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 1239 products
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MOX 82 - 04/10/2006
Corno, A.F.; Prosi, M.; Fridez, P.; Zunino, P.; Quarteroni, A.;von Segesser, L.K.
The non-circular shape of FloWatch®-PAB prevents the need for pulmonary | Abstract | | Objective: To evaluate the differences between non-circular shape of
FloWatch®-PAB and conventional pulmonary artery (PA) banding.Methods: Geometrical analysis. Conventional banding and FloWatch®-PAB
perimeters were plotted against cross sections.Computational Fluid Dynamics (CFD) model. CFD compared non-circular
FloWatch®-PAB cross sections with conventional banding regarding pressure
gradients.Clinical data. Seven children, median age 2months (7days-3years), median
weight 4.2kg (3.2-9.8kg) with complex congenital heart defects underwent
PA banding with FloWatch®-PAB implantation.Results. Geometrical analysis. Conventional banding: progressive reduction
of cross sections was accompanied by progressive reduction of PA
perimeters. FloWatch®-PAB: with equal reduction of cross sections the PA
perimeter remained constant.CFD model. Non-circular and circular banding provided same trans-banding
pressure gradients for same cross sections at any given flow.Clinical data. Mean PA internal diameter at banding was 13.3±4.5mm. After
mean interval of 5.9±3.7 months, all children underwent intra-cardiac
repair and simple FloWatch®-PAB removal without PA reconstruction. Mean PA
internal diameter with FloWatch®-PAB removal increased from 3.0±0.8mm to
12.4±4.5mm (normal mean internal diameter for the age = 9.9±1.6). No
residual pressure gradient was recorded in correspondence of the site of
the previous FloWatch®-PAB implantation in 6/7 patients, 10mmHg peak and
5mmHg mean gradient in 1/7.Conclusions. The non-circular shape of FloWatch®-PAB can replace
conventional circular banding with the following advantages:a)the pressure gradient will remain essentially the same as for
conventional circular banding for any given cross section, but with
significantly smaller reduction of PA perimeter b)PA reconstruction at the time of de-banding for intra-cardiac repair can
be avoided.
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MOX 81 - 03/06/2006
Balossino, R., Pennati, G.; Migliavacca, F.; Formaggia, L.; Veneziani, A.; Tuveri, M.; Dubini, G.
Influence of boundary conditions on fluid dynamics in models of the cardiovascular system: a multiscale approach applied to the carotid bifurcation | Abstract | | Background:
This work aims at addressing an important problem in the simulation of detailed 3D hemodynamic models of vascular districts
with complex anatomy. Namely, to define appropriate boundary conditions accounting for both local as well as global effects.
Approach:
The approach devised in this work is based on a multiscale model, where the Navier-Stokes
equations for the district of interest are coupled to a non-linear system of ordinary differential equations which
describes the global circulatory system as a lumped parameter network. The multiscale approach is applied to three 3D models
of a carotid bifurcation which differ only in the severity of a stenosis in the internal carotid artery. The results of the
multiscale simulations are compared to those obtained by two stand-alone models of the carotid bifurcation, which differ in
the adopted strategy in prescribing the boundary conditions.
Results:
Significant differences are found in the results between the multiscale and the stand-alone models in
terms of flows, pressures and wall shear stresses distribution in the 3D domain.
Conclusions:
The capability to numerically predict the hemodynamic changes due to the presence of a stenosis is highly
dependent on the availability of correct boundary conditions. The geometrical multiscale approach offers a logical and
proper alternative to the use of measured data to prescribe realistic boundary conditions and predict new hemodynamic scenarios.
