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 1275 products
-
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. |
-
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.
|
-
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.
|
-
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.
|
-
MOX 90 - 10/23/2006
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. |
-
MOX 89 - 10/17/2006
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.
|
-
MOX 88 - 09/24/2006
Quarteroni, Alfio; Rozza, Gianluigi
Numerical solution of parametrized Navier-Stokes equations by reduced basis methods | Abstract | | We apply the reduced basis method to solve Navier-Stokes
equations in parametrized domains. Special attention is devoted to
the treatment of the parametrized non-linear transport term in
the reduced basis framework, including the case of non-affine
parametric dependence that is treated by an empirical
interpolation method. This method features (1) a rapid
global convergence owing to the property of the Galerkin
projection onto a space W_N spanned by solutions of the
governing partial differential equation at N (optimally)
selected points in the parameter space, and (2) the
off-line/on-line computational procedures which decouple the
generation and projection stages of the approximation process.
This method is well suited for the repeated and rapid evaluations
required in the context of parameter estimation, design,
optimization, and real-time control. Our analysis focuses on:
(i) the pressure treatment of incompressible Navier-Stokes
problem; (ii) the fulfillment of an equivalent inf-sup condition to
guarantee the stability of the reduced basis solutions. The applications that we consider involve parametrized geometries, like e.g. a channel with curved upper wall or an arterial bypass configuration.
|
-
MOX 87 - 09/15/2006
Peiro, J.; Formaggia, L.; Radaelli,A.; Rigamonti, V.
Shape reconstruction from medical images and quality mesh generation via implicit surfaces | Abstract | | The ability of automatically reconstructing physiological shapes, of generating computational meshes, and of calculating flow solutions from medical images is enabling the introduction of computational fluid dynamics (CFD) techniques as an additional tool to aid clinical practice.
This article presents a set of procedures for the shape reconstruction and triangulation of geometries derived from a set of medical images representing planar cross sections of the object. The reconstruction of the shape of the boundary is based on the interpolation of an implicit function through a set of points obtained from the segmentation of the images. This approach is favoured for its ability of smoothly interpolating between sections of different topology. The boundary of the object is an iso-surface of the implicit function that is approximated by a triangulation extracted by the method of marching cubes. The quality of this triangulation is often neither suitable for mesh generation nor for flow solution. We discuss the use of mesh enhancement techniques to maximize the quality of the triangulation together with curvature adaption to optimize mesh resolution.
The proposed methodology is applied to the reconstruction and discretization of two physiological geometries: a femoral by-pass graft and a nasal cavity.
Keywords: Mesh generation; shape reconstruction; mesh enhancement; radial basis functions; implicit surfaces; medical image processing.
|
|
