Quaderni di Dipartimento

Quaderni MOX

• MOX55 - 18/02/2005
  Dede', L.; Quarteroni, A.
  Optimal Control and Numerical Adaptivity for Advection-Diffusion Equations

  Abstract

  Abstract

  We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection-diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equation separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting the error on the cost functional into the sum of an iteration error plus a discretization error. Once the former is reduced below a given threshold (and therefore the computed solution is near the optimal solution), the adaptive strategy is operated on the discretization error. To prove the effectiveness of the proposed methods, we report some numerical tests, referring to problems in which the control term is the source term of the advection-diffusion equation.

• MOXP4 - 12/02/2005
  Veneziani, Alessandro; Foa, Erika
  Simulazione Numerica di Pompe per Macchine Lavatrici

  Abstract

  	Abstract

• MOX 54 - 21/01/2005
  Agoshkov, Valery; Quarteroni, Alfio; Rozza, Gianluigi
  A Mathematical Approach in the Design of Arterial Bypass Using Unsteady Stokes Equations

  Abstract

  	Abstract
  	In this paper we present an approach for the study of Aorto-Coronaric bypass anastomoses configurations using unsteady Stokes equations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary according to several optimality criteria.

• MOX 53 - 10/01/2005
  Formaggia, Luca; Quarteroni, Alfio; Veneziani, Alessandro
  The circulatory system: from case studies to mathematical modeling
• MOX 52 - 25/11/2004
  Bottasso, Carlo L.; Maisano, Giorgio; Micheletti, Stefano; Perotto, Simona
  New recovery based a posteriori error estimators

  Abstract

  Abstract

  In this paper we formulate some new a posteriori recovery-based error estimators. The first one provides us with an improved approximation for the solution gradient. The other two furnish and estimate for the $L^2$-norm of the error on the solution itself. In more detail, the first estimator is a variant of the well-known Zienckiewicz-Zhu method and it turns out to be exact 1D for quadratic solution on non-uniform grids. The second one is based on a solution enrichment relying upon the Zienckiewicz-zhu recovered gradient. Finally the third estimator consists of a roughening of the solution followed by a Zienckiewicz-Zhu-like recovery applied to the solution itself. The three new proposed methods are compared in terms of their effectivity indices and solution accuracy on two and three dimensional problems

• MOX 51 - 11/11/2004
  Leupi, Celestin; Miglio, Edie; Altinakar, A.; Quarteroni, Alfio; Deville, M.O.
  Quasi-3D Finite Element Shallow-Water Flow with $k- epsilon$ Turbolence Model

  Abstract

  Abstract

  An extension of a three-dimensional (3D) finite element method is proposed for shallow-water equations (SWE). The method is based on the Raviart-Thomas finite element approximation. A numerical solution for shallow-water flows is developed based on the unsteady Reynolds-averaged Navier-Stokes (RANS) equations. In this work the assumption of hydrostatic pressure is applied. The SWE equations are solved in a given multilayered system (which consist of an a priori subdivision of the vertical direction of the domain into layers of fixed thickness), with a semi-implicit time stepping method. The eddy viscosity is calculated using the standard $k- epsilon$ turbolence model. The boundary conditions at the bed are based on the equilibrium assumption of the production terms with vertical diffusione terms using wall functions. To test the validity of the new algorithm the model is applied to three-dimensional flows for which experimental data and other numerical results are available for comparison.

• MOXP3 - 06/11/2004
  Formaggia, Luca; Miglio, Edie; Del Grosso, Luca; Montano, Antonio; Pandini, Stefano
  Modello Dinamico di una Imbarcazione da Canottaggio

  Abstract

  	Abstract

• MOX 50 - 03/11/2004
  Agoshkov, Valery
  Control and Inverse Problems Theory Approaches for Solving Some Hydrodynamics Equations

  Abstract

  Abstract

  In this study, we apply optimal control approaches and adjoint equations to construct iterative processes for some problems of hydrodynamics. First, the iterative processes are proposed for an abstract problem given by the system of operator equations. Second, the general methodology is applied to the generalized Stokes equations perturbed by a skew-symmetric bounded operator, to the stationary linearized Navier-Stokes equations (the Oseen problem) and to the non-stationary Stokes problem. the convergence rates of the iterative algorithms are studied.