Transonic flow analysis with discontinuous Galerkin method in SU2 DG-FEM solver

Abstract

Numerical simulations of fluid flows of interest to the aerospace community must always strike a balance between the accuracy of the results and the computational cost required to obtain them. Traditional second-order accurate numerical schemes have been successful in providing reliable solutions of reasonable accuracy at modest computational costs. However, such low-order methods may not be sufficient to resolve highly-dynamic flows with localized flow features such as vortices and discontinuities that can exist for long distances. For these reasons, researchers have sought to develop higher-order methods (higher than second-order accuracy in space) which can both provide accurate solutions and are computationally feasible. Because of its high arithmetic intensity and data locality, the discontinuous Galerkin (DG) method has become popular among several candidates for higher-order solutions. Although the DG method has numerous benefits to exploit, most researchers hesitate to use it in transonic flow analysis for several reasons. Firstly, transonic flows typically include the appearance of shock waves. If a DG method cannot properly capture the shocks, accuracy may be lost and in the worst case, the simulation may diverge. Secondly, a shock-capturing capability is rarely included with solvers which are based on DG discretizations. To address these issues, in our prior work we have suggested a simple shock detector and a resolving/filtering method to capture shocks within the framework of DG discretizations up to a polynomial order of four (p=4, formally fifth-order accurate in smooth flows). Since we have developed a new discontinuous Galerkin finite element method (DG-FEM) solver within the open-source SU2 framework during the past two years, we have implemented the shock-capturing capability in this solver. In this paper we present the shock-capturing capabilities of the SU2 DG-FEM solver and focus on the analysis of the transonic flow over a NACA0012 airfoil using the two-dimensional Euler equations. This allows us to compare the outcome of our higher-order transonic simulations to efforts published in the literature for the same test cases using a variety of lower-order solvers.