Indirect Unstructured Hex-dominant Mesh Generation Using Tetrahedra Recombination

in: ECMOR XIV, EAGE, Catania

Abstract

Corner-point gridding of reservoir and basin models is widely used but generally yields approximations in the geological interfaces representation in flow simulation. This paper introduces an indirect method to generate a hexdominant mesh conformal to 3D geological surfaces suitable for Finite-Element and Control-Volume Finite-Element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem, known to be N P-Complete. We propose five heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on complex 3D geological models including a discrete fracture network.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Botella, Arnaud and Levy, Bruno and Caumon, Guillaume },
     title = { Indirect Unstructured Hex-dominant Mesh Generation Using Tetrahedra Recombination },
 booktitle = { ECMOR XIV },
      year = { 2014 },
  location = { Catania },
organization = { EAGE },
       doi = { 10.3997/2214-4609.20141857 },
  abstract = { Corner-point gridding of reservoir and basin models is widely used but generally yields approximations in the geological interfaces representation in flow simulation. This paper introduces an indirect method to generate a hexdominant mesh conformal to 3D geological surfaces suitable for Finite-Element and Control-Volume Finite-Element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem, known to be N P-Complete. We propose five heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on complex 3D geological models including a discrete fracture network. }
}