Decomposition of Hexahedral Block Topology to Generate Initial Tetrahedral Grids for Complex Configurations

Abstract

Most three dimensional tetrahedral grid generators can refine an initial grid in matter of seconds. But making an initial tetrahedral grid for complex geometry can be a tedious and time consuming task. This paper describes a novel procedure for generation of starting tetrahedral cells using hexahedral block topology. Hexahedral blocks are arranged around an aerodynamic body to fill-up a computational flow domain. Each of the hexahedral blocks is then decomposed into six tetrahedral elements to obtain an initial tetrahedral grid around the same aerodynamic body. This resulted in an algorithm that enables users to produce starting tetrahedral grids for variety of aerodynamic configurations. To construct an initial starting tetrahedral grid suitable for computational flow simulations, representing a solid surface geometry (fuselage or a wing section) attached to a plane-of-symmetry, a topology containing at least 5 hexahedral blocks is required. This results in an initial starting grid consisting of 30 tetrahedral cells with 74 faces and 16 vertices, which is the same number of vertices as for the hexahedral blocks. Since the number of vertices and their coordinate locations are kept the same, a connectivity matrix can be produced to describe the forming faces of the tetrahedral grid. This procedure was performed for a single block, 5-block, and 9-block topologies to produce starting tetrahedral cells for numerous domain size and shapes.