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 1152 products
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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. |
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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 |
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MOX 16 - 03/05/2003
Canuto, Claudio; Quarteroni, Alfio
Spectral Methods | Abstract | | Spectral methods represent a family of methods for the numerical approximation of partial differential equations. Their common denominator is to rely on high order polynomial expansions, notably trigonometric polynomials for periodic problems, orthogonal Jacobi polynomials for non periodic boundary value problems. They have the potential of providing high rate of convergence when applied to problems with regular data. They can be regarded as members of the broad family of (generalized) Galerkin methods with munerical evaluation of integrals based on Gaussian nodes. In a first part we introduce the methods on a computational domain of simple shape, analyze their approximation properties as well as their algorithmic features. Next we address the issue of how these methods can be extended to more complex geometrical domains be retaining their distinctive approximation properties. |
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MOX 13 - 02/03/2003
Deparis, Simone; Fernandez, Miguel A.; Formaggia, Luca
Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions | 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. |
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MOX 14 - 02/03/2003
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 | | 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. |
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MOX 11 - 01/05/2003
Micheletti, Stefano; Sacco, Riccardo, Simioni, Riccardo
Numerical Simulation of Resonant Tunneling Diodes with a Quantum-Drift-Diffusion Model | 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. |
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MOX 12 - 01/05/2003
Causin, Paola; Sacco, Riccardo
Mixed-hybrid finite element methods for coupled problems in silicon dioxide technology | 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. |
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MOX 10 - 12/05/2002
Ferrari, Stefania; Saleri, Fausto
A new two-dimensional Shallow Water model including pressure effects | 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.
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