An efficient modified Gabriel method for triangulating complex fractured media for multiphase flow simulations

Fractured reservoirs and aquifers are complex domains where discrete fractures are internal constraining boundaries. The Delaunay triangulation of a fractured medium generally does not conform to the fracture boundaries and recovering the fracture elements may violate the Delaunay empty-circle (2D) criterion, which may lead to a low-quality triangulation. This paper presents a new approach based on the combined Gabriel and Delaunay methods. A modified Gabriel condition of edge-empty-circle is introduced. In a first stage, the fracture edges violating the modified Gabriel criterion are released and then followed by a Delaunay triangulation with the rest of the fracture constraints. The released fracture edges are approximated by the edges of the Delaunay triangles in a postprocessing stage. The final representation of the fractures might be slightly different, but a very accurate solution is always maintained. The method has the capability to generate fine grids and to offer an accurate and good-quality grid. Numerical examples are presented to assess the efficiency of the proposed method.