In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrovâ€“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.

%B Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34466 %1 34640 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by ngiuliani@sissa.it (ngiuliani@sissa.it) on 2015-05-04T12:32:04Z No. of bitstreams: 1 paper-free-surface.pdf: 888763 bytes, checksum: 68366266786e84b78a356acd6de50840 (MD5) %R 10.1016/j.enganabound.2015.04.006 %0 Conference Proceedings %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %D 2014 %T A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K ship hydrodynamics %X 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. %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %I SISSA %G en %1 7357 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2014-03-22T15:00:37Z No. of bitstreams: 1 MolaHeltaiDeSimone2014.pdf: 1241007 bytes, checksum: 1a56d909a08f1f470c7efc14018e37f8 (MD5) %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)