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 1237 products
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36/2013 - 08/25/2013
Ferran Garcia, Luca Bonaventura, Marta Net, Juan Sanchez
Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells | Abstract | | We assess the accuracy and efficiency of several exponential time integration methods coupled to a spectral discretization of the three-dimensional
Boussinesq thermal convection equations in rotating spherical shells. Exponential methods are compared to implicit-explicit (IMEX) multi-step methods. The results of a wide range of numerical simulations highlight the superior accuracy of exponential methods for a given time step, especially when employed with large time steps and at low Ekman number. However, presently available implementations of exponential methods appear to be in general computationally more expensive than those of IMEX methods and further research is needed to reduce their computational cost per time step. A physically justified extrapolation argument suggests that some exponential methods could be the most
efficient option for integrating flows near Earth’s outer core conditions.
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35/2013 - 08/24/2013
Cattaneo, L.; Formaggia, L.; Iori G. F.; Scotti, A,; Zunino, P.
Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces | Abstract | | We address a two-phase Stokes problem, namely the coupling of two fluids with different kinematic viscosities.
The domain is crossed by an interface corresponding to the surface separating the two fluids.
We observe that the interface conditions allow the pressure and the velocity gradients to be discontinuous across the interface. The eXtended Finite Element Method is applied to accommodate the weak discontinuity of the velocity field across the interface and the jump in pressure on computational meshes that do not fit the interface. Numerical evidence shows that the discrete pressure approximation may be unstable in the neighborhood of the interface, even though the spatial approximation is based on inf-sup stable finite elements. It means that XFEM enrichment locally violates the satisfaction of the stability condition for mixed problems.
For this reason, resorting to pressure stabilization techniques in the region of elements cut by the unfitted interface is mandatory. In alternative, we consider the application of stabilized equal order pressure / velocity XFEM discretizations and we analyze their approximation properties. On one side, this strategy increases the flexibility on the choice of velocity and pressure approximation spaces. On the other side, symmetric pressure stabilization operators, such as local pressure projection methods or the Brezzi-Pitkaranta scheme, seem to be effective to cure the additional source of instability arising from the XFEM approximation. We will show that these operators can be applied either locally, namely only in proximity of the interface, or globally, that is on the whole domain when combined with equal order approximations. After analyzing the stability, approximation properties and the conditioning of the scheme, numerical results on benchmark cases will be discussed, in order to thoroughly compare the performance of different variants of the method. |
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34/2013 - 08/23/2013
Tavakoli, A.; Antonietti, P.F.; Verani, M.
Automatic computation of the impermeability of woven fabrics through image processing | Abstract | | The aim of this paper is to develop a new image-processing based
method to compute the impermeability of a given textile, and to propose a mathematical description
of the basic knitting procedures together with a mathematical
parametrization of the textile structures.
The method will be then coupled with a numerical strategy to compute
the micro-impermeability of a yarn with the aim of obtaining
a multi-scale algorithm that incorporates the effects of the yarn micro-impermeability into the
model computing the textile macro-impermeability. Several numerical experiments will
assess the validity of our image-processing based approach.
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33/2013 - 08/22/2013
Menafoglio, A; Guadagnini, A; Secchi, P
A Kriging Approach based on Aitchison Geometry for the Characterization of Particle-Size Curves in Heterogeneous Aquifers | Abstract | | We consider the problem of predicting the spatial field of particle-size curves (PSCs) from a sample observed at a finite set of locations within an alluvial aquifer near the city of T {u}bingen, Germany.
We interpret particle-size curves as cumulative distribution functions and their derivatives as probability density functions. We thus (a) embed the available data into an infinite-dimensional Hilbert Space of compositional functions endowed with the Aitchison geometry and (b) develop new geo-statistical methods for the analysis of spatially dependent functional compositional data. This approach enables one to provide predictions at unsampled locations for these types of data, which are commonly available in hydrogeological applications, together with a quantification of the associated uncertainty.
The proposed functional compositional kriging (FCK) predictor is tested on a one-dimensional application relying on a set of 60
particle-size curves collected along a 5-m deep borehole at the test site.
The quality of FCK predictions of PSCs is evaluated through leave-one-out cross-validation on the available data, smoothed by means of Bernstein Polynomials. A comparison of estimates of hydraulic conductivity obtained via our FCK approach against those rendered by classical kriging of effective particle diameters (i.e., quantiles of the PSCs) is provided. Unlike traditional approaches, our method fully exploits the functional form of particle-size curves and enables one to project the complete information content embedded in the PSC to unsampled locations in the system. |
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32/2013 - 08/16/2013
Taddei, T.; Perotto, S.; Quarteroni, A.
Reduced basis techniques for nonlinear conservation laws | Abstract | | In this paper we present a new reduced basis technique for parametrized nonlinear scalar conservation laws in presence of shocks. The essential ingredients are an efficient algorithm to approximate the shock curve, a procedure to detect the smooth components of the solution at the two sides of the shock, and a suitable interpolation strategy to reconstruct such
smooth components during the online stage. The approach we propose is based on some theoretical properties of the solution to the problem. Some
numerical examples prove the effectiveness of the proposed strategy. |
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31/2013 - 08/06/2013
Dassi, F.; Ettinger, B.; Perotto, S.; Sangalli, L.M.
A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain | Abstract | | We present a new mesh simplification technique developed for a statistical analysis of cortical surface data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution and such that the
statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data
on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a region in R2. Then, existing planar spatial smoothing techniques
are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data. |
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30/2013 - 07/04/2013
Cagnoni, D.; Agostini, F.; Christen, T.; de Falco, C.; Parolini, N.; Stefanovic, I.
Multiphysics simulation of corona discharge induced ionic wind | Abstract | | Ionic wind devices or electrostatic fluid accelerators are becoming of increasing interest as tools for thermal management, in particular for semiconductor devices. In this work, we present a numerical model for predicting the performance of such devices, whose main bene t is the ability to accurately predict the amount of charge injected at the corona electrode. Our multiphysics numerical model consists of a highly nonlinear strongly coupled set of PDEs including the Navier-Stokes equations for fluid flow, Poisson s equation for electrostatic potential, charge continuity and heat transfer equations. To solve this system we employ a staggered solution algorithm that generalizes Gummel s algorithm for charge transport in semiconductors. Predictions
of our simulations are validated by comparison with experimental measurements and are shown to closely match. Finally, our simulation tool is used to estimate the eff ectiveness of the design of an electrohydrodynamic cooling apparatus for power electronics applications. |
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29/2013 - 07/03/2013
Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.
Model order reduction in fluid dynamics: challenges and perspectives | Abstract | | This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration.
We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of
inf-sup stability, certification through error estimation, computational issues and - in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references. |
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