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 1238 products
-
MOX 23 - 06/23/2003
Paganoni, Anna Maria; Secchi Piercesare
Interacting reinforced urn systems | Abstract | | We introduce a class of a discrete time stochastic processes generated by interacting systems of reinforced urns. We show that such processes are asymptotically partially exchangeable and we prove a strong law of large numbers. Examples and the analysis of particular cases show that interacting reinforced urn systems are very flexible representations for modelling countable collections of dependents and asymptotically exchangeable sequences of random variables. First published in: Advances in Applied Probability - Vol. 36 No.3 (September 2004) by The Applied Probability Trust. |
-
MOX 22 - 06/13/2003
Formaggia, Luca; Nobile, Fabio
Stability analysis of second ordr time accurate schemes for ALE-FEM | Abstract | | In this work we will introduce and analyze the Arbitrary Lagrangian Eulerian formulation for a model problem of a scalar advection diffusion equation defined on a moving domain. Moving from the results illustrated in our previous work of the same authors we will consider first and second order time advancing schemes and analyze how the movement of the domain might affect accuracy and stability properties of the numerical schemes with respect to their counterpart on fixed domains. Theoretical and numerical results will be presented, showing that stability properties are not, in general preserved while accuracy is maintained. |
-
MOX 21 - 06/09/2003
Formaggia, Luca; Veneziani, Alessandro
Reduced and multiscale models for the human cardiovascular system | Abstract | | This report collects the notes of two lectures given by L. Formaggia at VKI Lecture Series on Biological Fluid Dynamics held at the Von Karman Institute, Belgium, on May 2003.
Tyhey give a summary of some aspects of the research activity carried out by the authors at Politecnico di Milano and at EPFL, Lausanne, under the direction of prof. Alfio Quarteroni, aimed at providing mathematical models and numerical techniques for the simulation of the human cardiovascular system.
This report is subdivided in two chapters, in correspondence with the two lectures. The first deals with the derivation of one dimensional models for blood flow in arteries. The second is more specifically devoted to the description and analysis of the geometrical multiscale technique. |
-
MOX 20 - 05/26/2003
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
A multiscale formulation of the discontinuous Petrov-Galerkin method for advective-diffusive problems | Abstract | | We consider the Discontinuous Petrov-Galerkin method for the advection-diffusion model problem and we investigate the application of the variational multiscale method to this formulation. We show the exact modeling of the fine scale modes at the element level for the linear case, and we discuss the approximate modeling both in the linear and in the non-linear cases. Furthermore, we highlight the existing link between this multiscale formulation and the $p$ version of the finite element method. Numerical examples illustrate the behavior of the proposed scheme. |
-
MOX 19 - 05/07/2003
Causin, Paola; Sacco, Riccardo
A discontinuous Petrov-Galerkin method with Lagrangian multipliers for second order elliptic problems | Abstract | | We present a discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG)) which is based on introducing variables defined in the interior and on the boundary of the element. The interface variables are suitable Lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivate, thus providing the proper connection between neighboring elements. The internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size having as unknowns the Lagrangian multipliers. A stability and convergence analysis of the novel formulation is carried out and its connection with mixed-hybrid and DG method is explored. Numerical tests on several benchmark problems are included to validate the convergence perfomance and the flux-conservation properties of the DPG method. |
-
MOX 18 - 04/16/2003
Causin, Paola; Restelli, Marco; Sacco, Riccardo
A simulation system based on mixed-hybrid finite elements for thermal oxidation in semiconductor technology | Abstract | | In this work we deal with the numerical simulation of thermal oxidation in silicon device technology. This application involves the coupled solution of a diffusion-reaction problem and of a fluid-structure interaction problem. These two problems are mutually dependent through the exchange of stresses and fluxes that are typically post-processed fields in standard finite element approaches, and as such they may suffer form a lack of accuracy and from physical inconsistencies. In this article, we propose a novel approach to the simulation of the thermal oxidation process, that is characterized by the use of mixed and hybrid finite elements. the main advantage of such formulations is that stresses and fluxes are directly computed quantities, rather than obtained from post-processing techniques. We also address the procedures and the techniques that must be devised for handling the coupled interaction problem and the presence of a computational grid moving in time. The numerical approach we propose is eventually validated on a realistic example of the thermal oxidation process in a local oxidation structure (LOCOS) |
-
MOX 17 - 04/05/2003
Abba', A.; Cercignani, C.; Valdettaro, L.
Modelli e simulazione LES di correnti turbolente e applicazione alla combustione | Abstract | | Le finalità della presente ricerca sono l analisi e sviluppo di modelli per la simulazione numerica di correnti turbolente incomprimibili e di fluidi turbolenti reagenti, mediante la tecnica della Large Eddy Simulation (LES).
La prima parte dell articolo è dedicata all analisi, sulla base di test a priori, di diversi modelli di turbolenza per correnti incomprimibili in assenza di reazioni chimiche. I modelli vengono valutati mediante test a priori avvalendoci di risultati provenienti da simulazioni numeriche dirette di turbolenza omogenea isotropa a Reynolds 1000 e di uno strato limite turbolento tridimensionale.
Nella seconda parte si troveranno invece le descrizioni delle equazioni e del metodo numerico utilizzato per la simulazione di correnti turbolente in presenza di reazioni chimiche secondo differenti approcci: il metodo dello scalare conservato, per reazioni chimiche veloci in fiamme di diffusione l approccio a fronte di fiamma per flussi premiscelati equazioni di conservazione delle specie chimiche per reazioni complesse, a più passi e non in equilibrio. Per ognuno di questi vengono formulati nuovi modelli basati sui modelli dinamici presentati nella prima parte, e vengono presentati i risultati delle simulazioni numeriche. |
-
MOX 15 - 03/05/2003
Formaggia, Luca; Micheletti, Stefano; Perotto, Simona
Anisotropic mesh adaption in Computational Fluid Dynamics: application to the advection-diffusion-reaction and the Stokes problems | Abstract | | In this work we develop an anisotropic a posteriori error analysis of the advection-diffusion-reaction and the Stokes problems. This is the first step towards the study of more complex situation, such as the Oseen and Navier-Stokes equations, which are very common in Computational Fluid Dynamic (CFD) applications. The leading idea of our analysis consists in combining the anisotropic interpolation error estimates for affine triangular finite element provided in [14,15] with a posteriori error analysis based on a dual problem associated with the problem at hand [6,34]. Anisotropic interpolation estimates take into account more in detail the geometry of the triangular elements, i.e. not just their diameter but also their aspect ratio and orientation. Ont he other hand, the introduction of the dual problem allows us to control suitable functionals of the discretization error, e.g. the lift and drag around bodies in external flows, mean and local values, etc. The combined use of both approaches yelds an adaptive algorithm which, via an iterative process, can be used for designing the optimal mesh for the problem at hand |
|
