Quaderni di Dipartimento

Quaderni MOX

• MOX 13 - 03/02/2003
  Deparis, Simone; Fernandez, Miguel A.; Formaggia, Luca
  Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

  Abstract

  Abstract

  In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to face when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standar strategies for solving this non-linear problems, are fixed point based methods such as Block-Gauss-Seidel (BGS) iteractions. Unfortunately, these methods are very CPU time consuming and usually show slow convergence. We propose a modified fixed-point algorithm which combines the standard BGS iteraction with transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard BGS method.

• MOX 14 - 03/02/2003
  Sherwin, S.J.; Formaggia, Luca; Peiro, Jaume; Franke, V.
  Computational Modelling of 1d blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system

  Abstract

  Abstract

  In this paper we numerically investigate a one-dimensional model of blood flow in human arteries using both discontinuous Galerkin and a Taylor-Galerkin formulation. The derivation of the model and the numerical schemes are detailed and applied to two model numerical experiments. We first study the effect of an intervenction, such the implantantion of a vascular prothesis (e.g. a stent), which leadsto an abrupt variation of the mechanical characteristics of an artery. We then discuss the simulation of the propagation of the pressure and velocity waveforms in the human arterial tree using a simplified model consisting of the 55 main arteries.

• MOX 11 - 05/01/2003
  Micheletti, Stefano; Sacco, Riccardo, Simioni, Riccardo
  Numerical Simulation of Resonant Tunneling Diodes with a Quantum-Drift-Diffusion Model

  Abstract

  Abstract

  We deal with a Quantum-Drift-Diffusion (QDD) model for the description of transport in semiconductors which generalizes the standard Drift-Diffusion model (DD) through extra terms that take into account some quantum dispersive corrections. We also study numerically the influence on the I-V curve of the electron effective mass, the barrier height width, and of the ambient temperature. The performance of several linearization algorithms, i.e. a two Gummel-type iteractions and the fully-coupled Newton method are also compared.

• MOX 12 - 05/01/2003
  Causin, Paola; Sacco, Riccardo
  Mixed-hybrid finite element methods for coupled problems in silicon dioxide technology

  Abstract

  Abstract

  In this work we deal with the numerical simulation of thermal oxidation in silicon device technology. This application is a complex coupled phenomen, involving the solution of a diffusion-reaction problem and of a fluid-structure interaction problem. Suitable iterative procedures are devised for handling nonlinearities and strong coupling between the sub-problems to be solved. In particular, we propose a unified dual-mixed hybrid formulation that allows for the simultaneous solution of the compressible/incompressible Navier equations in both solid and fluid domains. The accuracy and the flexibility of the proposed approach are demonstrated on benchmark test problems.

• MOX 10 - 05/12/2002
  Ferrari, Stefania; Saleri, Fausto
  A new two-dimensional Shallow Water model including pressure effects

  Abstract

  Abstract

  The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, togheter with bottom and lateral friction stresses are taken into account. We introduce appropriatescalings into a three-dimensional anisotropic eddy viscosity model: after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional modl, which approximates the three-dimensional model at second order with respect to the ratio between the vertical scale and the longitudinal scale. The derived model is shown to be symmetrizable through a suitable change of variables. Finally, we propose sone numerical tests with the aim to validate the proposed model.

• MOX 9 - 10/09/2002
  Quarteroni, Alfio; Sala, Marzio; Sawley, M.L.; Parolini, Nicola; Cowles, G.
  Mathematical Modelling and Visualisation of Complex Three-dimensional Flows

  Abstract

  Abstract

  Three-dimensional fluid flows are characterised by the presence of complex physical phenomena. Numerical Algorithms that provide accurate approximations to the governing flow equations and visualisation to enable the detection and analysis of particular flow features, both play important rolesin the mathematical modelling of such flows. Two specific three-dimensional flow applications are presented to illustrate the use of appropriate visualisation techniques.

• MOX 7 - 04/09/2002
  Gauthier, Alain; Saleri, Fausto; Veneziani, Alessandro
  A fast preconditioner for the incompressible Navier Stokes Equations

  Abstract

  Abstract

  The pressure matrix method is a well known scheme for the solution of the incompressible Navier-Stokes equations by splitting the computation of the velocity and the pressure fields (see e.g., [13]. However, the set-up of effective preconditioners for the pressure matrix is mandatory in order to have an acceptable computationsl cost. Different strategies can be pursued (see e.g. [4], [18]). Inexact block LU factorizations of the matrix obtained after the discretization and linearization of the problem, originally proposed as fractional step solvers, provide also a strategy for building effective preconditioners of the pressure matrix (see [19]). In this paper, we present numerical results about a new preconditioner, based on an inexact factorization: the new preconditioner applies to the case of the generalized Stokes problem and to the Navier-Stokes one, as well.In the former case, it improves the performances of the well known Cahouet-Chabard preconditioner (see[2[). In the latter one, numerical results presented here show an almost optimal behaviour (with respect to the space discretization) and suggest that the new preconditioner is welle suited also for flexible or inexact strategies, in which the systems for the preconditioner are solved inaccurately.

• MOX 8 - 15/07/2002
  Formaggia, Luca; Lamponi, Daniele; Quarteroni, Alfio
  One dimensional models for blood flow in arteries

  Abstract

  Abstract

  We investigate a family of one dimensional nonlinear systems which model the blood pulse propagation in compliant arteries. They are obtained by averaging the Navier-Stokes equation on each section of an arterial vessel and using simplified models for the vessel compliance. Different differential operators arise depending on the semplifications made on the structural model. Starting from the most basic assumption of pure elastic instantaneous equilibrium, which provides a well known algebraic relation between intramural pressure and vessel section area, we analyse in turn the effects of terms accounting for inertia, longitudinal pre-stress and viscoelasticity. We also consider the problem of how to account for branching and possible discontinuous wall properties, the latter aspect is relevant in the presence of prosthesis and stents. To this purpose we employ a domain decomposition approach and we provide conditions which ensure the stability of the coupling. We propose a numerical method based on a finite element Taylor-Galerkin scheme combined with operator splitting techniques, and carry out several test cases for the assessment of the proposed models.