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 1287 products
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58/2018 - 11/13/2018
Ferro, N.; Micheletti, S.; Perotto, S.
A sequential coupling of shape and topology optimization for structural design | Abstract | | We consider different algorithms to design lightweight and stiff structures exhibiting free-form features. First we apply a shape optimization and a topology optimization procedure, separately. Then, we couple these two techniques sequentially. Topology optimization is also enhanced by a structure-tailored computational mesh, made it possible by anisotropic mesh adaptation. This allows us to obtain an intrinsically smooth final layout which can be directly moved on to the production manufacturing phase. An extensive numerical assessment corroborates both qualitatively and quantitatively the performances of the proposed algorithms. |
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57/2018 - 11/13/2018
Ferro, N.; Micheletti, S.; Perotto, S.
POD-assisted strategies for structural topology optimization | Abstract | | We propose a new numerical tool for structural optimization design. To cut down the computational burden typical of the Solid Isotropic Material with Penalization method, we apply Proper Orthogonal Decomposition on SIMP snapshots computed on a fixed grid to construct a rough structure (predictor) which becomes the input of a SIMP procedure performed on an anisotropic adapted mesh (corrector). The benefit of the proposed design tool is to deliver smooth and sharp layouts which require a contained computational effort before moving to the 3D printing production phase. |
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56/2018 - 11/13/2018
Antonietti, P.F.; Manzini, G.; Verani, M.
The conforming virtual element method for polyharmonic problems | Abstract | | In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $Delta^p u =f$, $pge1$. More specifically, we develop and analyze the conforming virtual element method for the numerical approximation of polyharmonic boundary value problems, and prove an abstract result that states the convergence of the method in the energy norm. |
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55/2018 - 10/30/2018
Cerroni, D.; Laurino, F.; Zunino, P.
Mathematical analysis, finite element approximation and numerical solvers for the interaction of 3D reservoirs with 1D wells | Abstract | | We develop a mathematical model for the interaction of a three-dimensional reservoir with the flow through wells, namely narrow cylindrical channels cutting across the reservoir. Leak off or sink effects are taken into account. To enable the simulation of complex configurations featuring multiple wells, we apply a model reduction technique that represents the wells as one-dimensional channels. The challenge in this case is to account for the interaction of the reservoir with the embedded one- dimensional wells. The resulting problem consists of coupled partial differential equations defined on manifolds with heterogeneous dimensionality. The existence and regularity of weak solutions of such problem is thoroughly addressed. Afterwards, we focus on the numerical discretization of the problem in the framework of the finite element method. We notice that the numerical scheme does not require conformity between the computational mesh of the reservoir and the one of the wells. From the standpoint of the solvers, we discuss the application of multilevel algorithms, such as the algebraic multigrid method. Finally, the reduced mathematical model and the discretization method is applied to a few configurations of reservoir with wells, with the purpose of verifying the theoretical properties and to assess the generality of the approach. |
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54/2018 - 10/30/2018
Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.
Multi space reduced basis preconditioners for parametrized Stokes equations | Abstract | | We introduce a two-level preconditioner for the efficient solution of large scale saddle-point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (MSRB) preconditioning method proposed in [Dal Santo et al., 2018]; it combines an approximated block (fine grid) preconditioner with a reduced basis (RB) solver which plays the role of coarse component. A sequence of RB spaces, constructed either with an enriched velocity formulation or a Petrov-Galerkin projection, is built. Each RB coarse component is defined to perform a single iteration of the iterative method at hand. The flexible GMRES (FGMRES) algorithm is employed to solve the resulting preconditioned system and targets small tolerances with a very small iteration count and in a very short time. Numerical test cases for Stokes flows in three dimensional parameter-dependent geometries are considered to assess the numerical properties of the proposed technique in different large scale computational settings. |
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53/2018 - 10/30/2018
Giantesio, G.; Musesti, A.; Riccobelli, D.
A comparison between active strain and active stress in transversely isotropic hyperelastic materials | Abstract | | Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an additive stress P_act in the active stress case and a multiplicative strain F_a in the active strain one. Aim of this paper is the comparison between the two approaches on simple shears.
Considering an incompressible and transversely isotropic material, we design constitutive relations for P_act and F_a so that they produce the same results for a uniaxial deformation along the symmetry axis. We then study the two approaches in the case of a simple shear deformation. In a hyperelastic setting, we show that the two approaches produce different stress components along a simple shear, unless some necessary conditions on the strain energy density are fulfilled. However, such conditions are very restrictive and rule out the usual elastic strain energy functionals. Active stress and active strain therefore produce different results in shear, even if they both fit uniaxial data.
Our results show that experimental data on the stress-stretch response on uniaxial deformations are not enough to establish which activation approach can capture better the mechanics of active materials. We conclude that other types of deformations, beyond the uniaxial one, should be taken into consideration in the modeling of such materials. |
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52/2018 - 10/30/2018
Possenti, L.; di Gregorio, S.; Gerosa, F.M.; Raimondi, G.; Casagrande, G.; Costantino, M.L.; Zunino, P.
A computational model for microcirculation including Fahraeus-Lindqvist effect, plasma skimming and fluid exchange with the tissue interstitium | Abstract | | We present a two phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one-dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus-Lindqvist, plasma skimming and capillary leakage effects on the distribution of flow in a microvascular network. |
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51/2018 - 10/29/2018
Stella, S.; Vergara, C.; Giovannacci, L.; Quarteroni, A.; Prouse, G.
Assessing the disturbed flow and the transition to turbulence in the arteriovenous fistula | Abstract | | The arteriovenous fistula (AVF) is the main form of vascular access for
hemodialysis patients, but its maintenance is very challenging. Its failure
is mainly related to intimal hyperplasia, leading to stenosis.
The aim of this work is twofold: i) to perform a computational study for
the comparison of the disturbed blood dynamics in different configurations
of AVF and ii) to assess the amount of turbulence developed by the specific
geometric configuration of AVF.
To this aim, we reconstructed realistic 3D geometries of two patients
with a side-to-end AVF, performing a parametric study by changing the
angle of incidence at the anastomosis. We solved the incompressible Navier-
Stokes equations modeling the blood as an incompressible and Newtonian
fluid. Large Eddy Simulations (LES) were considered to capture the tran-
sition to turbulence developed at the anastomosis. The values of prescribed
boundary conditions are obtained from clinical Echo-Color Doppler mea-
surements.
To assess the disturbed flow, we considered hemodynamic quantities
such as the velocity field, the pressure distribution, and wall shear stresses derived quantities, whereas to quantify the transition to turbulence, we computed the standard deviation of the velocity field among different heartbeates and the turbulent kinetic energy.
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