Bicameral Mesh Gradation with a Controlled Advancing Front Approach. (June 2022) - Mukherjee, Nilanjan; Cabello, Jean; Makem, Jonathan E.
Abstract: This paper discusses an approach to controlling two-dimensional local sizing in a bicameral mesh. This concept was introduced in our prior International Meshing Roundtable conference paper, and we expand on it herein. We define bicameral gradation as a mesh size variation of two distinctly different types in two or more separate chambers or subdomains. The first chamber is controlled by constant to local size functions. The second subdomain is governed by a nonlinear sizing function leading to transitioning meshes. A controlled advancing front approach is proposed for both triangular and quadrangular meshes with the singular goal of ensuring a high local quality metric in the first chamber. A modified H-shock sizing scheme governs the second chamber. Virtual mesh topology is constructed at the face boundary both at geometry and node-loop levels to facilitate this type of bicameral meshing. Results clearly indicate the efficacy of the proposed approach leading to both a well-controlled desired size field and high local element quality. Graphical abstract: Highlights: Bicameralism or Bicameral mesh gradation is defined as a mesh size variation of two distinctly different types in two or more separate chambers or subdomains. There is a "local chamber" where mesh gradation is constant to linear to a specific governing equation and the rest of the area which is called "residual chamber" and where the size varies in a non-linear transition. Mesher-native virtual topological elements like soft-points and virtual vertices are used to define zonal boundaries. Local sizes can be applied on (a) vertex, (b) interior of edges and (c) interior of faces. 2D NodeLoop-segments are used to perform loop-based advancing front meshing in the local chambers with both triangles and quadrangles.