High-order modeling of applied multi-physics phenomena

A new physics-based simulation capability will be developed based on high-order discretizations in both space and time for application to practical engineering problems involving complex physical phenomena and complicated geometries. The goal is to develop a tool which can accurately handle simulations of various important physical problems relevant to the aerospace industry and the DoD, including computational fluid dynamics, aeroacoustics, and electromagnetics, both in analysis mode, and for design optimization purposes. The approach will rely on high-order (up to 6th order) Discontinuous Galerkin discretizations in space and second-order backwards difference as well as higher-order (up to 5th order) implicit Runge-Kutta temporal discretizations. Efficient solution techniques will be employed in order to make these methods competitive with current simulation tools in terms of required computational resources. Adaptive methods based on both mesh (h)-refinement and discretization order (p)-enrichment will be incorporated in order to achieve high accuracy at optimal cost. The favorable asymptotic properties of these methods, combined with the use of unstructured meshes, will enable accurate simulation of complex phenomena with wide ranges of scales from first principles. BENEFIT: The use of high-order methods will deliver much higher accuracy for complex multiscale problems while using coarser underlying grids. This in turn will reduce discretization errors to manageable levels, providing superior reliability in numerical analysis and optimization problems, while at the same time relieving the grid generation bottleneck for high resolution calculations, and enhancing scalability on massively parallel multi-core architectures. Commercial applications exist in computational fluid dynamics, particularly for difficult problems involving wakes or vortical flows such as rotorcraft and high incidence maneuvering aircraft, as well as other areas such as aeroacoustics and electromagnetics.