A gluing method for non-matching meshes

• We present a flexible gluing mesh method with arbitrary relative position of meshes.
• The method is implicit, PDE independent and naturally parallel.
• We have simulated the airflow in the respiratory system by joining independent meshes.
• Independent meshes could be coming from different centers.
• We have probed that the method could be valid to optimize the position of a bypass.

This paper presents a gluing method for composite meshes. Different meshes are generated independently and are glued together using some new elements to connect them, referred to as extension elements. The resulting global mesh is non-conforming and consists of connected overlapping meshes. The method is inherently implicit, parallel and versatile, in the sense that it is PDE independent. The most cited gluing method is probably the Chimera method, used for overset grids, where patch meshes are superimposed onto a background mesh. The method employed here was originally devised for such situations and is now applied to disjoint or overlapping meshes. One of the advantages of the method is that the meshes do not have to coincide and can present a gap between them. The method is illustrated through some simple examples to demonstrate the mesh convergence. Finally, we consider the solution of the airflow in the complete respiratory system, by joining independent meshes for the large and small airways, and the simulation of the flow passing through a bypass in a stenosed artery.