Solution of the 3D unsteady incompressible Navier-Stokes equations on adaptively refined grids : Challenges and Insights

Dionysios Angelidis, Computational Fluid Dynamics (CFD) Applied Program Leader, St. Anthony Falls Laboratory, University of Minnesota

Multi-resolution simulations coupled with an immersed boundary method constitutes a powerful framework for high-fidelity calculations, across a range of Reynolds numbers, with low computational cost. Nevertheless, most of the adaptive mesh refinement (AMR) incompressible flow solvers are either low-order accurate or algorithmically complex in order to satisfy the divergence free constraint.
The seminar will investigate the algorithmic strategies adopted in conventional AMR solvers. I will focus on presenting a novel numerical method for solving the 3D, unsteady, incompressible Navier–Stokes equations on locally refined fully unstructured Cartesian grids, in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries.
Several challenging examples including large-eddy simulations (LES) past wind turbines, geometry resolving LES past complete hydrokinetic turbines and two-phase turbulent flows will illustrate the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. Emphasis will also be given on the challenges and state-of-the-art strategies for performing massively parallel calculations on adaptively refined grids.