The disclosed embodiments include a method, apparatus, and computer program product for generating hybrid computational meshes around complex and discrete fractures for the purpose of reservoir simulation. For example, one disclosed embodiment is a computer-implemented method for modeling three-dimensional (3D) geological fractures. The method involves receiving a set of 3D fracture surfaces with geometry that has been discretized in a two-dimensional (2D) manifold by a collection of polygons. The method defines a family of non-cutting 2D cut surfaces for cutting the set of 3D fracture surfaces. The method then uses cutting the 2D slice surface and the 2D manifolds that define the fracture surfaces to create a set of 2D fractures on each slice surface. Following a series of steps, the method logically combines 2D fracture cells that correspond to the individual fractures of each slicing surface, with their neighbors above / below, to simulate three-dimensional geology using two-dimensional elements.
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