|Preprint-No.:||< 399 >||Published in:||July 2014||PDF-File:||IGPM399.pdf|
|Title:||A Hybridized Discontinuous Galerkin Method for Unsteady Flows with Shock-Capturing|
|Authors:||Alexander Jaust, Jochen Schütz, Michael Woopen|
We present a hybridized discontinuous Galerkin (HDG) solver for the time-dependent compressible Euler and Navier-Stokes equations. In contrast to discontinuous Galerkin (DG) methods, the number of globally coupled degrees of freedom is usually tremendously smaller for HDG methods, as these methods can rely on hybridization. However, apply- ing the method to a time-dependent problem amounts to solving a differential-algebraic nonlinear system of equations (DAE), rendering the problem extremely stiff. This implies that implicit time discretization has to be used. Suited methods for the treatment of these DAEs are, e.g., diagonally implicit Runge-Kutta (DIRK) methods, or the backward differ- entiation formulas (BDF). In order to solve a wide range of problems in an efficient manner, we employ adaptive time stepping using an embedded error estimator. Additionally, we investigate the use of artiﬁcial viscosity for shock-capturing in this setting, and we propose a new strategy of coarsening the mesh using non-standard polygonal elements.
|Keywords:||hybridized discontinuous Galerkin, instationary convection-diffusion equations, shock-capturing, mesh adaptation|
|Publication:||AIAA Paper 2014-2781|
AIAA Aviation, 44th AIAA Fluid Dynamic Conference
American Institute of Aeronautics and Astronautics , 2014