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 1242 prodotti
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44/2022 - 26/06/2022
Peli, R.; Dovera, L.; Fighera, G.; Menafoglio, A.; Secchi, P.
Forecasting Oil Production Rates in Primary Depletion using the Physics-based Residual Kriging functional approach | Abstract | | In this work, we illustrate a novel functional data analysis approach for the forecast of oil production rates in a mature single-phase reservoir. This model is based on the recently developed Physics-based Residual Kriging predictor, which represents oil rates as functional data and decomposes them as the sum of the predictions of a physical model and the geostatistical modelization of its residuals. In this context, we use the recently introduced FlowNet model to build up the physical term which, through a network-based representation of the reservoir, avoids the burden of three-dimensional full-physics simulations.
Furthermore, we propose an extension of the Physics-based Residual Kriging predictor in presence of ensemble of physical models, i.e. when the uncertainty in the model parameters is accounted for by simulating several models corresponding to different parameters samples.
The Physics-based Residual Kriging predictor is here applied to the oil rates produced in a realistic reservoir. We analyze three different scenarios in terms of wells drilling schedule, from a simple to a realistic scheme. In each scenario, we compare the predictions given by Physics-based Residual Kriging to the ones obtained with FlowNet and a pure geostatistical approach. |
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43/2022 - 20/06/2022
Zappon E.; Manzoni A.; Gervasio P.; Quarteroni A.
A reduced order model for domain decompositions with non-conforming interfaces | Abstract | | In this paper we propose a reduced order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems with Dirichlet and Neumann interface conditions, respectively. After discretization by (e.g.) the finite element method, the full-order model (FOM) is solved by Dirichlet-
Neumann iterations between the two sub-problems until interface convergence is reached. We, then, apply the reduced basis (RB) method to obtain a low-dimensional representation of the solution of each sub-problem. Furthermore, we use the discrete empirical interpolation method (DEIM) applied at the interface level to achieve a fully reduced-order representation of the DD techniques implemented. To deal with interface data when non-conforming FE interface discretizations are considered, we employ the INTERNODES method combined with the interface DEIM reduction. The reduced-order model (ROM) is then solved by sub-iterating between the two reduced-order sub-problems until convergence of the approximated high-fidelity interface solutions. The ROM scheme is numerically verified on both steady and unsteady coupled problems, in the case of non-conforming FE interfaces. |
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42/2022 - 14/06/2022
Gatti, F.; Fois, M.; de Falco, C.; Perotto, S.; Formaggia, L.
Parallel simulations for fast-moving landslides: space-time mesh adaptation and sharp tracking of the wetting front | Abstract | | We propose a highly scalable solver for a two-dimensional depth-integrated fluid dynamic model in order to simulate flow-like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two-step second-order Taylor-Galerkin scheme, enriched by a suitable flux correction in order to avoid spurious oscillations, in particular near discontinuities and close to the wetting-drying interface.
A mesh adaptation procedure based on a gradient-recovery a posteriori error estimator allows us to efficiently deal with a discretization of the domain customized to the phenomenon under investigation. Moreover, we resort to an adaptive scheme also in time to prevent filtering out the landslide dynamics, and to
an interface tracking algorithm
to avoid an excessive refinement in non-interfacial regions while preserving details along the wetting-drying front. Finally, after verifying the performance of the proposed numerical framework on idealized settings, we carry out a scalability analysis of the code both on idealized and real scenarios, to check the efficiency of the overall implementation. |
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41/2022 - 14/06/2022
Arnone, A.; Ferraccioli, F.; Pigolotti, C.; Sangalli, L.M.
A roughness penalty approach to estimate densities over two-dimensional manifolds | Abstract | | An innovative nonparametric method for density estimation over general two-dimensional Riemannian manifolds is proposed. The method follows a functional data analysis approach, combining maximum likelihood estimation with a roughness penalty that involves a differential operator appropriately defined over the manifold domain, thus controlling the smoothness of the estimate. The proposed method can accurately handle point pattern data over complicated curved domains. Moreover, it is able to capture complex multimodal signals, with strongly localized and highly skewed modes, with varying directions and intensity of anisotropy. The estimation procedure exploits a discretization in finite element bases, enabling great flexibility on the spatial domain. The method is tested through simulation studies, showing the strengths of the proposed approach. Finally, the density estimation method is illustrated with an application to the distribution of earthquakes in the world. |
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40/2022 - 14/06/2022
Fumagalli, A.; Patacchini, F. S.
Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media | Abstract | | Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure gradient and velocity. The actual shape of this relation is normally chosen at the outset of the problem, even though, in practice, the fluid may experience velocities outside of its range of applicability. We propose here an adaptive model, so that the most appropriate law is locally selected depending on the computed velocity. From the analytical point of view, we show well-posedness of the problem when the law is monotone in velocity and show existence in one space dimension otherwise. From the computational point of view, we present a new approach based on regularizing via mollification the underlying dissipation, i.e., the power lost by the fluid to the porous medium through drag. The resulting regularization is shown to converge to the original problem using $Gamma$-convergence on the dissipation in the monotone case. This approach gives rise to a variational numerical scheme which applies to very general problems and which we validate on three test cases. |
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39/2022 - 02/06/2022
Ferro, N.; Perotto, S.; Gavazzoni, M.
A new fluid-based strategy for the connection of non-matching lattice materials | Abstract | | We present a new algorithm for the design of the connection region between different lattice materials. We solve a Stokes-type topology optimization problem on a narrow morphing region to smoothly connect two different unit cells. The proposed procedure turns out to be effective and provides a local re-design of the materials, leading to a very mild modification of the mechanical behaviour characterizing the original lattices. The robustness of the algorithm is assessed in terms of sensitivity of the final layout to different parameters. Both the cases of Cartesian and non-Cartesian morphing regions are successfully investigated. |
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38/2022 - 31/05/2022
Burzacchi, A.; Landrò, M.; Vantini, S.
Object-oriented Classification of Road Pavement Type in Greater Maputo from Satellite Images | Abstract | | The information about pavement surface type is rarely available in road network databases of developing countries although it represents a cornerstone of the design of efficient mobility systems. This research develops an automatic classification algorithm for road pavement which makes use of satellite images to recognize road segment as paved or unpaved. The proposed methodology is based on an object-oriented approach, so that each road is classified by looking at the distribution of its pixels in the RGB space. The proposed approach is proven to be accurate, inexpensive, and readily replicable in other cities. |
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37/2022 - 31/05/2022
Boon, W. M.; Fumagalli, A.
A Reduced Basis Method for Darcy flow systems that ensures local mass conservation by using exact discrete complexes | Abstract | | A solution technique is proposed for flows in porous media that guarantees local conservation of mass. We first compute a flux field to balance the mass source and then exploit exact co-chain complexes to generate a solenoidal correction. A reduced basis method based on proper orthogonal decomposition is employed to construct the correction and we show that mass balance is ensured regardless of the quality of the reduced basis approximation. The method is directly applicable to mixed finite and virtual element methods, among other structure-preserving discretization techniques, and we present the extension to Darcy flow in fractured porous media. |
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