7 results on '"Settore MAT/08 - Analisi Numerica"'
Search Results
2. A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization
- Author
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Michele Girfoglio, Annalisa Quaini, and Gianluigi Rozza
- Subjects
Data-driven strategies ,Numerical Analysis ,Projection-based methods ,Physics and Astronomy (miscellaneous) ,Reduced order model ,Applied Mathematics ,Proper orthogonal decomposition ,Large Eddy Simulation ,Computer Science Applications ,Nonlinear filtering stabilization ,Settore MAT/08 - Analisi Numerica ,Computational Mathematics ,Modeling and Simulation - Published
- 2023
3. BR2 discontinuous Galerkin methods for finite hyperelastic deformations
- Author
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Luca Verzeroli and Lorenzo Alessio Botti
- Subjects
Numerical Analysis ,Lagrange multipliers ,Physics and Astronomy (miscellaneous) ,Applied Mathematics ,Nonlinear elasticity ,Numerical Analysis (math.NA) ,Finite deformations ,Computer Science Applications ,Settore MAT/08 - Analisi Numerica ,Computational Mathematics ,Modeling and Simulation ,Discontinuous Galerkin ,FOS: Mathematics ,Adaptive stabilisation ,Multigrid preconditioner ,Settore ICAR/08 - Scienza delle Costruzioni ,Mathematics - Numerical Analysis - Abstract
In this work we introduce a dG framework for nonlinear elasticity based on a Bassi-Rebay (BR2) formulation. The framework encompasses compressible and incompressible hyperelastic materials and is capable of dealing with large deformations. In order to achieve stability, we combine higher-order lifting operators for the BR2 stabilization term with an adaptive stabilization strategy which relies on the BR2 Laplace operator stabilization and a penalty parameter based on the spectrum of the fourth-order elasticity tensor. Dirichlet boundary conditions for the displacement can be imposed by means of Lagrange multipliers and Nitsche method. Efficiency of the solution strategy is achieved by means of state-of-the-art agglomeration based $h$-multigrid preconditioners and the code implementation supports distributed memory execution on modern parallel architectures. Several benchmark test cases are proposed in order to investigate some relevant computational aspects, namely the performance of the $h$-multigrid iterative solver varying the stabilization parameters and the influence of Dirichlet boundary conditions on Newton's method globalisation strategy.
- Published
- 2022
4. A POD-Galerkin reduced order model for a LES filtering approach
- Author
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Gianluigi Rozza, Annalisa Quaini, and Michele Girfoglio
- Subjects
Poisson equation for pressure ,Physics and Astronomy (miscellaneous) ,78M34, 97N40, 35Q35 ,010103 numerical & computational mathematics ,Large Eddy Simulation ,01 natural sciences ,Leray model ,Settore MAT/08 - Analisi Numerica ,symbols.namesake ,FOS: Mathematics ,Applied mathematics ,Cylinder ,Mathematics - Numerical Analysis ,0101 mathematics ,Galerkin method ,Parametric statistics ,Mathematics ,Numerical Analysis ,Finite volume method ,Spatial filter ,Basis (linear algebra) ,Reduced order model ,Applied Mathematics ,Reynolds number ,Numerical Analysis (math.NA) ,Proper orthogonal decomposition ,Computer Science Applications ,Filtering stabilization ,010101 applied mathematics ,Computational Mathematics ,Modeling and Simulation ,symbols ,Large eddy simulation - Abstract
We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0, 29 pages, 16 figures, 9 tables
- Published
- 2021
5. Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics
- Author
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Fabio Nobile, Matteo Pozzoli, and Christian Vergara
- Subjects
Fluid-structure Interaction ,Physics and Astronomy (miscellaneous) ,Discretization ,Physical interface ,Settore MAT/08 - Analisi Numerica ,symbols.namesake ,Error analysis ,Robin transmission conditions ,Fluid–structure interaction ,Finite elasticity ,BDF schemes ,Newton method ,Haemodynamics ,Elasticity (economics) ,finite elasticity ,Newton's method ,Mathematics ,Numerical Analysis ,haemodynamics ,Applied Mathematics ,Interface position ,Computer Science Applications ,Computational Mathematics ,Modeling and Simulation ,symbols ,Interaction problem ,Algorithm - Abstract
In this paper we consider the numerical solution of the three-dimensional fluid–structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant.
- Published
- 2014
6. A Dynamic Mesh Algorithm for Curvature Dependent Evolving Interfaces
- Author
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Maurizio Paolini, Ricardo H. Nochetto, and Claudio Verdi
- Subjects
Numerical Analysis ,Mean curvature flow ,Mean curvature ,Physics and Astronomy (miscellaneous) ,Applied Mathematics ,Curvature ,Topology ,Allen-Cahn equation ,Finite element method ,Computer Science Applications ,mean curvature flow ,Computational Mathematics ,Singularity ,Mesh generation ,Modeling and Simulation ,dynamic mesh ,Gravitational singularity ,Boundary value problem ,Settore MAT/08 - ANALISI NUMERICA ,Algorithm ,Mathematics - Abstract
A new finite element method is discussed for approximating evolving interfaces in2nwhose normal velocity equals mean curvature plus a forcing function. The method is insensitive to singularity formation and retains the local structure of the limit problem and, thus, exhibits a computational complexity typical of3n?1without having the drawbacks of front-tracking strategies. A graded dynamic mesh around the propagating front is the sole partition present at any time step and is significantly smaller than a full mesh. Time stepping is explicit, but stability constraints force small time steps only when singularities develop, whereas relatively large time steps are allowed before or past singularities, when the evolution is smooth. The explicit marching scheme also guarantees that at most one layer of elements has to be added or deleted per time step, thereby making mesh updating simple and, thus, practical. Performance and potentials are fully documented via a number of numerical simulations in 2D, 3D, 4D, and 8D, with axial symmetries. They include tori and cones for the mean curvature flow, minimal and prescribed mean curvature surfaces with given boundary, fattening for smooth driving force, and volume constraint.
- Published
- 1996
7. Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology
- Author
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Gianluigi Rozza, Annalisa Quaini, and Giuseppe Pitton
- Subjects
Physics and Astronomy (miscellaneous) ,Viscous liquid ,01 natural sciences ,Reduced basis method ,Parametrized Navier-Stokes equations ,Stability of flows ,Symmetry breaking bifurcation ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,symbols.namesake ,Settore MAT/08 - Analisi Numerica ,0103 physical sciences ,FOS: Mathematics ,Newtonian fluid ,Fluid dynamics ,Symmetry breaking ,Mathematics - Numerical Analysis ,0101 mathematics ,Bifurcation ,Mathematics ,Numerical Analysis ,Hydrodynamic stability ,Applied Mathematics ,Reynolds number ,Numerical Analysis (math.NA) ,Mechanics ,3. Good health ,Computer Science Applications ,010101 applied mathematics ,Computational Mathematics ,Classical mechanics ,Flow (mathematics) ,Modeling and Simulation ,symbols - Abstract
We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape., 31 pages, 21 figures
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