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 1152 products
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12/2009 - 04/06/2009
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 - 04/05/2009
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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10/2009 - 03/20/2009
Zunino, Paolo
Numerical approximation of incompressible flows with net flux defective boundary conditions by means of penalty techniques | Abstract | | We consider incompressible flow problems with defective boundary conditions prescribing only the net flux on some inflow and outflow sections of the boundary. As a pradigm for such problems, we simply refer to Stokes flow. After a brief review of the problem and of its well posedness, we discretize the corresponding variational formulation by means of finite elements and looking at the boundary conditions as constraints, we exploit a penalty method to account for them. We perform the analysis of the method in terms of consistency, boundedness and stability of the discrete bilinear form and we show that the application of the penalty method does not affect the optimal convergence properties of the finite element discretization.
Since the additional terms introduced to account for the defective boundary conditions are non local, we also analyze the spectral properties of the equivalent algebraic formulation and we exploit them to set up an efficient solution strategy. In contrast to alternative discretization methods based for instance on Lagrange multipliers accounting for the constraints on the boundary, the present scheme is particularly effective because it only mildly
affects the computational cost of the numerical approximation. Indeed, it does not require neither multipliers nor sub-iterations or additional adjoint problems with respect to the reference problem at hand. |
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09/2009 - 03/19/2009
Agostoni, Elio; Salsa, Sandro; Perego, Mauro; Veneziani, Alessandro
Mathematical and numerical Modeling of Focal Cerebral Ischemia | Abstract | | Cerebral focal ischemia is a local degeneration of brain tissue induced by a reduction of blood supply. We introduce a mathematical model that
includes the blood dynamics, represented by a
ow in a porous medium and ion dynamics (calcium and potassium), together with other variables (energy stores, tissue integrity, oxygen and glucose) representing the biochemical events consequent to the vessel occlusion. The accurate description of the coupling between fuid dynamics and Biochemics is one of the distinctive features of the present work. We present both 2D and 3D simulations.
Occurrence of peculiar ion dynamics, called spreading depression waves, formerly pointed out in the literature, is observed in 2D results. The role of some parameters of the problem in suppressing these waves is discussed.
We moreover simulate in 3D the e ects of a forced reperfusion of the occluded vessel ( brinolysis) and the consequent blood leakage (hemorrhagic
infarct).
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08/2009 - 03/16/2009
Antonietti, Paola F.; Houston, Paul
An hr-adaptive discontinuous Galerkin method for advection-diffusion problems | Abstract | | We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation.
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07/2009 - 02/16/2009
Perego, Mauro; Veneziani, Alessandro
An efficient generalization of the Rush-Larsen method for solving electro-physiology membrane equations | Abstract | | In this paper we address a second-order class of methods for solving ordinary differential systems coming from some problems in electro-physiology.
The set of methods generalizes to the second order a previous proposal by Rush and Larsen (1978). We prove that the methods are second-order
convergent and are in general more stable than the corresponding multistep methods. Moreover, they feature better positivity properties. We
present their time-adaptive formulation, which is well suited for our electrophysiology problems. In particular, numerical results are presented on the Monodomain model coupled to Luo-Rudy I ionic models for the propagation of the cardiac potential.
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06/2009 - 02/15/2009
Formaggia, Luca; Veneziani, Alessandro; Vergara, Christian
Numerical solution of flow rate boundary problems for an incompressible fluid in deformable domains | Abstract | | In this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain. As well known, in this case there is the problem of prescribing realistic boundary data on the artificial sections, when only partial data are available. This problem has been investigated extensively for the rigid case. In this work we start considering the compliant case, by focusing on the flow rate conditions for the fluid. We propose three formulations of this problem, different algorithms for its numerical solution and carry out several 2D numerical simulations with the aim of comparing the performances of the different algorithms.
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05/2009 - 02/14/2009
Ieva, Francesca; Paganoni, Anna Maria
A case study on treatment times in patients with ST-Segment Elevation Myocardial Infarction | Abstract | | In this paper we conduct a statistical analysis of data coming from an observational case study about patients with ST-Segment Elevation Acute
Myocardial Infarction treated in one of the 23 hospitals of the Milano net-work for acute coronary syndromes and emergency services. The principal aim of this article is to identify from a statistical perspective the most important prognostic factors for in-hospital survival and reperfusion efficacy. We model the dependency between outcome variables and predictors
with Generalized Additive Models. These statistical analyses have demonstrated the clinical guess that an early pre-alarm of the Emergency Room is an essential step to improve the clinical treatment of patients. |
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