Delaunay triangulation and computational fluid dynamics meshes

In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable for CFD calculations, particularly with regard to high aspect ratio, skewed quadrilateral elements

Quadrilateral meshes with provable angle bounds

In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than 18.43∘(=arctan(13)) or greater than 171.86∘(=135∘+2arctan(13)). This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles

Quadrilateral meshes with provable angle bounds

In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than 18.43∘(=arctan(13)) or greater than 171.86∘(=135∘+2arctan(13)). This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles

Quadrilateral Meshes with Bounded Minimum Angle

This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than . This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle

Quadrilateral Meshes with Bounded Minimum Angle

This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than . This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle

Survey of two-dimensional acute triangulations

AbstractWe give a brief introduction to the topic of two-dimensional acute triangulations, mention results on related areas, survey existing achievements–with emphasis on recent activity–and list related open problems, both concrete and conceptual

Subquadratic nonobtuse triangulation of convex polygons

A convex polygon with n sides can be triangulated by O(n^1.85) triangles, without any obtuse angles. The construction uses a novel form of geometric divide and conquer

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology