Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1239 prodotti
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MOX 15 - 05/03/2003
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 - 05/03/2003
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 - 03/02/2003
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 - 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 | | 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 - 05/01/2003
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 - 05/01/2003
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 - 05/12/2002
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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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 | | 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. |
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