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 1312 prodotti
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59/2024 - 07/09/2024
Carbonaro, D.; Ferro, N.; Mezzadri, F.; Gallo, D.; Audenino, A.; Perotto, S.; Morbiducci, U.; Chiastra, C.
Easy-to-use formulations based on the homogenization theory for vascular stent design and mechanical characterization | Abstract | | Vascular stents are scaffolding structures implanted in the vessels of patients with obstructive disease. Stents are typically designed as cylindrical lattice structures characterized by the periodic repetition of unit cells. Their design, including geometry and material characteristics, influences their mechanical performance and, consequently, the clinical outcomes. Computational Optimization frameworks have proven to be effective in assisting the design phase of vascular stents, facilitating the achievement of enhanced mechanical performances. However,
the reliance on time-consuming simulations and the challenge of automating the design process limit the number of design evaluations and reduce Optimization efficiency. In this context, a rapid and automated method for the mechanical characterization of vascular stents is presented, taking the stent geometry, conceived as the periodic repetition of a unit cell, and material as input and providing the mechanical response of the stent as output.
Vascular stents were assumed to be thin-walled hollow cylinders sharing the same macroscopic geometrical characteristics as the cylindrical lattice structure but composed of an anisotropic homogenized material. Homogenization theory was applied to average the microscopic inhomogeneities at the stent unit cell level into a homogenized material at the macroscale, enabling the calculation of the associated homogenized material tensor. Analytical formulations were derived to relate the stent mechanical behavior to the homogenized stiffness tensor, considering linear elastic theory for thin-walled hollow cylinders and three loading scenarios of relevance for vascular stents: radial crimping; axial traction; torsion. Validation was conducted by
comparing the derived analytical formulations with results obtained from finite element analyses on typical stent designs.
Homogenized stiffness tensors were computed for the unit cells of three stent designs, revealing insights into their mechanical performance, including whether they exhibit auxetic behavior. The derived analytical formulations were successfully validated with finite element analyses, yielding low relative differences in the computed values of foreshortening, radial, axial and torsional stiffnesses for all three stents.
The proposed method offers a rapid, fully automated procedure that facilitates the assessment of the mechanical behavior of vascular stents and is suitable for effective integration into computational optimization frameworks. |
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60/2024 - 07/09/2024
Temellini, E.; Ferro, N.; Stabile, G.; Delgado Avila, E.; Chacon Rebollo, T.; Perotto, S.
Space - time mesh adaptation for the VMS - Smagorinsky modeling of high Reynolds number flows | Abstract | | Traditional methods, such as Reynolds-Averaged Navier-Stokes (RANS) equations and Large Eddy Simulations (LES), provide consolidated tools for the numerical approximation of high Reynolds number flows in a wide range of applications - from green energy to industrial design. In general, RANS modeling is practical when the main interest is the time-averaged flow behavior. LES equations offer detailed insights into flow dynamics and a more accurate solution, but the high computational demand necessitates innovative strategies to reduce costs while maintaining precision. In this study, we enhance the Variational MultiScale (VMS)-Smagorinsky LES model by relying on an adaptive discretization strategy in both space and time, driven by a recovery-based a posteriori error analysis. We assess the effectiveness of the approach in capturing flow characteristics across a wide range of Reynolds numbers through benchmark tests. |
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61/2024 - 07/09/2024
Speroni, G.; Ferro, N.
A novel metric - based mesh adaptation algorithm for 3D periodic domains | Abstract | | We present a novel metric-based mesh adaptation algorithm, named 3DPAMA, to be employed for discretization of three-dimensional periodic domains. The proposed method - based on mathematically rigorous assumptions - utilizes established techniques for unconstrained mesh adaptation and resorts to localized manipulations on the external boundary of the mesh. In particular, the scheme comprises four steps: (i) a non-periodic initial mesh adaptation, (ii) the splitting of the obtained volumetric grid into interior and exterior tessellations, (iii) minimal local operations to yield a periodic external surface, and (iv) the assembly of the final adapted grids. To demonstrate the robustness, efficacy, and flexibility of the proposed methodology, 3DPAMA algorithm is employed in a continuous finite element setting to tackle test cases established in the literature as well as challenging scenarios that involve various periodic requirements, domain geometries, and metric fields. Finally, 3DPAMA is employed in a practical use case where mesh adaptation is tightly coupled with the solution of a time-dependent partial differential equation. |
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58/2024 - 03/09/2024
Ciaramella, G.; Vanzan, T.
Variable reduction as a nonlinear preconditioning approach for optimization problems | Abstract | | When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear elimination could be used to reduce the number of optimization variables by artificially constraining them to satisfy a subset of the optimality conditions. Consequently, a reduced objective function is derived which can now be minimized with any optimization algorithm. By choosing suitable variables to eliminate, the conditioning of the reduced optimization problem is largely improved. We here focus in particular on a right preconditioned gradient descent and show theoretical and numerical results supporting the validity of the presented approach. |
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56/2024 - 02/09/2024
Parolini, N.; Covello, V.; Della Rocca, A.; Verani, M.,
Design of a checkerboard counterflow heat exchanger for industrial applications | Abstract | | This work is devoted to the design of a checkerboard air-gas heat exchanger suitable for industrial applications. The design of the heat exchanger is optimized in order to obtain the maximum increase of the outlet air temperature, considering different geometrical design parameters and including manufacturing constraints. The heat exchanger efficiency has been assessed by means of the $epsilon$-NTU method. The perfomances are compared with traditional finned recuperators and appreciable enhancement of the exchanger efficiency has been observed adopting the new design. |
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57/2024 - 02/09/2024
Negrini, G.: Parolini, N.; Verani, M.
An Immersed Boundary Method for Polymeric Continuous Mixing | Abstract | | We introduce a new implementation of the Immersed Boundary method in the finite-volume library OpenFOAM. The implementation is tailored to the simulation of temperature-dependent non-Newtonian polymeric flows in complex moving geometries, such as those characterizing the most popular polymeric mixing technologies. |
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55/2024 - 01/09/2024
Artoni, A.; Ciaramella, G.; Gander, M.J.; Mazzieri, I.
Schwarz Waveform Relaxation and the Unmapped Tent-Pitching Method in 3D | Abstract | | Several Parallel-in-Time (PinT) algorithms, especially multilevel methods like Parareal and MGRIT, struggle when applied to hyperbolic partial differential equations. There are however also very effective PinT methods for hyperbolic problems which use the hyperbolic nature of the problem to their advantage. Typical examples are Schwarz Waveform Relaxation methods, and the Mapped and Unmapped Tent Pitching methods. We present and study here for the first time the Unmapped Tent Pitching method in three spatial dimensions, applied to a second order wave equation. We give a general equivalence result with the Mapped Tent Pitching algorithm using Schwarz Waveform Relaxation to build the link, and also characterize in detail the resulting 4D space-time tents generated implicitly by the Unmapped Tent Pitching method. This leads to a complete convergence analysis of the method in 3D. |
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54/2024 - 14/08/2024
Antonietti, P.F.; Botti, M.; Cancrini, A.; Mazzieri, I.
A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem | Abstract | | This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest in non-Newtonian flows and coupled interface problems, where stress assumes a fundamental role.
The space-time discretization of the problem is achieved by combining the PolydG approach with the implicit theta-method time integration scheme. For both the semi- and fully-discrete problems we present a detailed stability analysis. Moreover, we derive convergence estimates for the fully discrete space-time discretization. A set of verification tests is presented to verify the theoretical estimates and the application of the method to cases of engineering interest. |
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