Scientific Reports

MOX Reports

• 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

  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.

• MOX 80 - 01/31/2006
  Ponzini, R.; Vergara, Christian; Redaelli, A.; Veneziani, Alessandro
  Reliable CFD-based estimation of flow rate in haemodynamics measures

  Abstract

  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.

• MOX 79 - 01/30/2006
  Quarteroni, Alfio; Rozza, Gianluigi; Quaini, Annalisa
  Reduced basis methods for optimal control of advection-diffusion problems

  Abstract

  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.

• MOX 78 - 01/23/2006
  Agoshkov, Valery; Gervasio, Paola; Quarteroni, Alfio
  Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations

  Abstract

  	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.

• MOX 77 - 01/16/2006
  Quarteroni, Alfio
  What mathematics can do for the simulation of blood circulation

  Abstract

  	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.

• MOX 76 - 01/13/2006
  Formaggia, Luca; Micheletti, Stefano; Sacco, Riccardo; Veneziani, Alessandro
  Mathematical modelling and numerical simulation of a glow-plug

  Abstract

  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.

• 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

  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.

• MOX 74 - 12/14/2005
  Aletti, G.; May, C.; Secchi, Piercesare
  On the distribution of the limit proportion for a two-color, randomly reinforced urn with equal reinforcement distributions

  Abstract

  	Abstract
  	We consider a two-color randomly reinforced urn with equal reinforcement distributions and we characterize the distribution of the urn s limit proportions as the unique continous solution of a functional equation involving unknown probability distributions on [0.1].