A Unifying High-Order Method for the Navier-Stokes Equations on Hybrid Unstructured Meshes

Abstract : This final report documents the major developments and findings during the grant period from March 2009 to November 2012. The main objective of this project was to develop a new discontinuous formulation named correction procedure via reconstruction (CPR) for hyperbolic conservation laws, and demonstrate its capability for the Euler and Navier-stokes equations on hybrid 3D unstructured prismatic and tetrahedral grids. We achieved the following accomplishments: * Extended the CPR formulation to 3D hybrid meshes, including tetrahedral, hexahedral, prismatic elements; * Extended the CPR formulation to the Navier-Stokes equations on hybrid elements, and demonstrate the method for benchmark 3D problems; * Implemented the CPR method on clusters of CPUs and GPUs, and achieved up to two orders of magnitude speedup on the GPU than the CPU; * Extended the method for dynamic moving grids satisfying the so-called geometric conservation laws, and demonstrated the capability for bio-inspired flow problems; * Implemented solution-based hp-adaptations using a variety of adaptation criteria including residual, adjoint and entropy based adaptation criteria.