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

摘要

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.