370 RWTH Publication No: 230058        2013        IGPM370.pdf
TITLE A Temporally Adaptive Hybridized Discontinuous Galerkin Method for Instationary Compressible Flows
AUTHORS Alexander Jaust, Jochen Schütz
ABSTRACT The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to instationary problems can, e.g., be done by backward difference formulae (BDF) or diagonally implicit Runge-Kutta (DIRK) methods. In this publication, we investigate the use of embedded DIRK methods in an HDG solver, including the use of adaptive timestep control. Numerical results are shown that demonstrate the performance of the method for both linear and nonlinear (systems of) instationary convection-diffusion equations.
KEYWORDS hybridized discontinuous Galerkin, embedded diagonally implicit Runge-Kutta methods, instationary convection-diffusion equations
DOI 10.1016/j.compfluid.2014.01.019
PUBLICATION Computers & Fluids
Volume 98, 2 July 2014, Pages 177–185