Method of generating a hex-dominant mesh of a faulted underground medium

A method of generating a mesh of an underground medium comprising at least one sedimentary layer crossed by at least one fault, the at least one layer being vertically delimited by two geological horizons discretized by first and second triangulated three-dimensional surfaces, comprising:

• (a) converting, using a computer, the first triangulated three-dimensional surface into a triangulated two-dimensional surface onto which the at least one fault is projected, by an isometric unfolding wherein the at least one fault is projected forming segments describing an open curve;
• (b) generating a regular two-dimensional grid pattern for the first triangulated two-dimensional surface using only quadrilaterals;
• (c) accounting for the at least one fault within the regular grid pattern by deforming the quadrilaterals of the grid pattern which are intersected by the open curve;
• (d) converting the deformed regular grid pattern into a three-dimensional gridded surface and converting each quadrilateral, which is crossed by the at least one fault at a diagonal into only two triangles;
• (e) repeating steps (a)-(d) for the second triangulated three-dimensional surface while keeping an identical number of quadrilaterals in each direction;
• and
• (f) generating the mesh of the underground medium by creating links between each node of the two three-dimensional gridded surfaces with respect to the at least one fault;
• and wherein
• the medium comprises faults which are accounted for within the regular grid pattern by steps comprising IF this displacement does not generate a quadrilateral, at least one angle of the quadrilateral is greater than a fixed angle threshold, and IF this end of the edge intersected by the open curve has not been displaced yet, THEN deforming the grid displacing the end or the edge that is the closest to the intersection point towards the intersection point, ELSE IF this end has not been displaced yet, THEN deforming the grid by displacing the other end of the edge towards the intersection point, and ELSE refining the mesh until one end can be displaced, and displacing this end.