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International audienceThe proposed method regularizes as far as possible some verticals of a hex-dominant basin mesh; this regularization is used to optimize the numerical simulation of hydrocarbons flow in basins. The studied basins contain faults and constitute complex geometries. This mesh optimization is adapted for a new way to mesh basins called the "Constrained Grid Method" (CGM). Data constitutes some horizon surfaces; the surfaces contain tags to reconstruct the fault surfaces which represent in our case some constraints to generate a hexdominant mesh. To make a regular hex-dominant mesh, the following steps are applied: first, the borders of horizon surfaces are extracted and optimized to get the connections between the borders as vertical as possible; this means that the border nodes have approximately the same xy directions. Next, a Dirichlet equation is solved to apply a Laplacian smoothing 2D on xy directions for each horizon surface. And as the connected (x,y) between the borders are approximately the same, as well as the implied the harmonic solutions, then the positions on (x,y) are minimized

Hex-Dominant Mesh Improving Quality to Tracking Hydrocarbons in Dynamic Basins