Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1349 prodotti
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MOX 96 - 21/12/2006
Massimi, Paolo; Quarteroni, Alfio; Saleri, Fausto; Scrofani, Giovanni
Modeling of Salt Tectonics | Abstract | | In this work a general framework for the simulation of sedimentary basins in presence of salt structures is addressed. Sediments and evaporites are modeled as non-Newtonian fluids and the thermal effects induced by the presence of salt are taken into account. The computational strategy is based on a Lagrangian methodology
with intensive grid adaptivity, together with a kinematic modeling of faults and different kinds of boundary conditions representing sedimentation, erosion, basement evolution, lithospheric compression and extension. The proposed methodology is applied to simple test cases as well as to a realistic geological reconstruction of industrial interest.
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MOX 95 - 12/12/2006
Babuška, Ivo; Nobile, Fabio; Tempone Raul
Reliability of Computational Science | Abstract | | Today’s computers allow us to simulate large, complex physical problems.
Many times the mathematical models describing such problems are
based on a relatively small amount of available information such as experimental
measurements. The question arises whether the computed data
could be used as the basis for decision in critical engineering, economic,
medicine applications. The representative list of engineering accidents occurred
in the past years and their reasons illustrates the question. The
paper describes a general framework for Verification and Validation which
deals with this question. The framework is then applied to an illustrative
engineering problem, in which the basis for decision is a specific quantity of
interest, namely the probability that the quantity does not exceed a given
value. The V&V framework is applied and explained in detail. The result
of the analysis is the computation of the failure probability as well as
a quantification of the confidence in the computation, depending on the
amount of available experimental data.
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MOX 94 - 20/11/2006
Formaggia, Luca; Moura, Alexandra; Nobile, Fabio
On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations | Abstract | | We consider the coupling between three-dimensional
(3D) and one-dimensional (1D) fluid-structure interaction
(FSI) models describing blood flow inside compliant vessels.
The 1D model is a hyperbolic
system of partial differential equations.
The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the coupling of the models. With this we derive an energy estimate for the fully 3D-1D FSI coupling. We consider several possible models for the mechanics of the vessel wall in the $3$D problem and show how the 3D-1D coupling depends on them.
Several comparative numerical tests illustrating the coupling are presented. |
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MOX 93 - 31/10/2006
Migliavacca, Francesco.; Gervaso, Francesca; Prosi, Martin; Zunino, Paolo; Minisini, Sara; Formaggia, Luca; Dubini, Gabriele
Expansion and drug elution model of a coronary stent | Abstract | | The present study illustrates a possible methodology to investigate drug elution from an expanded coronary stent. Models based on finite element method have been built including the presence of the atherosclerotic plaque, the artery and the coronary stent. These models take into account the mechanical effects of the stent expansion as well as the effect of drug transport from the expanded stent into the arterial wall. Results allow to quantify the stress field in the vascular wall, the tissue prolapse within the stent struts, as well as the drug concentration at any location and time inside the arterial wall, together with several related quantities as the drug dose and the drug residence times.
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MOX 92 - 30/10/2006
Dede', L.; Micheletti, S.; Perotto, S.
Anisotropic error control for environmental applications | Abstract | | In this paper we aim at controlling physically meaningful quantities with emphasis on environmental applications. This is carried out by an efficient numerical procedure combining the goal-oriented framework [Acta Numer. 10 (2001) 1] with the anisotropic setting introduced in [Numer. Math. 89 (2001) 641].
A first attempt in this direction has been proposed in [Appl.
Numer. Math. 51 (2004) 511]. Here we improve this analysis by carrying over to the goal-oriented framework the good property of the a posteriori error estimator to depend on the error itself, typical of the anisotropic residual based error analysis presented in [Comput. Methods Appl. Mech. Engrg. 195 (2006) 799; Numerical Mathematics and Advanced Applications - Enumath2001 Springer Verlag Italia (2003) 731]. On the one hand this dependence makes the estimator not immediately computable; nevertheless, after approximating this error via the Zienkiewicz-Zhu gradient recovery procedure [Internat. J. Numer.
Methods Engrg. 24 (1987) 337; Internat. J. Numer. Methods Engrg. 33 (1992) 1331], the resulting estimator is expected to exhibit a higher convergence rate than the one in [Appl. Numer. Math. 51 (2004) 511]. As the broad numerical validation attests, the proposed estimator turns out to be more efficient in terms of d.o.f. s per accuracy or equivalently, more accurate for a fixed number of elements.
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MOX 91 - 24/10/2006
Burman, Erik; Zunino, Paolo
A domain decomposition method based on weighted interior penalties for advection-diffusion-reaction problems | Abstract | | We propose a domain decomposition method for advection-diffusion-reaction equations based on Nitsche s transmission conditions.
The advection dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries. We prove the convergence of the finite element solutions of the discrete problem to the exact solution and we propose a parallelizable iterative method.
The convergence of the resulting domain decomposition method is proved and this result holds true uniformly with respect to the diffusion parameter. The numerical scheme that we propose here can thus be applied straightforwardly to diffusion dominated, advection dominated and hyperbolic problems. Some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method and we compare with some other domain decomposition techniques for advection--diffusion equations.
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MOX 90 - 23/10/2006
Quaini, Annalisa; Quarteroni, Alfio
A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method | Abstract | | We address the numerical simulation of fluid-structure interaction problems dealing with an incompressible fluid whose density is
close to the structure density. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The
basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and geometrical non-linearities) are treated explicitly. Thanks to this kind of explicit-implicit splitting, computational costs can be reduced (in comparison to
fully implicit coupling algorithms) and the scheme remains stable for a wide range of discretization parameters. In this paper we propose to derive this kind of splitting from the algebraic
formulation of the coupled fluid-structure problem (after finite-element space discretization). This approach extends for the first time to fluid-structure problems the algebraic
fractional step methodology that was previously advocated to treat the pure fluid problem in a fixed domain. More particularly, for
the specific semi-implicit method presented in this report we adapt the Yosida scheme to the case of a coupled fluid-structure problem. This scheme relies on an approximate LU block factorization of the matrix obtained after the discretization in time and space of the fluid-structure
system.
We analyze the numerical performances of this scheme on 2D fluid-structure simulations performed with a simple 1D structure model. |
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MOX 89 - 17/10/2006
Formaggia, Luca; Veneziani, Alessandro; Vergara, Christian
A new approach to numerical solution of defective boundary problems in incompressible fluid dynamics | Abstract | | We consider the incompressible Navier-Stokes equations with flow rate and mean pressure boundary conditions. There are basically two strategies for solving these defective boundary problems: the variational approach (see J. Heywood, R. Rannacher, S. Turek, Int J Num Meth Fluids 22 (1996), pp. 325-352) and the augmented formulation (see L. Formaggia, J. F. Gerbeau, F. Nobile, A. Quarteroni, SIAM J Num Anal, 40-1 (2002), pp. 376--401, and A. Veneziani, C. Vergara, Int J Num Meth Fluids, 47 (2005), pp. 803--816).
However, these approaches present some drawbacks.
The former, for the flow rate problem, resorts to non standard functional spaces, which are quite difficult to discretize. On the other hand, for the mean pressure problem, it yealds exact solutions only in very specific cases. The latter is applicable only to the flow rate problem, since for the mean pressure problem it provides unfeasible boundary conditions.
In this paper, we propose a new strategy, based on a control reformulation of the problems at hand. This approach allows to treat the two problems successfully within the same framework. We carry out the well-posedness analysis of the problems obtained with this approach and we propose some algorithms for their numerical solution. Several numerical results are presented supporting the effectiveness of our approach.
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