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 9 - 09/10/2002
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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MOX 7 - 09/04/2002
Gauthier, Alain; Saleri, Fausto; Veneziani, Alessandro
A fast preconditioner for the incompressible Navier Stokes Equations | Abstract | | The pressure matrix method is a well known scheme for the solution of the incompressible Navier-Stokes equations by splitting the computation of the velocity and the pressure fields (see e.g., [13]. However, the set-up of effective preconditioners for the pressure matrix is mandatory in order to have an acceptable computationsl cost. Different strategies can be pursued (see e.g. [4], [18]). Inexact block LU factorizations of the matrix obtained after the discretization and linearization of the problem, originally proposed as fractional step solvers, provide also a strategy for building effective preconditioners of the pressure matrix (see [19]). In this paper, we present numerical results about a new preconditioner, based on an inexact factorization: the new preconditioner applies to the case of the generalized Stokes problem and to the Navier-Stokes one, as well.In the former case, it improves the performances of the well known Cahouet-Chabard preconditioner (see[2[). In the latter one, numerical results presented here show an almost optimal behaviour (with respect to the space discretization) and suggest that the new preconditioner is welle suited also for flexible or inexact strategies, in which the systems for the preconditioner are solved inaccurately. |
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MOX 8 - 07/15/2002
Formaggia, Luca; Lamponi, Daniele; Quarteroni, Alfio
One dimensional models for blood flow in arteries | Abstract | | We investigate a family of one dimensional nonlinear systems which model the blood pulse propagation in compliant arteries. They are obtained by averaging the Navier-Stokes equation on each section of an arterial vessel and using simplified models for the vessel compliance. Different differential operators arise depending on the semplifications made on the structural model. Starting from the most basic assumption of pure elastic instantaneous equilibrium, which provides a well known algebraic relation between intramural pressure and vessel section area, we analyse in turn the effects of terms accounting for inertia, longitudinal pre-stress and viscoelasticity.
We also consider the problem of how to account for branching and possible discontinuous wall properties, the latter aspect is relevant in the presence of prosthesis and stents. To this purpose we employ a domain decomposition approach and we provide conditions which ensure the stability of the coupling.
We propose a numerical method based on a finite element Taylor-Galerkin scheme combined with operator splitting techniques, and carry out several test cases for the assessment of the proposed models. |
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MOX 6 - 07/01/2002
Micheletti, Stefano; Perotto, Simona; Picasso, Marco
Some remarks on the stability coefficients and bubble stabilization of FEM on anisotropic meshes | Abstract | | In this paper we re-address the anisotropic recipe provided for the stability
coefficients in [13].
By comparing our approach with the residual-free bubbles theory, we
improve on our a priori analysis for both the advection-diffusion and the
Stokes problems. In particular, in the case of the advection-diffusion problem
we derive a better interpolation error estimate
by taking into account in a more anisotropic way the contribution
associated with the convective term. Concerning the Stokes problem,
we provide a numerical evidence that our ani -so -tro -pic approach is
thoroughly comparable with the bubble stabilization, which we study more
in detail in our anisotropic framework. |
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MOX 5 - 06/01/2002
Causin, Paola; Sacco, Riccardo
A Dual-Mixed Hybrid Formulation for Fluid Mechanics Problems: Mathematical Analysis and Application to Semiconductor Process Technology | Abstract | | In this paper we propose a dual-mixed hybrid formulation capable of treating uner a unified framework both compressible and incompressible problems in continuoum mechanics. A theoretical analysis of the method is carried out and optimal error estimates are derived for both mixed and hybrid variables. The potentialities of the novel approach are exploited in the computation of the stress field required in the simulation of the thermal oxidation process in semiconductor technology. The numerical formulation is validated both on model problems in continuoum mechanics and on a realistic example of the thermal oxidation process in a local oxidation structure (LOCOS) |
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MOX 4 - 05/01/2002
Quarteroni, Alfio; Veneziani, Alessandro
Analysis of a Geometrical Multiscale Model Based on the Coupling of ODE S and PDE S for Blood Flow Simulations | Abstract | | In hemodynamics, local
phenomena, such as the perturbation of flow pattern in a specific vascular region, are
strictly related to the global features of the whole circulation (see e.g. cite{FNQV}).
In cite{QRV1} we have proposed a heterogeneous model where a
local, accurate, 3D description of blood flow by means of the Navier-Stokes equations
in a specific artery is coupled with a
systemic, 0D, lumped model of the remainder of circulation. This is a geometrical multiscale strategy,
which couples an initial-boundary value problem to be used in a specific vascular region with
an initial-value-problem in the rest of the circulatory system. It has been
succesfully adopted to predict the outcome of a surgical operation (see cite{Biorheo,eccom}).
However, its interest goes beyond the context of blood flow simulations,
as we point out in the Introduction.
In this paper we provide a well posedness analysis
of this multiscale model, by proving a local-in-time existence result
based on a fixed-point technique.
Moreover, we investigate the role of matching conditions between the two submodels for the numerical simulation. |
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MOX 3 - 02/01/2002
Discacciati, Marco; Quarteroni, Alfio
Analysis of a Domain Decomposition Method for the Coupling of Stokes and Darcy Equations
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MOX1 - 01/01/2002
Quarteroni, Alfio; Formaggia, Luca
Mathematical Modelling and Numerical Simulation of the Cardiovascular System | Abstract | | In these notes we will address the problem of developing models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries |
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