High performance adaptive finite element methods for turbulent fluid flow

Abstract: Understanding the mechanics of turbulent fluid flow is of key importance for industry and society as for example in aerodynamics and aero-acoustics. The massive computational cost for resolving all turbulent scales in a realistic problem makes direct numerical simulation of the underlying Navier-Stokes equations impossible. 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 where the mesh is adaptively resolved, based on a posteriori error control. These adaptive methods have 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 for modern parallel computer architectures. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallellization of local mesh refinement methods such as recursive longest edge bisection.We also address the load balance problem with the development of an a priori predictive dynamic load balancing method. Current results are encouraging with almost linear strong scaling to thousands of cores on several modern architectures.