fluid and structural problem during the coupling process. Each solution of the fluid/structural solver in the coupling process can be seen as a sensitivity response of an applied displacement/pressure mode. The applied modes and their responses are used to build up a reduced-order model. The proposed model is used to predict the unsteady flow fields of a particular flow-induced vibrational phenomenon - a fixed cubic rigid body is submerged in an incompressible fluid flow (water), an elastic plate is attached to the rigid body in the centre of the downstream face, and the vortices, which separate from the corners of the rigid body upstream, generate lift forces which excite continuous oscillations of the elastic plate downstream. The computational results show that a fairly good convergence solution is achieved by using the reduced-order model that is based on only a few displacement and stress modes, which largely reduces the computational cost, compared with traditional approaches. At the same time, comparison of the numerical results of the model with available experimental data validates the methodology and assesses its accuracy. ?? 2010.