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.

%B Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %I SISSA %G en %U http://hdl.handle.net/1963/5669 %1 5457 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-16T11:19:51Z\\nNo. of bitstreams: 1\\nMolaHeltaiDeSimone-2012-aa.pdf: 1981527 bytes, checksum: 8a82da009242da0cf884e2c7f04009a6 (MD5) %0 Book Section %B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %D 2012 %T Computing optimal strokes for low reynolds number swimmers %A Antonio DeSimone %A Luca Heltai %A François Aouges %A Lefebvre-Lepot Aline %K Numerical analysis. %XWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

%B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %I Springer %@ 9781461439967 %G en %U http://hdl.handle.net/1963/6445 %1 6381 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:33:50Z\\nNo. of bitstreams: 0 %R 10.1007/978-1-4614-3997-4_13 %0 Report %D 2012 %T A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library %A Luca Heltai %A Saswati Roy %A Francesco Costanzo %K Finite Element Method %K Immersed Boundary Method %K Immersed Finite Element Method %X We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution 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. %I SISSA %G en %U http://hdl.handle.net/1963/6255 %1 6172 %2 Mathematics %3 Functional Analysis and Applications %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-09-28T11:06:13Z\\nNo. of bitstreams: 1\\n1209.2811v1.pdf: 4766431 bytes, checksum: a46803f7f8daf3195359f65c9161b944 (MD5) %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %D 2012 %T Reverse engineering the euglenoid movement %A Marino Arroyo %A Luca Heltai %A Daniel Millán %A Antonio DeSimone %K microswimmers %X Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. %B Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %G en %U http://hdl.handle.net/1963/6444 %1 6380 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:29:31Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1213977109 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %D 2012 %T Variational implementation of immersed finite element methods %A Luca Heltai %A Francesco Costanzo %K Turbulent flow %B Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %I Elsevier %G en %U http://hdl.handle.net/1963/6462 %1 6389 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2013-02-04T16:21:56Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2012.04.001 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %D 2011 %T Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers %A Francois Alouges %A Antonio DeSimone %A Luca Heltai %K Optimal swimming %X We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. %B Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3657 %1 648 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-23T17:30:51Z\\r\\nNo. of bitstreams: 1\\r\\nSissa33_2009M.pdf: 708341 bytes, checksum: 6134bd52f083488620fb5bb24bcf9b93 (MD5) %R 10.1142/S0218202511005088 %0 Report %D 2011 %T Variational Implementation of Immersed Finite Element Methods %A Luca Heltai %A Francesco Costanzo %X Dirac-delta distributions are often crucial components of the solid-fluid\\r\\ncoupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational\\r\\nstructure of the problem is exploited to avoid Dirac-delta distributions at\\r\\nboth the continuous and the discrete level. In this paper, we generalize the\\r\\nFEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic\\r\\nof differential type or purely elastic, and (iii) the solid to be and either\\r\\ncompressible or incompressible. At the continuous level, our variational\\r\\nformulation combines the natural stability estimates of the fluid and\\r\\nelasticity problems. In immersed methods, such stability estimates do not\\r\\ntransfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization. %I SISSA %G en %U http://hdl.handle.net/1963/4700 %1 4465 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-12T10:45:58Z\\nNo. of bitstreams: 1\\n1110.2063v1.pdf: 1433103 bytes, checksum: 73954809755f81dc1fe363ee99978e74 (MD5) %0 Report %D 2010 %T Optimally swimming Stokesian Robots %A Francois Alouges %A Antonio DeSimone %A Luca Heltai %A Aline Lefebvre %A Benoit Merlet %X We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 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\\nthe 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. %G en_US %U http://hdl.handle.net/1963/3929 %1 472 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:02:56Z\\nNo. of bitstreams: 1\\nHeltai_54M_2010.pdf: 993075 bytes, checksum: 77225380bab031438ac940e694ea0e6c (MD5) %0 Report %D 2010 %T The role of membrane viscosity in the dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %A Luca Heltai %X 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. %G en_US %U http://hdl.handle.net/1963/3930 %1 471 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:13:35Z\\nNo. of bitstreams: 1\\nArroyo_55M.pdf: 4419667 bytes, checksum: ca8a9c175a457ad33996d46a08e85e44 (MD5) %0 Report %D 2009 %T Stratos: a code for 3D free surface flows with floating constraints %A Antonio DeSimone %A B. Bianchi %A Luca Heltai %X This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... %G en_US %U http://hdl.handle.net/1963/3701 %1 604 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:37:01Z\\nNo. of bitstreams: 1\\nBianchiDeSimoneHeltai.pdf: 899803 bytes, checksum: aff44eb1a39c6fd4acd4b3cb285e2d64 (MD5) %0 Report %D 2009 %T Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II %A Antonio DeSimone %A Luca Heltai %A Cataldo Manigrasso %X The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia 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\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. %G en_US %U http://hdl.handle.net/1963/3700 %1 605 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:20:01Z\\nNo. of bitstreams: 1\\nDeSimoneHeltaiManigrasso.pdf: 915137 bytes, checksum: c3144348b6aab67a5f547060049c7847 (MD5)