Abstract

This work presents a comparative study of different feature-based polynomial adaptation strategies for high-order unstructured methods applied to unsteady turbulent flows. Recently, the Flux Reconstruction (FR) approach has been introduced as a unifying framework for high-order unstructured spatial discretizations. To achieve high-order accuracy, FR utilizes an element-wise polynomial representation of the solution. In the current work, we consider three indicators for local adaptation of this polynomial degree. These are based on non-dimensional indicators that track the maximal vorticity norm, Frobenius norm of the velocity gradient, or eigenvalue modulus of the velocity gradient with respect to the effective maximal local grid spacing and free stream velocity. These feature-based methods are simple to implement and have the potential to track small-scale turbulent structures that arise in scale-resolving simulations, such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). The vorticity, gradient, and eigenvalue-based polynomial adaptation strategies with the FR approach are used to solve the compressible Navier-Stokes equations. DNS simulations are performed for unsteady laminar flow over a two-dimensional circular cylinder, turbulent flow over a three-dimensional sphere, and massively separated flow over a Martian helicopter rotor airfoil section. The results show a reduction in computational cost, with approximately one-quarter of the number of degrees of freedom relative to a non-adaptive case. The gradient-based method remains consistent for each numerical application, concluding to be the most well-suited feature-based indicator among the three considered.