A method for generating moving, orthogonal, area preserving polygonal meshes

A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Because Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, a generalization of Voronoi polygon meshes was formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method's ability to simulate various physical scenarios is shown. The advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper presents a new method for generating locally orthogonal polygonal meshes from a set of generator points, considering polygon areas as a constraint. The method can be used for particle-based numerical computations and has advantages in incompressible fluid flow calculations.