367 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
Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins
In this work we propose an Uncertainty Quantification methodology for
sedimentary basins evolution under mechanical and geochemical compaction
processes, which we model as a coupled, time-dependent, non-linear,
monodimensional (depth-only) system of PDEs with uncertain parameters. While in
previous works (Formaggia et al. 2013, Porta et al., 2014) we assumed a
simplified depositional history with only one material, in this work we
consider multi-layered basins, in which each layer is characterized by a
different material, and hence by different properties. This setting requires
several improvements with respect to our earlier works, both concerning the
deterministic solver and the stochastic discretization. On the deterministic
side, we replace the previous fixed-point iterative solver with a more
efficient Newton solver at each step of the time-discretization. On the
stochastic side, the multi-layered structure gives rise to discontinuities in
the dependence of the state variables on the uncertain parameters, that need an
appropriate treatment for surrogate modeling techniques, such as sparse grids,
to be effective. We propose an innovative methodology to this end which relies
on a change of coordinate system to align the discontinuities of the target
function within the random parameter space. The reference coordinate system is
built upon exploiting physical features of the problem at hand. We employ the
locations of material interfaces, which display a smooth dependence on the
random parameters and are therefore amenable to sparse grid polynomial
approximations. We showcase the capabilities of our numerical methodologies
through two synthetic test cases. In particular, we show that our methodology
reproduces with high accuracy multi-modal probability density functions
displayed by target state variables (e.g., porosity).Comment: 25 pages, 30 figure
A mathematical model for thermal single-phase flow and reactive transport in fractured porous media
In this paper we present a mathematical model and a numerical workflow for
the simulation of a thermal single-phase flow with reactive transport in porous
media, in the presence of fractures. The latter are thin regions which might
behave as high or low permeability channels depending on their physical
parameters, and are thus of paramount importance in underground flow problems.
Chemical reactions may alter the local properties of the porous media as well
as the fracture walls, changing the flow path and possibly occluding some
portions of the fractures or zones in the porous media. To solve numerically
the coupled problem we propose a temporal splitting scheme so that the
equations describing each physical process are solved sequentially. Numerical
tests shows the accuracy of the proposed model and the ability to capture
complex phenomena, where one or multiple fractures are present
A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones
In this work we present a new conceptual model to describe fluid flow in a
porous media system in presence of a large fault. Geological faults are often
modeled simply as interfaces in the rock matrix, but they are complex structure
where the high strain core is surrounded by the so called damage zones,
characterized by the presence of smaller fractures which enhance the
permeability of the medium. To obtain reliable simulation outcomes these damage
zone, as well as the fault, have to be accurately described. The new model
proposed in this work considers both these two regions as lower dimensional and
embedded in the rock matrix. The model is presented, analyzed, and tested in
several configurations to prove its robustness and ability to capture many
important features, such as hight contrast and heterogeneity of permeability
Local Embedded Discrete Fracture Model (LEDFM)
The study of flow in fractured porous media is a key ingredient for many
geoscience applications, such as reservoir management and geothermal energy
production. Modelling and simulation of these highly heterogeneous and
geometrically complex systems require the adoption of non-standard numerical
schemes. The Embedded Discrete Fracture Model (EDFM) is a simple and effective
way to account for fractures with coarse and regular grids, but it suffers from
some limitations: it assumes a linear pressure distribution around fractures,
which holds true only far from the tips and fracture intersections, and it can
be employed for highly permeable fractures only. In this paper we propose an
improvement of EDFM which aims at overcoming these limitations computing an
improved coupling between fractures and the surrounding porous medium by a)
relaxing the linear pressure distribution assumption, b) accounting for
impermeable fractures modifying near-fracture transmissibilities. These results
are achieved by solving different types of local problems with a fine
conforming grid, and computing new transmissibilities (for connections between
fractures and the surrounding porous medium and those through the porous medium
itself near to the fractures). Such local problems are inspired from numerical
upscaling techniques present in the literature. The new method is called Local
Embedded Discrete Fracture Model (LEDFM) and the results obtained from several
numerical tests confirm the aforementioned improvements.Comment: 44 pages, 29 figures, submitted to "Advances in Water Resources
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
Subjective impact of osteoarthritis flare-ups on patients' quality of life
BACKGROUND: Clinical trials on osteoarthritis (OA) flare-ups treatment usually focus only on objective measures of health status, albeit recent literature suggestions on the importance of patients' subjectivity. Aim of the study was to evaluate the effects of OA and of its different types of medical treatment(s) on Health Related Quality of Life (HRQoL) in terms of both subjective satisfaction and functional status. METHODS: An observational study on prospective data collected from the Evaluation of Quality of life in OA (EQuO) clinical trial (April 1999-November 2000) was conducted; outpatients from 70 participating centers (Orthopedy or Rheumatology Departments in Italy) with a diagnosis of OA of the hip or knee were consecutively enrolled. Patients were observed at OA flare-ups (baseline) and at follow up 4 weeks after treatment. Patients' objective and subjective HRQoL were assessed by means of the SF-36 and the Satisfaction Profile (SAT-P, which focuses on subjective satisfaction); Present Pain at baseline and Pain Relief at follow up were also evaluated. RESULTS: Among the 1323 patients, 1138 (86%) were prescribed one drug/treatment of osteoarthritis, 169 (13%) 2 drugs/treatments, and 16 (1%) 3 drugs/treatments; most of treatments involved the prescription of NSAIDs; non-coxib, COX2 selective NSAIDs were prescribed in about 50% of patients. Follow-up visits were performed after 29.0 days on average (± 7.69 SD). For all SF-36 domains, all SAT-P items and factors, the differences between baseline and follow up scores resulted statistically significant (p < 0.001), enlighting an improvement both in health status and in subjective HRQoL. CONCLUSION: Besides the classic health status measures, the assessment of patients' subjective satisfaction provides important clues on treatments efficacy of OA within the patient-centered medicine model. In clinical practice this could lead to a better doctor-patient communication and to higher levels of treatment adherence
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
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
Numerical simulation of geochemical compaction with discontinuous reactions
The present work deals with the numerical simulation of porous media subject to the coupled effects of mechanical compaction and reactive flows that can significantly alter the porosity due to dissolution, precipitation or transformation of the solid matrix. These chemical processes can be effectively 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
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