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 1275 products
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21/2007 - 11/06/2007
Massimi, Paolo; Quarteroni, Alfio; Saleri, Fausto; Scrofani, Giovanni
Modeling of Salt Tectonics | Abstract | | In this work a general framework for the simulation of sedimentary basins in presence of salt structures is addressed. Sediments and evaporites are modeled as non-Newtonian fluids and the thermal effects induced by the presence of salt are taken into account. The computational strategy is based on a Lagrangian methodology with intensive grid adaptivity, togheter with a kinematic modeling of faults and different kinds of boundary conditions representing sedimentation, erosion, basement evolution, lithospheric compression and extension. The proposed methodology is applied to simple test cases as well as to a geological reconstruction of industrial interest. |
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20/2007 - 11/05/2007
Burman, Erik; Quarteroni, Alfio; Stamm, Benjamin
Stabilization Strategies for High Order Methods for Transport Dominated Problems | Abstract | | Standard high order Galerkin methods, such as pure spectral or high order finite element methods, have
insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization
strategies for pure spectral methods and spectral multidomain approaches.
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19/2007 - 10/31/2007
Burman, Erik; Quarteroni, Alfio; Stamm, Benjamin
Interior Penalty Continuous and Discontinuous Finite Element Approximations of Hyperbolic Equations | Abstract | | In this paper we present the continuous and discontinuous Galerkin
methods in a unified setting for the numerical approximation of the transport
dominated advection-reaction equation. Both methods are stabilized by the
interior penalty method, more precisely by the jump of the gradient in the continuous
case whereas in the discontinuous case the stabilization of the jump of
the solution and optionally of its gradient is required to achieve optimal convergence.
We prove that the solution in the case of the continuous Galerkin
approach can be considered as a limit of the discontinuous one when the stabilization
parameter associated with the penalization of the solution jump tends
to infinity. As a consequence, the limit of the numerical flux of the discontinuous
method yields a numerical flux for the continuous method too. Numerical
results will highlight the theoretical results that are proven in this paper.
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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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