Hybrid finite element–finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks

TLDR

Generating computational meshes for complex geological objects is challenging because the mesh must preserve shape, adapt resolution to local detail, and represent material property variations while also resolving variations in computed variables. The study introduces an unstructured hybrid finite element–finite volume discretization for solving fluid flow, reactive transport, and mechanical PDEs on complex geometries with heterogeneous materials. The method represents elements and volumes in parametric space, performs numerical integration, maps integrals to physical space using Jacobian transformations, and introduces an error metric for the elliptic pressure equation to guide mesh refinement. The resulting meshes accurately capture free‑form material interfaces defined by NURBS curves and surfaces, remain valid under mesh deformation, and the generic formulation was demonstrated on a transport calculation in a complex discrete fracture model.

Abstract

Abstract The generation of computational meshes of complex geological objects is a challenge: their shape needs to be retained, resolution has to adapt to local detail, and variations of material properties in the objects have to be represented. Also mesh refinement and adaptation must be sufficient to resolve variations in the computed variable(s). Here, we present an unstructured hybrid finite element, node‐centred finite‐volume discretization suitable for solving fluid flow, reactive transport, and mechanical partial differential equations on a complex geometry with inhomogeneous material domains. We show that resulting meshes accurately capture free‐form material interfaces as defined by non‐uniform rational B‐spline curves and surfaces. The mesh discretization error is analysed for the elliptic pressure equation and an error metric is introduced to guide mesh refinement. Finite elements and finite volumes are represented in parametric space and integrations are conducted numerically. Subsequently, integral properties are mapped to physical space using Jacobian transformations. This method even retains its validity when the mesh is deformed. The resulting generic formulation is demonstrated for a transport calculation performed on a complex discrete fracture model.