High Performance Adaptive Finite Element Methods : With Applications in Aerodynamics

The massive computational cost for resolving all scales in a turbulent flow makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized by adaptively resolution of the mesh, based on a posteriori error estimation. Such adaptive methods have previously been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method that enables efficient computation of time resolved approximations of turbulent flow for complex geometries with a posteriori error control. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallelization of local mesh refinement methods such as recursive longest edge bisection, and the development of an a priori predictive dynamic load balancing method, based on a weighted dual graph. We also address the challenges of emerging supercomputer architectures with the development of new hybrid parallel programming models, combining traditional message passing with lightweight one-sided communication. Our implementation has proven to be both general and efficient, scaling up to more than twelve thousands cores.