Resolution and Boundary Placement Effects on Discontinuous Galerkin Simulations of Counter-rotating Vortex Interaction in a Confined Domain

Abstract

The wakes of fixed-wing and rotary-wing aircraft present some of the most complex and challenging problems for numerical simulation, as fully capturing the interaction of the various vortices and coherent structures requires immense computational power and time. With current methods, the cost of performing such simulations is prohibitive or even impossible, so it is thought that a more advanced and efficient algorithm is needed to make such investigations feasible now, rather than waiting for computational power to increase over time. One promising option that has the potential to provide such efficiency is the discontinuous Galerkin method.

The discontinuous Galerkin method is a locally conservative, robust, flexible, and high-order accurate numerical scheme. It is relatively new to applications in the field of computational fluid dynamics, so its sensitivity to certain parameter changes is not thoroughly documented. This work uses a test case of two-dimensional vortex interaction to catalogue the effects of varying resolution through the use of polynomial degree and cell density. The vortices are confined to a box with reflective boundaries, so the effect of moving the boundaries closer or further is also investigated while applying a new initialization to ensure an initial condition that is consistent with the boundary conditions. Changes are noted by considering comparisons of vortex trajectory and kinetic energy error for each case. The results present data for polynomials as high as 14th order and confirm that the method not only works with large cell sizes, but actually excels.