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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27/2018 - 04/24/2018
Antonietti, P.F.; Verani, M.; Vergara, C.; Zonca, S.
Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids
| Abstract | | We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes.
In particular, we consider a method where the fluid mesh is on the background and fixed, apart at the interface with the moving immersed structure, that cuts the fluid mesh elements generating polygons of arbitrary shape. The new idea of this work is to handle the discretization on such polygons by using the Discontinuous Galerkin method on polyhedral grids (PolyDG), which has been recently developed for different differential equations and here adapted for the first time to an heterogeneous problem. We prove a stability result of the proposed semi-discrete formulation and discuss how to deal with the partial or total covering of a fluid mesh element due to the structure movement.
We finally present some numerical results with the aim of showing the effectiveness of the proposed method. |
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26/2018 - 04/24/2018
Vergara, C.; Zonca, S.
Extended Finite Elements method for fluid-structure interaction with an immersed thick non-linear structure | Abstract | | We consider an Extended Finite Element method to
solve fluid-structure interaction problems in the case of an immersed thick
structure described by non-linear finite elasticity. This method, that belongs to the family of the Cut Finite Element methods, allows to consider unfitted meshes for the fluid and solid domains by maintaining the fluid mesh fixed in time as the solid moves. We review the state of the art about the numerical methods for fluid-structure interaction problems and we present an overview of the Cut Finite Element methods. We describe the numerical discretization proposed here to handle the case of a thick immersed structure with size comparable or smaller than the fluid mesh element size in the case of non-linear finite elasticity. Finally, we present some three-dimensional numerical results of the proposed method. |
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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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