MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1249 products
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37/2014 - 10/12/2014
Giuliani, N.; Mola, A.; Heltai, L.; Formaggia,L.
FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows | Abstract | | In 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. |
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36/2014 - 10/11/2014
Abbà,A.;Bonaventura,L.; Nini, M.;Restelli,M.;
Anisotropic dynamic models for Large Eddy Simulation of compressible flows with a high order DG method | Abstract | | The impact of anisotropic dynamic models for applications to LES of compressible flows is assessed in the framework of a numerical model based on high order discontinuous finite elements. The projections onto lower dimensional subspaces associated to lower degree basis function are used as LES filter, along the lines proposed in Variational Multiscale templates. Comparisons with DNS results available in the literature for channel flows at Mach numbers 0.2, 0.7 and 1.5 show clearly that the anisotropic model is able to reproduce well some key features of the flow, especially close to the wall, where the flow anisotropy plays a major role. |
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35/2014 - 10/07/2014
Tricerri, P.; Dedè, L.; Deparis, S.; Quarteroni, A.; Robertson, A.M.; Sequeira, A.
Fluid-structure interaction simulations of cerebral arteries modeled by isotropic and anisotropic constitutive laws | Abstract | | This paper considers numerical simulations of fluid-structure interaction (FSI) problems in hemodynamics for idealized geometries of healthy cerebral arteries modeled by means of both nonlinear isotropic and anisotropic material constitutive laws. In particular, it focuses on an anisotropic model initially proposed for cerebral arteries, to characterize the activation of collagen fibers at finite strains. In the current work, this constitutive model is implemented for the first time in the context of an FSI formulation. In this framework, we investigate the influence of the material model on the numerical results and, in the case of the anisotropic laws, the importance of the collagen fibers on the overall mechanical behavior of the tissue. With this aim, we compare our numerical results by analyzing fluid dynamic indicators, vessel wall displacement, Von Mises stress, and deformations of the collagen fibers. Specifically, for an anisotropic model with collagen fiber recruitment at finite strains, we highlight the progressive activation and deactivation processes of the fibrous component of the tissue throughout the wall thickness during the cardiac cycle. The inclusion of collagen recruitment is found to have a substantial impact on the intramural stress, which will in turn impact the biological response of the intramural cells. Hence, the methodology presented here will be particularly useful for studies of mechanobiological processes in the healthy and diseased vascular wall. |
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34/2014 - 09/12/2014
Antonietti, P.F.; Pacciarini, P.; Quarteroni, A.
A discontinuous Galerkin Reduced Basis Element method for elliptic problems | Abstract | | We propose and analyse a new discontinuous reduced basis element method for the approximation of parametrized elliptic PDEs in partitioned domains. The method is built upon an offline stage (parameter independent) and an online (parameter dependent) one. In the offline stage we build a non-conforming (discontinuous) global reduced space as a direct sum of local basis functions built independently on each subdomain. In the online stage, for a given value of the parameter, the approximate solution is obtained by ensuring the weak continuity of the fluxes and of the solution itself thanks to a discontinuous Galerkin approach. The new method extends and generalizes the methods introduced by L. Iapichino, G. Rozza and A. Quarteroni [Comput. Methods Appl. Mech. Engrg. 221/222 (2012), 63–82] and by L. Iapichino [PhD thesis, EPF Lausanne, 2012]. We prove stability and convergence properties of the proposed method, as well as conditioning properties of the associated algebraic online system. We also propose a two-level preconditioner for the online problem which exploits the pre-existing decomposition of the domain and is based upon the introduction of a global coarse finite element space. Numerical tests are performed to validate our theoretical results. |
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33/2014 - 08/06/2014
Canuto, C.; Simoncini, V.; Verani, M.
Contraction and optimality properties of an adaptive Legendre-Galerkin method: the multi-dimensional case | Abstract | | We analyze the theoretical properties of an adaptive Legendre-Galerkin method in the multidimensional case. After the recent investigations for Fourier-Galerkin methods in a periodic box and for Legendre-Galerkin methods in the one dimensional setting, the present study represents a further step towards a mathematically rigorous understanding of adaptive spectral/hp discretizations of elliptic boundary-value problems. The main contribution of the paper is a careful construction of a multidimensional Riesz basis in H^1, based on a quasi-orthonormalization procedure. This allows us to design an adaptive algorithm, to prove its convergence by a contraction argument, and to discuss its optimality properties (in the sense of non-linear approximation theory) in certain sparsity classes of Gevrey type. |
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32/2014 - 08/04/2014
Agosti, A.; Formaggia, L.;Scotti, A.
Analysis of a model for precipitation and dissolution coupled with a Darcy flux | Abstract | | In this paper we deal with the numerical analysis of an upscaled model of a reactive flow in a porous medium, which describes the transport of solutes undergoing precipitation and dissolution, leading to the formation/degradation of crystals inside the porous matrix. The model is defined at the Darcy scale, and it is coupled to a Darcy flow characterized by a permeability field that changes in space and time according to the precipitated crystal concentration. The model involves a non-linear multi-valued reaction term, which is treated exactly by solving an inclusion problem for the solutes and the crystals dynamics. We consider a weak formulation for the coupled system of equations expressed in a dual mixed form for the Darcy field and in a primal form for the solutes and the precipitate, and show its well posedness without resorting to regularization of the reaction term. Convergence to the weak solution is proved for its finite element approximation. We perform numerical experiments to study the behavior of the system and to assess the effectiveness of the proposed discretization strategy. In particular we show that a method that captures the discontinuity yields sharper dissolution fronts with respect to methods that regularize the discontinuous term. |
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31/2014 - 08/03/2014
Corno, J.; de Falco, C.; De Gersem, H.; Schöps, S.
Isogeometric Simulation of Lorentz Detuning in Superconducting Accelerator Cavities | Abstract | | Cavities in linear accelerators suffer from eigenfrequency shifts due to mechanical de- formation caused by the electromagnetic radiation pressure, a phenomenon known as Lorentz detuning. Estimating the frequency shift up to the needed accuracy by means of standard Finite Element Methods, is a very complex task due to the poor representation of the geometry and to the necessity for mesh refinement due to the typical use of low order basis functions. In this paper, we use Isogeometric Analysis for discretising both mechanical deformations and electromagnetic fields in a coupled multiphysics simulation approach. The combined high-order approximation of both leads to high accuracies at a substantially lower computational cost. |
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30/2014 - 07/23/2014
Ferroni, A.; Formaggia, L.; Fumagalli, A.;
Numerical analysis of Darcy problem on surfaces | Abstract | | Surface problems play a key role in several theoretical and applied fields. In this work the main focus is the presentation of a detailed analysis of the approximation of the classical flow porous media problem: the Darcy equation, where the domain is a regular surface. The formulation require the mixed form and the numerical approximation consider the classical pair of finite element spaces: piecewise constant for the scalar fields and Raviart-Thomas for vector fields, both written on the tangential space of the surface. The main result is the proof of the order of convergence where the discretization error, due to the finite element approximation, is coupled with a geometrical error. The latter takes into account the approximation of the real surface with a discretized one. Several examples are presented to show the correctness of the analysis, including surfaces without boundary. |
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