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 1249 products
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56/2016 - 12/24/2016
Guerciotti, B.; Vergara, C.; Ippolito, S.; Quarteroni, A.; Antona, C.; Scrofani, R.
A computational fluid-structure interaction analysis of coronary Y-grafts | Abstract | | Coronary artery disease is one of the leading causes of death worldwide. The stenotic coronary vessels are generally treated with coronary artery bypass grafts (CABG), which can be either arterial (internal mammary
artery, radial artery) or venous (saphenous vein). However, the different
mechanical properties of the graft can influence the outcome of the procedure in terms of risk of restenosis and subsequent graft failure. In this paper, we perform a computational fluid-structure interaction (FSI) analysis of patient-specific multiple CABGs (Y-grafts) with the aim of better understanding the influence of the choice of bypass (arterial vs venous) on the risk of graft failure. Our results show that the use of a venous bypass results in a more disturbed flow field at the anastomosis and in higher stresses in the vessel wall with respect to the arterial one. This could explain the better long-term patency of the arterial bypasses experienced in the clinical practice. |
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55/2016 - 12/15/2016
Antonietti, P. F.; Facciola' C.; Russo A.; Verani M.;
Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids | Abstract | | We present a numerical approximation of Darcy's flow through
a fractured porous medium which employs discontinuous Galerkin
methods on polytopic grids. For simplicity, we analyze the case of a
single fracture represented by a (d-1)-dimensional interface between
two d-dimensional subdomains, d = 2; 3. We propose a discontinuous
Galerkin finite element approximation for the
flow in the porous matrix which is coupled with a conforming finite element scheme for the flow in the fracture. Suitable (physically consistent) coupling conditions complete the model. We theoretically analyse the resulting formulation, prove its well-posedness, and derive optimal a priori error estimates in a suitable (mesh-dependent) energy norm. Two-dimensional numerical experiments are reported to assess the theoretical results. |
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54/2016 - 12/13/2016
Vergara, C.; Le Van, D.; Quadrio, M.; Formaggia, L.; Domanin, M.
Large Eddy Simulations of blood dynamics in abdominal aortic aneurysms | Abstract | | In this work we address the study of transition to turbulence effects
in abdominal aortic aneurysms (AAA). The formation of transitional ef-
fects in such districts is caused by the heart pulsatility and the sudden
change of diameter, and has been recorded by means of clinical measures
and computational studies. Here we propose, for the first time, the use
of a large eddy simulation (LES) model to describe transition to turbu-
lence in realistic scenarios of AAA obtained from radiological images. To
this aim, we post-process the obtained numerical solutions to produce sig-
nificant quantities, such as the ensemble-averaged velocity and wall shear
stress, the standard deviation of the velocity field, the Q-criterion. The
results show the suitability of the considered LES model and the presence
of significant transitional effects during the mid-deceleration phase around the impingement region.
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53/2016 - 12/07/2016
Antonietti, P. F.; Manzini, G.; Verani, M.
The fully nonconforming Virtual Element method for biharmonic problems | Abstract | | In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbi- trary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numer- ical results to assess the validity of the theoretical estimates. |
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52/2016 - 12/07/2016
Paolucci, R.; Evangelista, L.; Mazzieri, I.; Schiappapietra, E.
The 3D Numerical Simulation of Near-Source Ground Motion during the Marsica Earthquake, Central Italy, 100 years later | Abstract | | In this paper we show 3D physics-based numerical simulations of ground motion during one of the most devastating earthquakes in the recent Italian history, occurred on Jan 13, 1915, Marsica, Central Italy. The results provide a realistic estimate of the earthquake ground motion and fit reasonably well both the geodetic measurements of permanent ground settlement, and the observed macroseismic distribution of damage. In addition, these results provide a very useful benchmark to improve the current knowledge of near-source earthquake ground motion, including evaluation of the best distance metrics to describe the spatial variability of the peak values of ground motion, the relative importance of fault normal vs fault parallel components, the conditions under which vertical ground motion may prevail, as well as the adequacy of 1D vs 3D modelling of site amplification effects. |
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51/2016 - 12/04/2016
Guzzetti, S.; Perotto, S.; Veneziani, A.
Hierarchical Model Reduction for Incompressible Flows in Cylindrical Domains: The Axisymmetric Case | Abstract | | Hierarchical Model (HiMod) Reduction provides an efficient way to solve Partial Differential Equations in domains with a geometrically dominant direction, like slabs or pipes. The associated solution is regarded as the combination of mainstream dynamics driven by the geometry and trans- verse components. The latter are generally of secondary importance so to be described by few degrees of freedom of a spectral approximation in- troduced at the top of a finite element discretization of the mainstream. Thus, the 3D nature of the problem is broken into a basically 1D descrip- tion added by transverse details. The versatility of this approach is that the accuracy of the method can be adaptively refined when needed, by judi- ciously selecting the number of transverse modes - as opposed to purely 1D models popular in computational hemodynamics and gasdynamics. After having investigated the basic features of the method in slab-like domains - where the Cartesian tensor product framework facilitates the practical implementation, in this paper we consider cylindrical pipes with polar co- ordinates. The selection of a different coordinate system rises several issues in particular for the most appropriate selection of the modal basis func- tions. Having computational hemodynamics as reference application, we address here the HiMod approximation of Advection-Diffusion-Reaction as well as Incompressible Navier-Stokes equations in axisymmetric domains. |
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50/2016 - 11/23/2016
Ambrosi, D.; Pezzuto, S.; Riccobelli, D.; Stylianopoulos, T.; Ciarletta, P.
Solid tumors are poroelastic solids with a chemo--mechanical feedback on growth | Abstract | | The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties
(the ``constitutive equations'') of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the ``growth law'') that relates stress and mitotic--apoptotic rate is far to be identified.
We address these questions on the basis of a theoretical analysis of in vitro and in vivo experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression. Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern. By a novel numerical approach we correlate the measured opening angle and the underlying residual stress in a sphere. The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.
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49/2016 - 11/23/2016
Formaggia, L.; Scotti, A.; Sottocasa, F.
ANALYSIS OF A MIMETIC FINITE DIFFERENCE APPROXIMATION OF FLOWS IN FRACTURED POROUS MEDIA | Abstract | | We consider the mixed formulation for Darcy’s flow in fractured media. We give a well-posedness result that does not rely on the imposition of pressure in part of the boundary of the fracture network, thus including a fully immersed fracture network. We present and analyze a mimetic finite difference formulation for the problem, providing convergence results and numerical tests. |
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