The receding front method applied to hexahedral mesh generation of exterior domains

Abstract

Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside-outside approach. On the other hand, advancing front methods generate highquality hexahedra near the boundary using an outside-inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside-outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.

Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

“…Using Equation (14), and according to Equation (10), the regularized shape quality measure for quadrilateral (hexahedral) elements is defined as:…”

“…The simultaneous untangling and smoothing algorithm for quadrilateral and hexahedral meshes is based on the optimization of an objective function defined in terms of the regularized distortion measure (14) of the elements in the local sub-mesh. Let x v be the coordinates of a free node v ∈ V, and assume that the local sub-mesh, M v , is composed by M elements (quadrilaterals or hexahedra in our case).…”

“…On the other hand, several methods have been developed to mesh any geometry with an unstructured hexahedral mesh. For instance, 1. dual methods such as wisker weaving [7] or the local dual contributions [8]; 2. primal methods that directly generates the hexahedral mesh such as grid based methods [9,10,11], advancing front methods [12,13], or the receding front method [14], and 3. primal methods that transform a tetrahedral mesh into a hexahedral mesh [15,16]. However, fully automatic unstructured hexahedral mesh generation algorithms are still not available and, at this stage, no automated technique exists which compares to tetrahedral methods such as Delaunay or advancing front techniques.…”

Untangling and Smoothing of Quadrilateral and Hexahedral Meshes

“…The fourth example shows an application of the proposed optimization method to the receding front method [14]. Using this method we generate an hexahedral mesh around an airplane.…”

“…Taking into account this modification, see Equation (14), the new objective function for the local mesh is…”