Finite Element Mesh Design With Quadrilateral Transition

The focus of the research was the design of finite element meshes with direct application to computational fluid mechanics. This design concentrated primarily on coarsening a dense mesh or refining a coarse mesh. Structured meshes have been produced using the fundamentals of analytical geometry. Source codes in MATLAB and in Fortran have been written that transform the meshes into figures and can be readily used in computer codes of finite elements. To the best of our knowledge, there is no relevant literature that documents this kind of effort that has been produced in this work, although there are figures that can be found on the internet with relevant content that lack documentation. There are numerous applications in fluid mechanics where this kind of work is useful, such as, flow around submerged objects (flow around a cylinder, submarine, automobile), surface mounted obstacles (flow around a cube, building), and in channel flows with emphasis on the outflow boundary conditions where a refined mesh at the exit of the domain is crucial for accurate results. Additionally, the meshes produced in the study can be directly applied to the area of computational structured mechanics.