High-order modeling of applied multi-physics phenomena

The gap between research in numerical methods and popular commercial solvers in CFD and related areas has been gradually widening in the recent past, particularly in the realm of high order accurate algorithms. At HyPerComp we are advancing a suite of high order codes based on the discontinuous Galerkin (DG) technique that can be used in electromagnetics, fluid mechanics, MHD and radiative heat transfer. The intention is for these solvers to mature into commercial grade software that can be an attractive alternative to conventional offerings in the market at the present time. In this project, with the collaboration of key researchers at the University of Michigan, we seek to equip our multiphysics solvers with state of the art advances in code acceleration, moving geometries, accurate treatment of shock waves, and dissipative phenomena. In Phase-I we have incorporated a new strategy to handle higher order accurate derivatives in our DG solver named HOME, based on the recovery DG scheme. We have begun to migrate HOME to graphical processors (GPUs). In addition, in phase-II we shall seek to port software developed for electromagnetics that incorporates local time-stepping, uncertainty analysis and multi-order DG into the CFD setting. These modifications will equip the HOME solver with pioneering capabilities in the analysis of external aerodynamics, acoustics and multiphysical modeling, and will significantly advance the state-of-the-art in industrial CFD. BENEFIT: We intend to transition the usage of high order accurate calculations in CFD and allied fields to practical applications. This will be a revolutionary departure from customary methods used in commercial software which bear all the limitations of their legacy, while aspiring to solve enormously larger and more complex problems. We believe that a successful implementation of the goals of this research will make a highly marketable product, as well as an invaluable research tool.