Parallel Vertex Approximate Gradient discretization of hybrid dimensional Darcy flow and transport in discrete fracture networks

TL;DR

This paper introduces a parallel numerical algorithm for simulating flow and transport in discrete fracture networks, utilizing advanced discretization schemes and parallel computing to handle complex geometries efficiently.

Contribution

It presents a novel parallel discretization method combining Vertex Approximate Gradient and explicit transport schemes for fracture network simulations.

Findings

Validated convergence on analytical solutions with intersecting fractures

Achieved efficient parallel performance up to 512 processes

Demonstrated robustness across various mesh types and fracture complexities

Abstract

This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on the Vertex Approximate Gradient finite volume scheme adapted to polyhedral meshes and to heterogeneous anisotropic media, and the transport equation is discretized by a first order upwind scheme combined with an Euler explicit integration in time. The parallelization is based on the SPMD (Single Program, Multiple Data) paradigm and relies on a distribution of the mesh on the processes with one layer of ghost cells in order to allow for a local assembly of the discrete systems. The linear system for the Darcy flow is solved using different linear solvers and preconditioners implemented in the PETSc and Trilinos libraries. The convergence of the scheme is validated on two original analytical solutions with one and four intersecting fractures. Then, the parallel efficiency of the algorithm is assessed on up to 512 processes with different types of meshes, different matrix fracture permeability ratios, and different levels of complexity of the fracture network.