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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50/2012 - 11/28/2012
Carcano, S.; Bonaventura, L.; Neri, A.; Esposti Ongaro, T.
A second order accurate numerical model for multiphase underexpanded volcanic jets | Abstract | | An improved version of the PDAC (Pyroclastic Dispersal Analysis Code) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation
of multiphase volcanic jets in supersonic regimes.
The present version of PDAC includes second-order time and space discretizations and fully multidimensional advection discretizations, in order to reduce numerical diffusion and
enhance the accuracy of the original model.
The resulting numerical model is tested against the problem of jet decompression in
both two and three dimensions. For homogeneous jets, numerical results show a good quantitative agreement
with experimental results on the laboratory scale in terms of Mach disk location. For multiphase jets, we consider monodisperse and polydisperse mixtures of particles
with different diameter. For fine particles, for which the pseudogas limit is valid,
the multiphase model correctly reproduces
predictions of the pseudogas model. For both fine and coarse particles, we
measure the importance of multiphase
effects with relation to the characteristic time scales of multiphase jets and we quantify how
particles affect the average jet dynamics in terms of pressure, mixture density, vertical velocity and temperature.
Furthermore, time
dependent vent conditions are introduced, in order to achieve numerical
simulation of eruption regimes characterized by transient jet behaviour. We show how in case of rapid change in vent conditions, volcanic jet structures do not evolve through a succession of steady state configurations and the transition between different flow
conditions can result in the collapse of the volcanic column. |
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49/2012 - 11/27/2012
Migliorati, G.; Nobile, F.; von Schwerin, E.; Tempone, R.
Approximation of Quantities of Interest in stochastic PDEs by the random discrete L2 projection on polynomial spaces | Abstract | | In this work we consider the random discrete L2 projection on polynomial spaces (hereafter RDP) for the approximation of scalar Quantities of Interest (QOIs) related to the solution of a Partial Differential Equation model with random input parameters. The RDP technique consists of randomly sampling the input parameters and computing the corresponding values of the QOI, as in a standard Monte Carlo approach. Then, the QOI is approximated as a multivariate polynomial
function of the input parameters by a discrete least squares approach.
We consider several examples including the Darcy equations with random permeability; the linear elasticity equations with random elastic coefficient; the Navier-Stokes equations in random geometries and with random fluid viscosity.
We show that the RDP technique is well suited for QOIs that depend smoothly on a moderate number of random parameters. Our numerical tests confirm the
theoretical findings in [14], which have shown that, in the case of a single random parameter uniformly distributed, the RDP technique is stable and optimally convergent if the number of sampling points scales quadratically with the dimension of the polynomial space. However, in the case of several random input parameters, numerical evidence shows that this condition could be relaxed and a linear scaling seems enough to achieve stable and optimal convergence, making the RDP technique very promising for high dimensional uncertainty quantification. |
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48/2012 - 11/26/2012
Ghiglietti, A.; Paganoni, A.M.
Statistical properties of two-color randomly reinforced urn design targeting fixed allocations | Abstract | | This paper deals with the statistical properties of a response adaptive design, described in terms of a two colors urn model, targeting prespecified asymptotic allocations. Results on the rate of convergence of number of patients assigned to each treatment are proved as well as on the asymptotic behavior of the urn composition. Suitable statistics are introduced and studied to test the hypothesis on treatment s differences. |
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47/2012 - 10/30/2012
Astorino, M.; Chouly, F.; Quarteroni, A.
Multiscale coupling of finite element and lattice Boltzmann methods for time dependent problems | Abstract | | In this work we propose a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the lattice Boltzmann method. The two methods are regarded as macroscale and mesoscale solvers, respectively. The procedure is based on the Parareal paradigm and allows for a truly multiscale coupling between two numerical methods having optimal efficiency at different space and time scales. The motivations behind this approach are manifold. Among others, we have that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational
domain. The theoretical and numerical framework is presented for parabolic equations even though its potential applicability is much wider (e.g. Navier-Stokes equations). Various numerical examples on the heat equation will validate the proposed procedure and illustrate its multiple advantages.
Keywords: finite element method, lattice Boltzmann method, multiscale coupling, Parareal, parallel-in-time domain decomposition. |
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46/2012 - 10/26/2012
Dassi, F.; Perotto, S.; Formaggia, L.; Ruffo, P.
Efficient geometric reconstruction of complex geological structures | Abstract | | Complex geological structures pose a challenge to domain discretization. Indeed data are normally given as a set of intersecting surfaces, sometimes with incomplete data, from which one has to identify the computational domain to build a mesh suited for numerical simulations. In this paper we describe a set of tools which have been developed for this purpose. Specialized data structures have been developed to efficiently identify intersections of triangulated surfaces and to conformally include these intersections in the starting meshes, while improving the mesh quality. Then, an effective algorithm has been implemented to detect the different sub-regions forming the computational domain; this algorithm has been properly enhanced to take into account the specific characteristics involved in the simulation of geological basins. |
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45/2012 - 10/24/2012
Negri, F.; Rozza, G.; Manzoni, A.; Quarteroni, A.
Reduced basis method for parametrized elliptic optimal control problems | Abstract | | We propose a suitable model reduction paradigm -the certied reduced basis method (RB) - for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations (PDEs). In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as constraint. Firstly, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of
the RB methodology are provided: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling to perform competitive Offine-Online splitting in the computational procedure; an efficient and rigorous a posteriori error estimate on the state, control and adjoint variables as well as on the cost functional. Finally, the reduction scheme is applied to some numerical tests conrming the theoretical results and showing the efficiency of the proposed technique.
Keywords: reduced basis methods, parametrized optimal control problems, saddle-point problems, model order reduction, PDE-constrained optimization, a posteriori error estimate |
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43/2012 - 10/19/2012
Secchi, P.; Vantini, S.; Vitelli, V.
A Case Study on Spatially Dependent Functional Data: the Analysis of Mobile Network Data for the Metropolitan Area of Milan | Abstract | | We analyze geo-referenced high-dimensional data describing the use over time of the mobile-phone network in the urban area of Milan, Italy. Aim of the analysis is segmenting the metropolitan area of Milan into subregions sharing a similar pattern along time, possibly related to activities taking place in specific locations and/or times within the city. To tackle this problem, we develop a non-parametric method for the analysis of spatially dependent functional data, named Bagging Voronoi Treelet Analysis. Indeed, this novel approach integrates the treelet decomposition with a proper treatment of spatial dependence, obtained through a Bagging Voronoi strategy. The latter relies on the aggregation of different replicates of the analysis, each involving a set of functional local representatives associated to random Voronoi-based neighborhoods covering the investigated area. In the presence of spatial dependence the method appears to be both computationally and statistically efficient. Indeed results clearly point out some interesting temporal patterns interpretable both in terms of population density and mobility (e.g., daily work activities in the tertiary district, leisure activities in residential areas in the evenings and in the weekend, commuters movements along the highways during rush hours, and localized mob concentrations related to occasional events). Moreover we perform two simulation studies, aimed at investigating the properties and performances of the method.
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44/2012 - 10/19/2012
Fumagalli, A.; Scotti, A.
A numerical method for two-phase flow in fractured porous media with non-matching grids | Abstract | | We propose a novel computational method for the efficient simulation of two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent them as immersed interfaces with a reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fractures to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method that is able to handle cut cells and matrix-fracture interactions for the saturation equation. The choice of a suitable flux function in the case of discontinuous flux function at the interface between the fracture and the porous matrix is also addressed through numerical experiments.
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