A New Method for Triangular Mesh Generation

TL;DR

This paper introduces a novel method for generating triangular meshes on curved domains by deforming Cartesian meshes using divergence and curl equations solved via least squares finite element methods, enhancing CFD mesh adaptivity.

Contribution

The paper presents a new mesh generation technique that effectively handles curved boundaries through deformation fields computed by divergence and curl equations.

Findings

Successfully generates meshes on curved boundaries

Uses least squares finite element method for solving deformation equations

Improves mesh quality and adaptivity for CFD applications

Abstract

Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generation of CFD capacity that is accurate, automatic, and fast. A key component of the next generation of CFD is a greatly enhanced capacity for mesh generation and adaptivity of the mesh according to solution and geometry. In this paper, we propose a new method that generates triangular meshes on domains of curved boundary. The method deforms a Cartesian mesh that covers the domain to generate a mesh with prescribed boundary nodes. The deformation fields are generated by a system of divergence and curl equations which are solved effectively by the least square finite element method.