283 research outputs found
A three-field based optimization formulation for flow simulations in networks of fractures on non-conforming meshes
A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field domain decomposition framework, in which independent variables are introduced at the interfaces generated in the process of decoupling the original problem on the whole network into a set of fracture-local problems. A PDE-constrained formulation is then used to enforce compatibility conditions at the interfaces. The combination of the three-field domain decomposition and of the optimization based coupling strategy results in a novel method which can handle non-conforming meshes, independently built on each geometrical object of the computational domain, and ensures local mass conservation property at fracture intersections, which is of paramount importance for hydro-geological applications. An iterative solver is devised for the method, suitable for parallel implementation on parallel computing architectures
Dual virtual element method for discrete fractures networks
Discrete fracture networks is a key ingredient in the simulation of physical
processes which involve fluid flow in the underground, when the surrounding
rock matrix is considered impervious. In this paper we present two different
models to compute the pressure field and Darcy velocity in the system. The
first allows a normal flow out of a fracture at the intersections, while the
second grants also a tangential flow along the intersections. For the numerical
discretization, we use the mixed virtual finite element method as it is known
to handle grid elements of, almost, any arbitrary shape. The flexibility of the
discretization allows us to loosen the requirements on grid construction, and
thus significantly simplify the flow discretization compared to traditional
discrete fracture network models. A coarsening algorithm, from the algebraic
multigrid literature, is also considered to further speed up the computation.
The performance of the method is validated by numerical experiments
Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations
Simulations of fluid flow in naturally fractured rocks have implications for
several subsurface applications, including energy storage and extraction, and
waste storage. We are interested in flow in discrete fracture networks, which
explicitly represent flow in fracture surfaces, but ignore the impact of the
surrounding host rock. Fracture networks, generated from observations or
stochastic simulations, will contain intersections of arbitrary length, and
intersection lines can further cross, forming a highly complex geometry. As the
flow exchange between fractures, thus in the network, takes place in these
intersections, an adequate representation of the geometry is critical for
simulation accuracy. In practice, the intersection dynamics must be handled by
a combination of the simulation grid, which may or may not resolve the
intersection lines, and the numerical methods applied on the grid. In this
work, we review different classes of numerical approaches proposed in recent
years, covering both methods that conform to the grid, and non-matching cases.
Specific methods considered herein include finite element, mixed and virtual
finite elements and control volume methods. We expose our methods to an
extensive set of test cases, ranging from artificial geometries designed to
test difficult configurations, to a network extruded from a real fracture
outcrop. The main outcome is guidances for choice of simulation models and
numerical discretization with a trade off on the computational cost and
solution accuracy
A five field formulation for flow simulations in porous media with fractures and barriers via an optimization based domain decomposition method
The present work deals with the numerical resolution of coupled 3D-2D
problems arising from the simulation of fluid flow in fractured porous media
modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM
model, fractures are represented as planar interfaces immersed in a 3D porous
matrix and can behave as preferential flow paths, in the case of conductive
fractures, or can actually be a barrier for the flow, when, instead, the
permeability in the normal-to-fracture direction is small compared to the
permeability of the matrix. Consequently, the pressure solution in a DFM can be
discontinuous across a barrier, as a result of the geometrical dimensional
reduction operated on the fracture.
The present work is aimed at developing a numerical scheme suitable for the
simulation of the flow in a DFM with fractures and barriers, using a mesh for
the 3D matrix non conforming to the fractures and that is ready for domain
decomposition. This is achieved starting from a PDE-constrained optimization
method, currently available in literature only for conductive fractures in a
DFM. First, a novel formulation of the optimization problem is defined to
account for non permeable fractures. These are described by a filtration-like
coupling at the interface with the surrounding porous matrix. Also the extended
finite element method with discontinuous enrichment functions is used to
reproduce the pressure solution in the matrix around a barrier.
The method is presented here in its simplest form, for clarity of exposition,
i.e. considering the case of a single fracture in a 3D domain, also providing a
proof of the well posedness of the resulting discrete problem. Four validation
examples are proposed to show the viability and the effectiveness of the
method.Comment: 21 pages, 14 figure
Applications of the Virtual Element Method to Discrete Fracture Networks
We put forward in this work several novel applications of the Virtual Element Method in the context of Discrete Fracture Networks. A family of methods is presented here for solving Darcy flow, time dependent-problems and the complete transport equation in both diffusion-dominated and convection-dominated problems. We present as well an implementation of mixed Virtual Elements in the context of Discrete Fracture Networks
Parallel meshing, discretization and computation of flow in massive discrete fracture networks
In the present work a message passing interface (MPI) parallel implementation of an optimization-based approach for the simulation of underground flows in large discrete fracture networks is proposed. The software is capable of parallel execution of meshing, discretization, resolution, and postprocessing of the solution. We describe how optimal scalability performances are achieved combining high efficiency in computations with an optimized use of MPI communication protocols. Also, a novel graph-topology for communications, called the multi-Master approach, is tested, allowing for high scalability performances on massive fracture networks. Strong scalability and weak scalability simulations on random networks counting order of 10^5 fractures are reported
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