5,280 research outputs found
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
Dual virtual element method in presence of an inclusion
We consider a Darcy problem for saturated porous media written in dual
formulation in presence of a fully immersed inclusion. The lowest order virtual
element method is employ to derive the discrete approximation. In the present
work we study the effect of cells with cuts on the numerical solution, able to
geometrically handle in a more natural way the inclusion tips. The numerical
results show the validity of the proposed approach
Computation of effective dynamic properties of naturally fractured reservoirs: Comparison and validation of methods
Imperial Users onl
Cut Finite Elements for Convection in Fractured Domains
We develop a cut finite element method (CutFEM) for the convection problem in
a so called fractured domain which is a union of manifolds of different
dimensions such that a dimensional component always resides on the boundary
of a dimensional component. This type of domain can for instance be used
to model porous media with embedded fractures that may intersect. The
convection problem can be formulated in a compact form suitable for analysis
using natural abstract directional derivative and divergence operators. The cut
finite element method is based on using a fixed background mesh that covers the
domain and the manifolds are allowed to cut through a fixed background mesh in
an arbitrary way. We consider a simple method based on continuous piecewise
linear elements together with weak enforcement of the coupling conditions and
stabilization. We prove a priori error estimates and present illustrating
numerical examples
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
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