Kanevsky, AlexCarpenter, Mark H.Gottlieb, DavidHesthaven, Jan S.2013-11-122013-11-122013-11-12200710.1016/j.jcp.2007.02.021https://infoscience.epfl.ch/handle/20.500.14299/96934WOS:000255304500029Despite the popularity of high-order explicit Runge-Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very stiff problems. We implement a discontinuous Galerkin finite element method (DGFEM) along with recently introduced high-order implicit-explicit Runge-Kutta (IMEX-RK) schemes to overcome geometry-induced stiffness in fluid-flow problems. The IMEX algorithms solve the non-stiff portions of the domain using explicit methods, and isolate and solve the more expensive stiff portions using an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta method (ESDIRK). Furthermore, we apply adaptive time-step controllers based on the embedded temporal error predictors. We demonstrate in a number of numerical test problems that IMEX methods in conjunction with efficient preconditioning become more efficient than explicit methods for systems exhibiting high levels of grid-induced stiffness. (c) 2007 Elsevier Inc. All rights reserved.high-orderdiscontinuous Galerkin finite element method (DGFEM)implicit-explicit (IMEX) methodNavier-Stokes equationsApplication of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemestext::journal::journal article::research article