A conservative implicit multirate method for hyperbolic problems

This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the spatial domain. We propose a novel mass conservative multirate approach, that can be generalized to various implicit time discretization methods. It is based on flux partitioning, so that flux exchanges between a cell and its neighbors are balanced. A number of numerical experiments on both non-linear scalar problems and systems of hyperbolic equations have been carried out to test the efficiency and accuracy of the proposed approach

Multi-Level quasi-Newton methods for the partitioned simulation of fluid-structure interaction

In previous work of the authors, Fourier stability analyses have been performed of Gauss-Seidel iterations between the flow solver and the structural solver in a partitioned fluid-structure interaction simulation. These analyses of the flow in an elastic tube demonstrated that only a number of Fourier modes in the error on the interface displacement are unstable. Moreover, the modes with a low wave number are most unstable and these modes can be resolved on a coarser grid. Therefore, a new class of quasi-Newton methods with more than one grid level is introduced. Numerical experiments show a significant reduction in run time

The LifeV library: engineering mathematics beyond the proof of concept

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis. Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar

A reduced model for Darcy’s problem in networks of fractures

Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures at the intersections and allows for jumps of pressure across intersections. This fact permits to describe the flow when fractures are characterized by different properties more accurately with respect to other models that impose pressure continuity. The main mathematical properties of the model, derived in the two-dimensional setting, are analyzed. As concerns the numerical discretization we allow the grids of the fractures to be independent, thus in general non-matching at the intersection, by means of the extended finite element method (XFEM). This increases the flexibility of the method in the case of complex geometries characterized by a high number of fractures

On Parallel Computation of Blood Flow in Human Arterial Network Based on 1-D Modelling

In this study, parallel computation of blood flow in a 1-D model of human arterial network has been carried out employing a Taylor Galerkin Finite Element Method. Message passing interface libraries have been used on Origin 2000 SGI machine. A Greedy strategy for load-distribution has been devised and data-flow graphs necessary for parallelization have been generated. The performance of parallel implementation measured in terms of speedup and efficiency factors is found to be good. Further, the parallel code is used in simulating the propagation of pressure and velocity waveforms in our 1-D arterial model for two different inflow pressure pulses. Also, the influence of consideration of terminal resistance on pressure and velocity waveforms have been analyze

Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Accepted versio

Dynamic tests' plastic strains estimation through thermal imaging measurement

LAUREA MAGISTRALEIn questo lavoro è stata studiata la possibilità di utilizzare le misure di temperatura attraverso termocamera per stimare le deformazioni plastiche durante prove dinamiche. Per prima cosa sono state analizzate le proprietà meccaniche del materiale per definire la regola di indurimento. I campioni di alluminio sono stati testati in un intervallo compreso tra 1 mm/min e 5 m/s e le deformazioni sono state ricavate attraverso l'analisi DIC, dimostrando l'indipendenza del materiale dalla velocità di deformazione. Una volta caratterizzato il materiale, sono state eseguite prove con la termocamera, con velocità comprese tra 50 mm/s e 3 m/s. Attraverso uno schema di integrazione temporale, l'equazione dell'energia è stata integrata con la deformazione come variabile di integrazione e, confrontandola con il DIC, si è accertata la validità dei risultati. Una volta ricavate le deformazioni e messe in relazione con le rispettive variazioni di temperatura, è stata eseguita una regressione polinomiale sui dati per ricavare una curva di caratterizzazione da poter utilizzare durante le prove dinamiche. La curva di caratterizzazione è stata poi testata su prove dinamiche di compressione di cilindri circolari dimostrando la capacità del metodo di mostrare la distribuzione delle deformazioni.In this work, the possibility of using temperature measurements via thermal imaging to estimate plastic deformation during dynamic tests was investigated. First the mechanical proprieties of the material ear fuond to define the hardening rule. Aluminum specimens were tested in the range between 1 mm/min and 5 m/s, and strains were derived through DIC analysis, showing the material's independence of strain rate. Once the material was characterized, tests with the thermal imaging camera, with velocities between 50 mm/s and 3 m/s, are carried out. Through a time integration scheme, the energy equation was integrated with the deformation as integration variable and, by comparing them with the DIC, we ascertained the validity of the results. Once the strains were derived and related to the respective temperature changes, a polynomial regression was performed on the data to derive a characterization curve that could be used for subsequent tests. The characterization curve was then tested on dynamic compression tests of circular cylinders demonstrating the ability of the method to show the deformations distribution

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure