On the Application of the Discontinuous Galerkin Method to Turbomachinery Flows

Abstract

This article describes the development of a Discontinuous Galerkin (DG) solver for 2D Euler flows with special emphasis on the implementation of robust and accurate boundary conditions for turbomachinary applications. For curved solid wall boundaries an extension of the standard linear element representation is implemented and shown to eliminate the spurious generation of entropy. Furthermore, we address the typical problem of numerical reflections arising due to the proximity of the domain boundaries to the airfoils in turbomachinary configurations. The exact two-dimensional non-reflecting entry and exit boundary conditions are integrated into the DG framework. The results demonstrate that using high-order DG discretisation schemes in combination with appropriate non-reflecting boundary conditions accurate predictions of turbomachinery flows can be obtained on coarse grids with artificial boundaries close to the blades.