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 1287 products
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01/2007 - 01/10/2007
Nobile, Fabio; Vergara, Christian
An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions | Abstract | | In this work we focus on the modelling and numerical simulation of the fluid-structure interaction mechanism in vascular dynamics. We first propose a simple membrane model to describe the deformation of the arterial wall, which is derived from the Koiter s shell equations and is
applicable to an arbitrary geometry. Secondly, we consider a reformulation of the fluid-structure problem, in which the newly derived membrane model, thanks to its simplicity, is embedded into the fluid equations and will appear as a generalized Robin boundary condition. The original problem is then reduced to the solution of
subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver, only. We also derive a stability estimate for the resulting numerical scheme. Finally, we propose new outflow absorbing boundary conditions, which
are easy to implement and allow to reduce significantly the spurious pressure wave reflections that typically appear in artificially
truncated computational domains. We present several numerical results showing the effectiveness of the proposed approaches. |
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MOX 97 - 12/22/2006
Badea, Lori; Discacciati, Marco; Quarteroni, Alfio
Mathematical analysis of the Navier-Stokes/Darcy coupling | Abstract | | We consider a differential system based on the coupling of the Navier Stokes and Darcy equations for modeling the interaction between surface and subsurface flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness. |
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MOX 96 - 12/21/2006
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 - 11/20/2006
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 - 10/31/2006
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 - 10/30/2006
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 - 10/24/2006
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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