Browsing by Author "Heltai, Luca"

Now showing 1 - 11 of 11
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    Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems
    (SISSA, 2013-06-05) Heltai, Luca; Costanzo, Francesco; Roy, Saswati; Mathematics
    We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.
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    The deal.II Library, Version 8.0
    (SISSA, 2013-12-08) Bangerth, Wolfgang; Heister, Timo; Heltai, Luca; Kanschat, Guido; Kronbichler, Martin; Maier, Matthias; Turcksin, Bruno; Young, Toby D.; Mathematics
    This paper provides an overview of the new features of the finite element library deal.II version 8.0.
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    A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library
    (SISSA, 2012-09-13) Heltai, Luca; Roy, Saswati; Costanzo, Francesco; Mathematics; Functional Analysis and Applications
    We present the implementation of a solution scheme for fluid-structure interaction problems via the finite element software library deal.II. The solution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.
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    A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures
    (SISSA, 2014-03) Mola, Andrea; Heltai, Luca; DeSimone, Antonio; Mathematics
    We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.
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    Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes
    (Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences, 2016) Salmoiraghi, Filippo; Ballarin, Francesco; Heltai, Luca; Rozza, Gianluigi; Mathematics
    In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.
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    A Numerical study of the Jerky crack growth in elastoplastic materials with localized plasticity
    (SISSA, 2020) Dal Maso, Gianni; Heltai, Luca
    We present a numerical implementation of a model of quasi-static crack growth in linearly elastic-perfectly plastic materials. We assume that the displacement is antiplane, and that the cracks and the plastic slips are localized on a prescribed path. We provide numerical evidence of the fact that the crack growth is intermittent, with jump characteristics that depend on the material properties.
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    Optimally swimming Stokesian Robots
    (2010-07-29T11:02:56Z) Alouges, Francois; DeSimone, Antonio; Heltai, Luca; Lefebvre, Aline; Merlet, Benoit; Mathematics; Functional Analysis and Applications
    We study self propelled stokesian robots composed of assemblies of balls, in dimen- sions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow's theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically the analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.
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    The role of membrane viscosity in the dynamics of fluid membranes
    (2010-07-29T11:13:36Z) Arroyo, Marino; DeSimone, Antonio; Heltai, Luca; Mathematics; Functional Analysis and Applications
    Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.
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    A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions
    (SISSA, 2012-03) Mola, Andrea; Heltai, Luca; DeSimone, Antonio; Mathematics; Functional Analysis and Applications
    We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.
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    Stratos: a code for 3D free surface flows with floating constraints
    (2009-07-30T14:37:02Z) DeSimone, Antonio; Bianchi, B.; Heltai, Luca; Mathematics; Functional Analysis and Applications
    This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation of hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a floating object via Lagrange multipliers......
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    Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II
    (2009-07-30T14:20:03Z) DeSimone, Antonio; Heltai, Luca; Manigrasso, Cataldo; Mathematics; Functional Analysis and Applications
    The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly via the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or three spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.