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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18/2007 - 10/30/2007
Micheletti, Stefano; Perotto, Simona
Output functional control for nonlinear equations driven by anisotropic mesh adaption. The Navier-Stokes equations. | Abstract | | The contribution of this paper is twofold: firstly, a general
approach to the goal-oriented a posteriori analysis of nonlinear
partial differential equations is laid down, generalizing the standard
DWR method to Petrov-Galerkin formulations. This accounts for:
different approximations of the primal and dual problems;
nonhomogeneous Dirichlet boundary conditions, even
different on passing from the primal to the dual problem;
the error due to data approximation; the effect of stabilization
(e.g. for advective-dominated problems).
Secondly, moving from this framework, and employing anisotropic interpolation
error estimates, a sound anisotropic mesh adaption
procedure is devised for the numerical approximation of the
Navier-Stokes equations by continuous piecewise linear finite elements.
The resulting adaptive procedure is thoroughly addressed and
validated on some relevant test cases.
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17/2007 - 10/26/2007
Decoene, Astrid; Bonaventura, Luca; Miglio, Edie; Saleri, Fausto
Asymptotic Derivation of the Section-Averaged Shallow Water Equations for River Hydraulics. | Abstract | | A section-averaged shallow water model for application to river hydraulics is derived asymptotically,
starting from the three-dimensional Reynolds-averaged} Navier-Stokes equations for incompressible
free surface flows. The resulting section-averaged equations take into account the effects of eddy
viscosity, friction and of the three-dimensional geometry of the domain, up to the second order in the
ratio between vertical and longitudinal scales. This novel derivation yields a friction term that is similar
to that of the classical section-averaged shallow water model, but includes a correction that is
dependent on the turbulent vertical viscosity model.
Steady state analytic solutions for open channel flow have been computed for the derived model,
obtaining solutions that are much closer to those of the three-dimensional model than the solutions
computed by the classical one-dimensional shallow-water models. |
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16/2007 - 10/17/2007
Quarteroni Alfio
Modellistica Matematica e Calcolo Scientifico | Abstract | | Nel seguito verrà discusso il ruolo della modellistica matematica e del calcolo scientifico nelle scienze applicate, la loro rilevanza come strumenti di simulazione, indagine e supporto alle decisioni, il loro contributo all’innovazione tecnologica. Si citeranno alcuni risultati conseguiti e le prospettive che si aprono in svariati settori quali l’industria, l’ambiente, le scienze della vita e lo sport. |
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15/2007 - 10/16/2007
Vergara, Christian; Zunino, Paolo
Multiscale modeling and simulation of drug release from cardiovascular stents | Abstract | | In this study, we focus on a specific application, the modeling and simulation of drug release from cardiovascular drug eluting stents.
In particular, we analyze the drug release dynamics from the stent coating, where the drug is initially stored, to the arterial wall surrounding the stent. The main challenge in addressing this problem consists in accounting for multiple space scales.
We propose a new multiscale model for the drug release that significantly cuts down the computational cost. This model allows us to consider a realistic problem setting, which is applied for the numerical experiments.
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14/2007 - 09/06/2007
Dede', L.
Reduced Basis Method for Parametrized Advection-Reaction Problems | Abstract | | In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For generation of the basis we adopt a stabilized Finite Element method and we define the Reduced Basis method in the primal-dual formulation for this stabilized problem. We provide both a priori and a posteriori Reduced Basis error estimates and we discuss the effects of the Finite Element approximation on the Reduced Basis error. We propose an adaptive algorithm for the selection of the sample sets upon which thew basis are built. The basis idea of this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests shows the convenience, in terms of computational costs, of the prime-dual Reduced Basis approach. |
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13/2007 - 08/30/2007
Zunino Paolo
Discontinuous Galerkin methods based on weighted interior penalties for second order PDEs with non-smooth coefficients | Abstract | | We develop and analyze a Discontinuous Galerkin (DG) method based on weighted interior penalties (WIP) applied to second order PDEs and in particular to advection-diffusion-reaction equations featuring non-smooth and possibly vanishing diffusivity.
First of all, looking at the derivation of a DG scheme with a bias to domain decomposition methods, we carefully discuss the set up of the discretization scheme in a general framework putting into evidence the helpful role of the weights and the connection with the well known Local Discontinuous Galerkin schemes (LDG).
Then, we address the a-priori and the a-posteriori error analysis of the method, recovering optimal error estimates in suitable norms. By virtue of the introduction of the weighted penalties, these results turn out to be robust with respect to the diffusion parameter.
Furthermore, we discuss the derivation of an a-posteriori local error indicator suitable for advection-diffusion-reaction problems with higly variable, locally small diffusivity.
Finally, all the theoretical results are illustrated and discussed by means of numerical experiments.
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12/2007 - 07/27/2007
Deponti, Alberto; Bonaventura, Luca; Rosatti; Giorgio, Garegnani, Giulia
An Accurate and Efficient Semi-Implicit Method for Section Averaged Free Surface Flow Modelling | Abstract | | An accurate, efficient and robust numerical method for the
solution of the section averaged equations of open channel flow is
presented and discussed.
The method allows for river sections of arbitrary shape and for arbitrary bottom topography. The continuity equation is formulated in a conservative fashion, while a non conservative form is chosen for the momentum equation, thus avoiding the need for well balanced schemes to handle rapidly varying bathymetry.
In order to achieve unconditional stability with respect to flow celerity, a semi-implicit time discretization is introduced, which requires the solution of a weakly nonlinear system for the free surface at each time step by a fixed point iteration technique.
A semi-Lagrangian discretization is introduced, to achieve full unconditional stability and increase efficiency at no accuracy loss in subcritical flow regimes.
An appropriate upwind discretization is also introduced for the momentum equation, which allows to recover correct solutions also in presence of discontinuities and strong gradients. Numerical experiments show that the semi-Lagrangian method yields indeed accurate results also in the case of stationary hydraulic jumps.
The model is validated in a wide range of
idealised test cases, highlighting its accuracy and efficiency
characteristics, especially for long time range simulations of subcritical river
flow. Finally, a first model validation on realistic data is presented, concerning simulations of flooding events of the Adda river.
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11/2007 - 07/26/2007
Badia, Santiago; Nobile, Fabio; Vergara, Christian
Fluid-structure partitioned procedures based on Robin transmission conditions | Abstract | | In this article we design new partitioned procedures for fluid-structure
interaction problems, based on Robin-type transmission conditions. The
choice of the coefficient in the Robin conditions is justified via simplified
models. The strategy is effective whenever an incompressible fluid interacts
with a relatively thin membrane, as in haemodynamics applications. We
analyze theoretically the new iterative procedures on a model problem,
which represents a simplified blood-vessel system. In particular, the Robin-
Neumann scheme exhibits enhanced convergence properties with respect to
the existing partitioned procedures. The theoretical results are checked
using numerical experimentation.
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