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

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