In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/complete-data-driven-framework-efficient-solution-parametric-shape-design-and02567nas a2200169 4500008004100000245009100041210006900132520193100201100001702132700001902149700002102168700002502189700001902214700002102233700002102254856012202275 2019 eng d00aEfficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design0 aEfficient Reduction in Shape Parameter Space Dimension for Ship 3 aIn this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

1 aMola, Andrea1 aTezzele, Marco1 aGadalla, Mahmoud1 aValdenazzi, Federica1 aGrassi, Davide1 aPadovan, Roberta1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/efficient-reduction-shape-parameter-space-dimension-ship-propeller-blade-design02307nas a2200169 4500008004100000245011900041210006900160260000800229300000700237490000600244520167500250100001901925700002501944700001701969700002101986856013002007 2018 eng d00aDimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems0 aDimension reduction in heterogeneous parametric spaces with appl cSep a250 v53 aWe present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

1 aTezzele, Marco1 aSalmoiraghi, Filippo1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/dimension-reduction-heterogeneous-parametric-spaces-application-naval-engineering-shape02869nas a2200241 4500008004100000022002200041245016200063210006900225260007400294520193000368653002102298653002802319653003102347653003202378653002602410653003002436653002602466100001702492700001902509700001702528700002102545856006102566 2018 eng d a978-1-880653-87-600aAn efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment0 aefficient shape parametrisation by freeform deformation enhanced aSapporo, JapanbInternational Society of Offshore and Polar Engineers3 aIn this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.10aActive subspaces10aBoundary element method10aDynamic mode decomposition10aFluid structure interaction10aFree form deformation10aFully nonlinear potential10aNumerical towing tank1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.onepetro.org/conference-paper/ISOPE-I-18-48101777nas a2200157 4500008004100000245013300041210006900174260003000243520120300273100001901476700001701495700002101512700001701533700002101550856004801571 2018 eng d00aModel Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics0 aModel Order Reduction by means of Active Subspaces and Dynamic M aTrieste, ItalybIOS Press3 aWe present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.1 aTezzele, Marco1 aDemo, Nicola1 aGadalla, Mahmoud1 aMola, Andrea1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4927000574nas a2200133 4500008004100000245012000041210007000161300001200231490000800243100002100251700001700272700001700289856013400306 2018 eng d00aπ-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods0 aπBEM A flexible parallel implementation for adaptive geometry aw a39–580 v1211 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca uhttps://www.math.sissa.it/publication/%CF%80-bem-flexible-parallel-implementation-adaptive-geometry-aware-and-high-order-boundary01821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342400424nas a2200145 4500008004100000245005000041210004700091260002500138300001400163490000700177100001800184700001700202700001300219856004600232 2017 eng d00aCurvature-adapted remeshing of {CAD} surfaces0 aCurvatureadapted remeshing of CAD surfaces bSpringer Naturecdec a565–5760 v341 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1007/s00366-017-0558-200603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-001102562nas a2200145 4500008004100000245012400041210006900165300001100234490000700245520198000252100001702232700001702249700002202266856012802288 2017 eng d00aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations0 aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear P a1–140 v613 aWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/wet-and-dry-transom-stern-treatment-unsteady-and-nonlinear-potential-flow-model-naval02112nas a2200217 4500008004100000245018600041210006900227260003600296520123100332100002501563700002401588700002001612700001701632700001901649700002101668700002101689700002101710700001701731700001601748856013001764 2016 en d00aAdvances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives0 aAdvances in geometrical parametrization and reduced order models aCrete, GreecebECCOMASc06/20163 aSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aCorsi, Giovanni1 aMola, Andrea1 aTezzele, Marco1 aRozza, Gianluigi1 aPapadrakakis, M.1 aPapadopoulos, V.1 aStefanou, G.1 aPlevris, V. uhttps://www.math.sissa.it/publication/advances-geometrical-parametrization-and-reduced-order-models-and-methods-computational00651nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012900364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model01899nas a2200133 4500008004300000245010100043210006900144520142800213100002101641700001701662700001701679700001801696856005101714 2015 en_Ud 00aFEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows0 aFEM SUPG stabilisation of mixed isoparametric BEMs application t3 aIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

