Assessing the Recovery-based Discontinuous Galerkin Method for Turbulence Simulations

The Discontinuous Galerkin (DG) method offers significant advantages over traditional finite difference and finite volume methods, such as high parallel scalability, portability to complex geometries and super-convergence. However, DG has yet to emerge as a viable option for turbulence simulations, due to the lack of a consistent and accurate diffusion scheme. Currently, orders of $p+1$ are achieved, where $p$ is the polynomial order within a cell. A promising approach is that of recovery, which has been shown to exhibit convergence rates up to $3p+2$ in one dimension. This technique is based on the idea of enhanced recovery, where the underlying solution is recovered over neighboring cells and appropriately enhanced in the face-tangential directions. We use several test problems (pure diffusion, Taylor-Green vortex) to show that we achieve the same convergence rates in multiple dimensions, and compare this approach to other common diffusion schemes.