Higher Order Mesh Generation for Simulation of Complex Systems

ABSTRACT: We propose here a robust production-level high-order mesh generation software for complex geometries. High order accurate numerical methods are becoming increasingly popular in the present time and have demonstrated a great measure of success in efficient error-controlled simulations for a wide variety of important problems. A curved geometry and mesh generation system is essential in maintaining the accuracy of these methods, as has been amply demonstrated in the literature. The generation of such meshes is far from the standard practice at the present time, and there is a notable absence of commercial-grade tools to generate, use and visualize them. The proposed software will be based on a firm foundation in geometry, CAD modeling and high order accurate simulations. The proposing team consists of researchers from HyPerComp and the University of Michigan with extensive experience in these areas. The primary goal will be to generate high quality hybrid curved meshes to support fluid mechanics and electromagnetics simulations where linear element meshes are conventionally used. In order to enhance the applicability of this technology, output-based methods will be developed for optimal node placement and adaptive meshing. The software will be transitioned for use in the discontinuous Galerkin based solvers HDphysics (HyPerComp) and XFLOW (U.Michigan). BENEFIT: The proposed work will facilitate the usage of high order accurate simulations in CFD and allied fields in practical applications and a wider range of potential users. Such simulations will be a revolutionary departure from customary methods used in commercial software which bear all the limitations of their legacy when aspiring to solve vastly larger and more complex problems. We believe that a successful implementation of the goals of this research will make a highly desirable product, as well as an invaluable research tool in many markets: bio-medical, aerospace, chemical and so forth.