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 1239 products
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25/2018 - 04/24/2018
Chave, F.; Di Pietro, D.A.; Formaggia, L.
A Hybrid High-Order method for passive transport in fractured porous media | Abstract | | In this work, we propose a model for the passive transport of a solute in a fractured porous medium, for which we develop a Hybrid High-Order (HHO) space discretization. We consider, for the sake of simplicity, the case where the flow problem is fully decoupled from the transport problem. The novel transmission conditions in our model mimic at the discrete level the property that the advection terms do not contribute to the energy balance. This choice enables us to handle the case where the concentration of the solute jumps across the fracture. The HHO discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture for the flow problem, and on a primal formulation both in the bulk region and inside the fracture for the transport problem. Relevant features of the method include the treatment of nonconforming discretizations of the fracture, as well as the support of arbitrary approximation orders on fairly general meshes. |
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24/2018 - 04/13/2018
Bassi, C.; Abbà, A.; Bonaventura,L.; Valdettaro,L.
Direct and Large Eddy Simulation of three-dimensional non-Boussinesq gravity currents with a high order DG method | Abstract | | We present results of three-dimensional Direct Numerical Simulations
(DNS) and Large Eddy Simulations (LES) of turbulent
gravity currents with a Discontinuous Galerkin (DG) Finite Elements
method. In particular, we consider the three-dimensional
lock-exchange test case as a typical benchmark for gravity currents.
Since, to the best of our knowledge, non-Boussinesq threedimensional
reference DNS are not available in the literature for
this test case, we first perform a DNS experiment. The threedimensional
DNS allows to correctly capture the loss of coherence
of the three-dimensional turbulent structures, providing an accurate
description of the turbulent phenomena taking place in gravity currents.
The three-dimensional DNS is then employed to assess the
performance of di?erent LES models. In particular, we have considered
the Smagorinsky model, the isotropic dynamic model and
an anisotropic dynamic model. The LES results highlight the excessively
dissipative nature of the Smagorinsky model with respect
to the dynamic models and the fact that the anisotropic dynamic
model performs slightly better with respect to its isotropic counterpart. |
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23/2018 - 04/10/2018
Benacchio, T.;Bonaventura,L.
A seamless extension of DG methods for hyperbolic problems to unbounded domains | Abstract | | We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong collocation formulations, nodal and modal weak formulations, with either inflow or outflow boundary conditions, using either Gauss - Laguerre or Gauss - Laguerre - Radau quadrature nodes and based on either scaled Laguerre functions or scaled Laguerre polynomials. We show that some of these combinations give rise to intrinsically unstable schemes, while the combination of scaled Laguerre functions with Gauss - Laguerre - Radau nodes appears to be stable for both strong and weak formulations. We then show how a modal discretization approach for hyperbolic systems on an unbounded domain can be naturally and seamlessly coupled to a discontinuous finite element discretization on a finite domain. Examples of one dimensional hyperbolic systems are solved with the proposed domain decomposition technique. The errors obtained with the proposed approach are found to be small, enabling the use of the coupled scheme for the simulation of Rayleigh damping layers in the semi-infinite part. Energy errors and reflection ratios of the scheme in absorbing
wavetrains and single Gaussian signals show that a small number of nodes in the semi-infinite domain are sufficient to damp the waves. The theoretical insight and numerical results corroborate previous findings by the authors and establish the scaled Laguerre functions-based discretization as a flexible and efficient tool for absorbing layers as well as for the accurate simulation of waves in unbounded regions. |
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22/2018 - 04/10/2018
Pegolotti, L.; Dede', L.; Quarteroni, A.
Isogeometric Analysis of the electrophysiology in the human heart: numerical simulation of the bidomain equations on the atria | Abstract | | We consider Isogeometric Analysis (IGA) for the numerical solution of the electrophysiology of the atria, which in this work is modeled by means of the bidomain equations on thin surfaces. First, we consider the bidomain equations coupled with the Roger-McCulloch ionic model on simple slabs. Here, our goal is to evaluate the effects of the spatial discretization by IGA and the use of different B-spline basis functions on the accuracy of the approximation, in particular regarding the accuracy of the front
velocity and the dispersion error. Specifically, we consider basis functions with high polynomial degree, p, and global high order continuity, Cp?1, in the computational domain: our results show that the use of such basis functions is beneficial to the accurate approximation of the solution. Then, we consider a realistic application of the bidomain equations coupled with the Courtemanche-Ramirez-Nattel ionic model on the two human atria, which are represented by means of two NURBS surfaces. |
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21/2018 - 04/10/2018
Gervasio, P.; Dede', L.; Chanon, O.; Quarteroni, A.
Comparing Isogeometric Analysis and Spectral Element Methods: accuracy and spectral properties | Abstract | | In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods (SEM) and NURBS-based Isogeometric Analysis (IGA) in the framework of the Galerkin method for the approximation of the Poisson problem. Our focus is on their convergence properties, the algebraic structure and the spectral properties of the corresponding discrete arrays (mass and stiffness matrices). We review the available theoretical results for these methods and verify them numerically by performing error analysis on the solution of the Poisson problem. Where theory is lacking, we use numerical investigation of the results to draw conjectures on the behavior of the corresponding theoretical laws in terms of the design parameters, such as the (mesh) element size, the local polynomial degree, the smoothness of the NURBS basis functions, the space dimension, and the total number of degrees of freedom involved in the computations. |
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20/2018 - 03/25/2018
Bassi, C. ; Abbà, A.; Bonaventura L.; Valdettaro, L.
A priori tests of a novel LES approach to compressible variable density turbulence | Abstract | | We assess the viability of a recently proposed novel approach to LES for compressible variable density flows by means of a priori tests. The a priori tests have been carried out filtering a two-dimensional
DNS database of the classic lock-exchange benchmark. The tests confirm that additional terms should be accounted for in subgrid scale modeling of variable density flows, with respect to the terms usually considered in the traditional approach. Several alternatives for the modeling of these terms are assessed and discussed. |
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19/2018 - 03/01/2018
Menghini, F.; Dede', L.; Quarteroni, A.
Variational Multiscale LES modeling of blood flow in an idealized left human heart | Abstract | | In this work we build a realistic, although idealized, computational model of the left human heart for the study of the blood flow dynamics. We prescribe the left heart wall displacement based on physiological data and we take into account the presence of both the mitral and aortic valves through a resistive method. We simulate the left heart hemodynamics by means of the Finite Element method and compare different numerical stabilization techniques to account for the transitional and nearly turbulent nature of the blood flow in a physiological regime. In particular, we apply a Variational Multiscale Large Eddy Simulation (LES) model and a Streamwise Upwind Petrov-Galerkin method and we critically analyze the corresponding numerical results. |
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18/2018 - 02/26/2018
Antonietti, P.F.; Bonaldi, F.; Mazzieri, I.
A high-order discontinuous Galerkin approach to the elasto-acoustic problem | Abstract | | We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid (elastic) domain and the fluid (acoustic) domain. We state and prove a well-posedness result for the strong formulation of the problem, present a stability analysis for the semi-discrete formulation, and finally prove an a priori hp-version error estimate for the resulting formulation in a suitable (mesh-dependent) energy norm. The conver- gence results are validated by numerical experiments carried out in a two-dimensional setting. |
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