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Abstract: This paper presents a gluing method for composite meshes. Different meshes are generated independently and are glued together using some extension elements to connect them. 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 and finally applied to the solution of the airflow in the complete respiratory system, by joining independent meshes for the large and small airways. [Copyright &y& Elsevier]