Linear Sources for Mesh Generation

Abstract

Sources offer a convenient way to prescribe a size distribution in space. For each newly created mesh point, the mesh generator queries the local size distribution, either to create a new point or element, depending on the underlying mesh generation method, to smooth the mesh, or to get a local relevant length scale. Sources may have different shapes such as points, edges, triangles, or boxes. They provide the size distribution given some user defined parameters and the distance of a point location to the source. Traditionally, the source strength is considered as constant. In this work, extensions to linear sources in space are proposed. It is shown that in the case of curvature refined mesh generation, substantial savings may occur due to the much better approximation of the curvature variation for a simple modification of traditional sources. Even though curvature refinement is the main application of this work, improvements through linear sources are relevant to other contexts such as user defined sources. The technique is very general as it deals with a fundamental aspect of mesh generation and can be easily incorporated into an existing mesh generator with traditional sources. Thorough details of source approximations and source filtering are provided. Relations with lower envelopes are highlighted. Practical examples illustrate the accuracy and efficiency of the method.

On the ‘most normal’ normal—Part 2

“…The other two cells delimited by the great circles including the endpoints and the poles are closer to the endpoint they contain. There is a great similarity with the planar case [38] except that the two cells corresponding to the endpoints are not connected in the plane, while they meet at infinity on the sphere. Algorithm 3 describes the edge distance computation.…”

Sizing Function Based on Machine Learning for Unstructured Mesh Generation

“…Furthermore, to ensure the mesh quality in gradation regions so that the gradient of element scales must be limited in a reasonable range. Grid sources are effective ways to define sizing functions in many computational aerodynamics applications [1]. The time cost of defining sources may be affordable for simple configurations, but for complicated models, the interactive process that defines these sources is time-consuming and error-prone.…”

An automatic approach to constrained quadrilateral mesh generation

“…To specify the mesh size in the interior of the region, the distribution function of mesh size on the region can be defined, so that the mesh size at any point inside the region can be determined by the sizing function (Pirzadeh, 1993; Aubry et al , 2013; Chen et al , 2017).…”