Vorticity-based polynomial adaptation for moving and deforming domains

Abstract

This paper introduces a novel non-dimensional vorticity-based polynomial adaptation indicator for moving and deforming domains using a high-order unstructured spatial discretization. We verify the utility of this approach when applied to the Arbitrary Lagrangian–Eulerian (ALE) form of the compressible Navier–Stokes equations for a range of applications on moving and deforming domains. Specifically, we verify the ALE implementation by performing simulations of an Euler Vortex (EV), and then, illustrate the accuracy and efficiency of the adaptation routine by performing simulations of flow over an oscillating circular cylinder with two different flow settings, dynamic stall of a 2D NACA 0012 airfoil undergoing heaving and pitching motions, shallow dynamic stall of a 3D SD 7003 airfoil undergoing heaving and pitching motions, and flow over a Vertical Axis Wind Turbine (VAWT) composed of two NACA 0012 airfoils. Results demonstrate that the non-dimensional vorticity indicator can track regions of interest, such as vortices and boundary layers, and yields a significant reduction in degrees of freedom when paired with polynomial adaptation.