System and method of developing a hydrocarbon reservoir that includes the following: determining, for each of the layers, a reservoir model defining layers representing a portion of a hydrocarbon reservoir; determining points of intersection; generating, for each of the layers, a two-dimensional (2D) unstructured mesh layer including a triangulated mesh; generating, for each pair of adjacent 2D unstructured mesh layers of the reservoir model, a three-dimensional (3D) tetrahedral mesh; generating, for the 3D tetrahedral mesh, a 3D triangulated tetrahedral mesh; generating, for the 3D triangulated tetrahedral mesh, a 3D vertically-refined triangulated tetrahedral mesh; generating, for the 3D vertically-refined triangulated tetrahedral mesh, a 3D dual mesh; and generating, using the 3D dual mesh, a simulation of the hydrocarbon reservoir represented by the layers.