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MOX 80 - 01/31/2006
Ponzini, R.; Vergara, Christian; Redaelli, A.; Veneziani, Alessandro
Reliable CFD-based estimation of flow rate in haemodynamics measures | Abstract | | Physical useful measures in current clinical practice refer often to the blood ow rate, that is related to the mean velocity. However, the direct measure of the latter is currently not possible using a Doppler velocimetry technique. Therefore, the usual approach to calculate the
ow rate with this technique consists in measuring the maximum velocity and in estimating the
mean velocity, making the hypothesis of parabolic profile, that in realistic situations brings to strongly inaccurate estimates. In this paper, we propose a different way for estimating the
ow rate regarded as a function of maximum velocity and Womersley number. This relation is obtained by fixing a parametrized representation and by evaluating the parameters by means of a least square approach working on the numerical results of CFD simulations (about 200). Numerical simulations are carried out by prescribing the
ow rate, not the velocity profile. In this way, no bias are implicitly induced in prescribing boundary conditions. Validation tests based on numerical simulations show that the proposed
relation improves the flow rate estimation. |
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MOX 79 - 01/30/2006
Quarteroni, Alfio; Rozza, Gianluigi; Quaini, Annalisa
Reduced basis methods for optimal control of advection-diffusion problems | Abstract | | The reduced basis (RB) method is proposed for the
approximation of multiparametrized
equations governing an optimal control problem. The idea
behind the RB method is to project the solution onto a space of small
dimension, specifically designed on the problem at hand, and to decouple
the generation and projection stages (off-line/on-line computational
procedures)
of the approximation process in order to solve parametrized equations
in a rapid and not expensive way.
The application that we investigate is an air pollution control problem: we
aim at regulating the emissions of industrial chimneys in order to keep the
pollutant concentration below a certain threshold over an observation area,
like a town. Adopting the RB method for both state and adjoint equations
of the optimal control problem leads to important computational savings
with respect to the use of the Galerkin-finite element method. We consider
different parametrization (control, physical and geometrical input
parameters)
so that we are able to solve the control problem from a global and
decisional point of view.
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MOX 78 - 01/23/2006
Agoshkov, Valery; Gervasio, Paola; Quarteroni, Alfio
Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations | Abstract | | New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed.
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MOX 77 - 01/16/2006
Quarteroni, Alfio
What mathematics can do for the simulation of blood circulation | Abstract | | In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physio-pathology.
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MOX 76 - 01/13/2006
Formaggia, Luca; Micheletti, Stefano; Sacco, Riccardo; Veneziani, Alessandro
Mathematical modelling and numerical simulation of a glow-plug | Abstract | | In this work we derive a mathematical model that
describes the working of a glow-plug of the type used in Diesel engines
to preheat the air-diesel fuel mixture.
The proposed model consists of a time dependent one dimensional
partial differential equation which incorporates the electro-thermal
interaction between the electric current flowing in the plug and the
temperature.
It has been obtained by integrating the heat
equation on each section of the plug, assuming axial symmetry and using
thermal equilibrium relation in the radial direction. The problem is
highly non-linear because of the radiation boundary conditions and the
dependence on temperature of several parameters. In particular, heat
is generated by an electric resistance whose characteristic strongly
depends on temperature.
We have adopted a quasi-Newton treatment of the non-linear term and a
mixed finite element formulation for the linearized problem. Time
advancing has been carried out using a semi-implicit Euler scheme.
Several numerical simulations have been carried in order to assess the
validity of the model, whose predictions have been compared with
available experimental data.
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MOX 75 - 01/12/2006
Baudisch, J.; Bonaventura, Luca; Iske, A.; Miglio, Edie
Matrix valued Radial Basis Functions for local vector field reconstruction: applications to computational fluid dynamic models | Abstract | | Matrix valued radial basis functions
are applied to achieve accurate local vector field reconstructions of smooth vector fields from normal components assigned at the edges of a computational mesh. The theory underlying this reconstruction approach is reviewed and reformulated so as to allow for more straightforward application.
The accuracy of the locally reconstructed fields is assessed by appropriate numerical tests. Applications to numerical models for geophysical fluid dynamics problems show that such reconstruction techniques can usefully complement low order discretization approaches with important discrete conservation properties.
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