1 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca1 aFormaggia, L. uhttp://urania.sissa.it/xmlui/handle/1963/3446601482nas a2200157 4500008004100000245004800041210004700089260001300136300001400149490000700163520105700170100001801227700001701245700001301262856004901275 2014 en d00aCurvature-adapted remeshing of CAD surfaces0 aCurvatureadapted remeshing of CAD surfaces bElsevier a253–2650 v823 aA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

1 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1016/j.proeng.2014.10.38801202nas a2200145 4500008004100000245010600041210006900147260001000216520062900226653002300855100001700878700001700895700002200912856012200934 2014 en d00aA fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures0 afully nonlinear potential model for ship hydrodynamics directly bSISSA3 aWe 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.10aship hydrodynamics1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/fully-nonlinear-potential-model-ship-hydrodynamics-directly-interfaced-cad-data00655nas a2200157 4500008004100000245010000041210006900141260005800210300001400268490000600282100001700288700001700305700002200322700002400344856012900368 2014 eng d00aPotential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures0 aPotential Model for Ship Hydrodynamics Simulations Directly Inte bInternational Society of Offshore and Polar Engineers a815–8220 v41 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/potential-model-ship-hydrodynamics-simulations-directly-interfaced-cad-data-structures01660nas a2200145 4500008004100000245010800041210006900149260001000218520115900228653003501387100001701422700001701439700002201456856003601478 2013 en d00aA stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions0 astable and adaptive semiLagrangian potential model for unsteady bSISSA3 aWe 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.

10aUnsteady ship-wave interaction1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/566900518nas a2200109 4500008004100000245011900041210006900160100001700229700001700246700002200263856012300285 2012 eng d00aA stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves0 astable semilagrangian potential method for the simulation of shi1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/stable-semi-lagrangian-potential-method-simulation-ship-interaction-unsteady-and00490nas a2200145 4500008004100000245008500041210006900126260002500195300001200220490000700232100001700239700001900256700002300275856004600298 2011 eng d00aMulti-physics modelling and sensitivity analysis of olympic rowing boat dynamics0 aMultiphysics modelling and sensitivity analysis of olympic rowin bSpringer Naturecnov a85–940 v141 aMola, Andrea1 aGhommem, Mehdi1 aHajj, Muhammad, R. uhttps://doi.org/10.1007/s12283-011-0075-201029nas a2200157 4500008004100000245008100041210006900122300001000191490000800201520055000209100001800759700001700777700001600794700001800810856004300828 2010 eng d00aA three-dimensional model for the dynamics and hydrodynamics of rowing boats0 athreedimensional model for the dynamics and hydrodynamics of row a51-610 v2243 aThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

1 aFormaggia, L.1 aMola, Andrea1 aParolini, N1 aPischiutta, M uhttps://doi.org/10.1243/17543371jset4600554nas a2200145 4500008004100000245010200041210006900143260005400212300001400266490000800280100001700288700002500305700002300330856005500353 2009 eng d00aLow-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners0 aLowFrequency Variations of Force Coefficients on Square Cylinder bAmerican Society of Civil Engineers ({ASCE})cjul a828–8350 v1351 aMola, Andrea1 aBordonaro, Giancarlo1 aHajj, Muhammad, R. uhttps://doi.org/10.1061/(asce)st.1943-541x.000003400433nas a2200157 4500008004100000245004500041210004300086260001500129300001400144490000700158100001800165700001700183700001700200700002100217856003700238 2009 eng d00aA model for the dynamics of rowing boats0 amodel for the dynamics of rowing boats bWileycsep a119–1430 v611 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aMontano, Antonio uhttps://doi.org/10.1002/fld.194000501nas a2200157 4500008004100000245009500041210007100136260001000207300001400217490000700231100001800238700001700256700001700273700001600290856003700306 2008 eng d00aFluid–structure interaction problems in free surface flows: Application to boat dynamics0 aFluid–structure interaction problems in free surface flows Appli bWiley a965–9780 v561 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aParolini, N uhttps://doi.org/10.1002/fld.158300524nas a2200145 4500008004100000245006800041210006800109300001400177490000700191100001800198700001700216700002300233700001900256856010300275 2004 eng d00aCalculation of impulsively started incompressible viscous flows0 aCalculation of impulsively started incompressible viscous flows a877–9020 v461 aMarra, Andrea1 aMola, Andrea1 aQuartapelle, Luigi1 aRiviello, Luca uhttps://www.math.sissa.it/publication/calculation-impulsively-started-incompressible-viscous-flows