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 1238 prodotti
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18/2009 - 23/07/2009
Silva Soares, Joao; Zunino, Paolo
A mathematical model for water uptake, degradation, erosion and drug release from degradable polydisperse polymeric networks | Abstract | | We introduce a general class of mixture models to study water uptake, degradation, erosion, and drug release from degradable polydisperse polymeric matrices.
The mathematical model is based on a finite number of constituents describing the polydisperse polymeric system, i.e. each representing collection of chains whose size
belongs to a finite interval of degree of polymerization. In order to model water uptake
and drug release, two additional constituents (water and drug) constitute the mixture.
Constituents diffuse individually accordingly to Fick’s first law and balances of mass of constituents yield partial differential equations that govern the reaction-diffusion system. Hydrolysis, a chemical reaction that breaks down larger chains into smaller ones, is accounted with reactions terms quantifying sources and sinks of polymeric chains and a sink of water. Hydrolysis couples the system of equations and nonlinearities appear through constitutive specification of the diffusivities of constituents on the current network, reaction rates, and boundary conditions.
The mathematical model is independent of the number of constituents describing the polydisperse polymeric system and hydrolysis kinetics describe with accuracy the overall decrease in molecular weight distribution and satisfies a monomer conservation principle. A shift between two different types of solutions of the system of partial differential equations, each identified to surface or bulk erosion, is obtained with the variation of a single non-dimensional number, the Thiele modulus, which measures the relative importance of the mechanisms of reaction and diffusion. Results of drug release confirm that drug release from bulk eroding matrices is diffusion-controlled, whereas for surface eroding polymers, drug release is enhanced in an erosion-controlled process. |
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17/2009 - 18/06/2009
Longoni, Matteo; Magistroni, Corrado; Ruffo, Paolo; Scrofani, Giovanni
3D Inverse and Direct Structural modeling Workflow | Abstract | | The description and the interpretation of the geological evolution of sedimentary basins has recently received a great support from the use of
mathematical models and numerical methods, taking advantage of more advanced hardware, both in graphic and computing power. We have developed a geological modeling workflow, based on gOcad, for the 3D inverse and direct structural modeling of sedimentary basins. The workflow is based on an appropriate number of time-steps of restoration modeling coupled with forward/evolution modeling. During each step a gOcad geological model provides support for data managing, pre- and post-processing for numerical solvers and the necessary interpretative model editing.
The capability of capturing and describing all the geometrical and structural features of an accurate geological model, leads to remarkable results in integrating available data, in validating restoration models and in reconstructing a reliable evolution of a basin.
The model is built with gOcad, starting from the basin geometrical data. Topological complexities such as faulted stratified layers and salt
diapirs are easily handled in a three-dimensional unstructured framework.
Then the geometrical model is enriched with its physical properties, coming from seismic, well and field data and from the modeller conceptual model. The domain is then described with a user-defined tetrahedral mesh, necessary for the numerical simulation of its geological evolution. The output results, for example the updated position of horizon and fault surfaces, and
the distributions in the domain of physical quantities such as stresses and displacements, are then imported in gOcad by means of a fully-automatic procedure, for data visualization and analysis. The workflow can be iterated starting from the last updated configuration.
We present the application of the workflow to the simulation of the dynamic structural evolution in two realistic cases: a multi-faulted system
and a diapir growth in a multi-layered sedimentary basin.
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16/2009 - 20/05/2009
Aletti, Giacomo; May, Caterina; Secchi, Piercesare
A functional equation whose unknown is P ([0, 1]) valued | Abstract | | We study a functional equation whose unknown maps a euclidean space into the space of probability distributions on [0,1].
We prove existence and uniqueness of its solution under suitable regularity and boundary conditions and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means
of a Randomly Reinforced Urn with different reinforcement distributions having equal means. |
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15/2009 - 07/05/2009
Perotto, Simona; Ern, Alexandre; Veneziani, Alessandro
Hierarchical local model reduction for elliptic problems I: a domain decomposition approach | Abstract | | Some engineering applications, for instance related to fluid dynamics in pipe or channel networks, feature a dominant spatial direction along which the most relevant dynamics develop. Nevertheless, local features of the problem depending on the other directions, that we call transverse, can be locally relevant to the whole problem. We propose in the context of ellip-
tic problems such as advection–diffusion–reaction equations, a hierarchical model reduction approach in which a coarse model featuring only the dominant direction dynamics is enriched locally by a fine model that accounts for the transverse variables via an appropriate modal expansion. We introduce a domain decomposition approach allowing us to employ a different
number of modal functions in different parts of the domain according to the local complexity of the problem at hand. The methodology is investigated numerically on several test cases. |
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14/2009 - 08/04/2009
Beirao da Veiga, Lourenco; Verani, Marco
A posteriori boundary control for FEM approximation of elliptic eigenvalue problems | Abstract | | We derive new a posteriori error estimates for the nite element solution of an elliptic eigenvalue problem, which take into account also the e ects of the polygonal approximation of the domain. This suggests local error indicators that can be used to drive a procedure handling the mesh re nement together with the approximation of the domain. |
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13/2009 - 07/04/2009
Miglio, Edie; Villa, Andrea
A mathematical derivation of compaction and basin models | Abstract | | In this paper we develop a theoretical and numerical model for the simulation of both the structural evolution and pore pressure evolution of a sedimentary basin. We use the volume averaging technique in order to get a complete macroscopical physical model and we introduce two different formulations of it. The relations with existing compaction and basin scale models are discussed. Then we introduce a temporal time-splitting scheme and study the existence and uniqueness of the solution of the semi discrete problem. We show the robustness of our scheme in a couple of one dimensional cases with smooth and non-smooth variations of the physical coefficients.
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¤ENI - Steam3D
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12/2009 - 06/04/2009
Badia, Santiago; Quaini, Annalisa; Quarteroni, Alfio
Coupling Biot and Navier-Stokes equations for modeling fluid-poroelastic media intercation | Abstract | | The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations with the Biot system.
The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design
residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier-Stokes/Biot system with the appropriate transmission conditions at the
interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it
happens in hemodynamics applications. |
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11/2009 - 05/04/2009
Formaggia, Luca; Villa, Andrea
Implicit tracking for multi-fluid simulations | Abstract | | In this work a new coupled level set - volume tracking method is introduced. To advance the solution in time, a MUSCL-type method combined
to a new °ux limiter is used. It is shown that our discrete method has many interesting properties that make it suitable for problems where the tracking of a large number of regions is needed. A dedicated reconstruction
algorithm for the level set reinizialization is also provided. We show some numerical tests demonstrating its effectiveness for multi-°uid problems. |
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