149 research outputs found
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
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 multi-layer reactive transport model for fractured porous media
An accurate modeling of reactive flows in fractured porous media is a key
ingredient to obtain reliable numerical simulations of several industrial and
environmental applications. For some values of the physical parameters we can
observe the formation of a narrow region or layer around the fractures where
chemical reactions are focused. Here the transported solute may precipitate and
form a salt, or vice-versa. This phenomenon has been observed and reported in
real outcrops. By changing its physical properties this layer might
substantially alter the global flow response of the system and thus the actual
transport of solute: the problem is thus non-linear and fully coupled. The aim
of this work is to propose a new mathematical model for reactive flow in
fractured porous media, by approximating both the fracture and these
surrounding layers via a reduced model. In particular, our main goal is to
describe the layer thickness evolution with a new mathematical model, and
compare it to a fully resolved equidimensional model for validation. As
concerns numerical approximation we extend an operator splitting scheme in time
to solve sequentially, at each time step, each physical process thus avoiding
the need for a non-linear monolithic solver, which might be challenging due to
the non-smoothness of the reaction rate. We consider bi- and tridimensional
numerical test cases to asses the accuracy and benefit of the proposed model in
realistic scenarios
Parallel mesh adaptive techniques for complex flow simulation: geometry conservation
Dynamic mesh adaptation on unstructured grids, by localised refinement and derefinement, is a very efficient tool for enhancing solution accuracy and optimising computational time. One of the major drawbacks, however, resides in the projection of the new nodes created, during the refinement process, onto the boundary surfaces. This can be addressed by the introduction of a library capable of handling geometric properties given by a CAD (computer-aided design) description. This is of particular interest also to enhance the adaptation module when the mesh is being smoothed, and hence moved, to then reproject it onto the surface of the exact geometry
Performances of the mixed virtual element method on complex grids for underground flow
The numerical simulation of physical processes in the underground frequently
entails challenges related to the geometry and/or data. The former are mainly
due to the shape of sedimentary layers and the presence of fractures and
faults, while the latter are connected to the properties of the rock matrix
which might vary abruptly in space. The development of approximation schemes
has recently focused on the overcoming of such difficulties with the objective
of obtaining numerical schemes with good approximation properties. In this work
we carry out a numerical study on the performances of the Mixed Virtual Element
Method (MVEM) for the solution of a single-phase flow model in fractured porous
media. This method is able to handle grid cells of polytopal type and treat
hybrid dimensional problems. It has been proven to be robust with respect to
the variation of the permeability field and of the shape of the elements. Our
numerical experiments focus on two test cases that cover several of the
aforementioned critical aspects
Numerical simulation of geochemical compaction with discontinuous reactions
The present work deals with the numerical simulation of porous media subject to the coupled eïŹects of mechanical compaction and reactive ïŹows that can signiïŹcantly alter the porosity due to dissolution, precipitation or transformation of the solid matrix. These chemical processes can be eïŹectively modelled as ODEs with discontinuous right hand side, where the discontinuity depends on time and on the solution itself. Filippov theory can be applied to prove existence and to determine the solution behaviour at the discontinuities. From the numerical point of view, tailored numerical schemes are needed to guarantee positivity, mass conservation and accuracy. In particular, we rely on an event-driven approach such that, if the trajectory crosses a discontinuity, the transition point is localized exactly and integration is restarted accordingly
A reduced model for Darcyâs 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
A Stability Analysis for the Arbitrary Lagrangian Eulerian Formulation with Finite Elements
In this paper we present some theoretical results on the Arbitrary Lagrangian Eulerian (ALE) formulation. This formulation may be used when dealing with moving domains and consists in recasting the governing differential equation and the related weak formulation in a frame of reference moving with the domain. The ALE technique is first presented in the whole generality for conservative equations and a result on the regularity of the underlying mapping is proven. In a second part of the work, the stability property of two types of finite element ALE schemes for parabolic evolution problems are analyzed and its relation with the so-called Geometric Conservation Laws is addressed
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