Quaderni di Dipartimento

Quaderni MOX

• MOX 39 - 10/05/2004
  Parolini, Nicola; Quarteroni, Alfio
  Mathematical Models and Numerical Simulation for the America s Cup

  Abstract

  Abstract

  This paper presents a review of the mathematical models which can be adopted to describe the different physical phenomena characterizing the flow around a sailing yacht. The complete model accounting for the laminar-turbulent transition regime, free-surface dynamics and fluid-sails interaction is introduced as long as some simplified models that have been used to reduce the computational complexity. Drawing on the experience of the Ecole Polytechnique Fédérale de Lausanne (EPFL) as Official Scientific Advisor to the Alinghi Team, winner of 2003 America s Cup, we discuss the role of Computational Fluid Dynamics simulations based on Reynolds Averages Navier-Stokes (RANS) equations and their integration in standard yacht design process. Numerical results in different areas (appendages design, free-surface flows, aerodynamics of sails) are presented and discussed.

• MOX 38 - 20/04/2004
  Fumagalli, Elena; Lo Schiavo,Luca; Salvati, Simonetta; Secchi,Piercesare
  Statistical Identification of Major Event Days: An Application to Continuity Of Supply Regulation In Italy

  Abstract

  Abstract

  The Italian regulatory mechanism for quality of service in electricity distribution links the tariff to the SAIDI indicator of average duration of interruptions per consumer. In order to separate major interruption events data from normal operation data the regulator introduced, in the year 2000, a criterion based on a given definition of Force Majeure. For the new regulatory period, beginning in 2004, the authors studied the possibility of substituting this criterion with one based on a statistical definition of major event days. The statistical two step methodology proposed here was tested using real data, compared with other statistical criteria found in the literature, and proposed to interested parties in the consultation process. It was found to be at the same time equitable, unambiguous and simple to implement. This criterion was thus adopted in the new regulatoy framework.

• MOX 36 - 16/04/2004
  Miglio, Edie; Perotto, Simona; Saleri, Fausto
  Strategies of model coupling: application to free surface flow problems

  Abstract

  Abstract

  The motion of water in a complex hydrodynamic configuration is characterized by a wide spectrum of space and time scales, due to coexistence of physical phenomena of different nature. Consequently, the numerical simulation of a hydrodynamic system of this type is characterized by a large computational cost. In this paper, after introducing a quite general setting for model coupling, we discuss two techniques to reduce such a computational effort by suitably coupling different hydrodynamic models. The first approach is based on a dimensionally heterogeneous-physically homogeneous coupling strategy driven a priori physical considerations. As second strategy we suggest a dimensionally homogeneous-physically heterogeneous coupling. This time the subdomain-to-model correspondence is identified automatically thanks to a suitable a posteriori modeling error estimator. The range of applicability of both the approaches is finally examined on some test cases.

• MOX 37 - 16/04/2004
  Micheletti, Stefano; Perotto, Simona
  Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator

  Abstract

  Abstract

  In this paper we study the efficiency and the reliability of an anisotropic a posteriori error estimator in the case of the Poisson problem supplied with mixed boundary conditions. The error estimator may be classified as a residual-basedone, but its novelty is twofold: firstly, it employs anisotropic estimates of the interpolation error for linear triangular finite elements and, secondly, it makes use of the Zienkiewicz-Zhu recovery procedure to approximate the gradient of the exact solution. Finally, we describe the adaptive procedure used to obtain a numerical solution satisfying a given accuracy, and we include some numerical test cases to assess the robustness of the proposed numerical algorithm.

• MOX 35 - 08/04/2004
  Veneziani, Alessandro; Vergara, Christian
  Flow rate defective boundary conditions in haemodynamics simulations

  Abstract

  Abstract

  In the numerical simulation of blood flow problems it might happen that the only available boundary conditions prescribe the flow rate incoming/outcoming the vascular district at hand. In order to have a well posed Navier-Stokes problem, these conditions need to be completed. In the bioengineering community, this problem is usually faced by choosing a priori a velocity profile on the inflow/outflow sections, to be fitted with the assigned flow rates. This approach strongly influences the accuracy of the numerical solutions. A less perturbative strategy is based on the so-called do-nothing approach, advocated in Heywood, Rannacher, turek, Int. J. Num. Fl, 1996. An equivalent approach, but easier from the numerical discretization viewpoint, has been proposed in Formaggia, Gerbeau, Nobile, Quarteroni, SIAM J Num An, 2002. It is based on an augmented formulation of the problem, in which the conditions on the flow rates are prescribed in a weak sense by means of Lagrangian multipliers. In this paper we analyze the unsteady augmented Navier-Stokes problem, proving a well posedness result. Moreover, we present some numerical methods for solving the augmented problem, based on a splitting of the computation of velocity and pressure on one side and the Lagrangian multiplier on the other one. In this way, we show how it is possible to solve the augmented problem resorting to available Navier-Stokes solvers.

• MOX 34 - 30/03/2004
  Bottasso, Carlo L.; Causin, Paola; Sacco, Riccardo
  Flux-Upwind Stabilization of the Discontinuous Petrov-Galerkin Formulation with Lagrange Multipliers for Advection-Diffusion Problems

  Abstract

  Abstract

  In this work we considerthe dual-primal Discontinuous Petrov-Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a discrete maximum principle under standard geometrical assumptions on the computational grid. A convergence analysis is developed, proving first-order accuracy of the method in a discrete $H^1-norm$, anf the numerical performance of the scheme is validated on benchmark problems with sharp internal and boundary layers.

• MOX 33 - 25/03/2004
  Abba', A.; Saleri, F.; D'Angelo, C.
  A 3D Shape Optimization Problem in Heat Transfer: Analysis and Approximation via BEM

  Abstract

  Abstract

  In this paper an optimal shape control problem dealing with heat transfer in enclosures is studied. We model and enclosure heated by a flame surface (taking account of radiation, conductor and convection effects), and we try to find an optimal flame shape which minimizes some cost functional defined on the temperature field. This kind of problem arises in industrial furnaces optimization, being temperature uniformity one of the most important aspects in industrial plant analysis and design. Analytical results (smoothness of the control-to-state mapping, existence of an optimal shape in a certain admissible class) as well as numerical optimization results by the boundary element method are obtained we employ the gradient method to optimize the flame shape, exploiting the adjoint equation associated with the state equation and the cost function.

• MOX 32 - 08/03/2004
  Carstensen, Carsten; Causin, Paola; Sacco, Riccardo
  A Posteriori Dual-Mixed (Hybrid) Adaptive Finite Element Error Control for Lamé and Stokes Equations

  Abstract

  Abstract

  A unified and robust mathematical model for compressible and incompressible elasticity can be obtained by rephrasing the Hermann formulation within the Hellinger-Reissner principle. The quasi-optimally converging extension of PEERS (Plane Elasticity Element with Reduced Symmetry) is called Dual-Mixed Hybrid formulation (DMH). Explicit residual-based a posteriori error estimates for DMII are introduced and are mathematically shown to be locking-free, reliable, and efficient. The estimator serves as a refinement indicator in an adaptive algorithm for effective automatic mesh generation. Numerical evidence supports that the adaptive scheme leads to optimal convergence for Lamé and Stokes benchmark problems with singularities.