Implicit-explicit Runge-Kutta methods for stiff combustion problems E. Lindblad 1 , D.M. Valiev 2 , B. M¨ uller 3 , J. Rantakokko 1 ,4 , P. L¨ otstedt 1 , and M.A. Liberman 5 1 Department of Information Technology, Uppsala University, Box 337, 751 05 Uppsala, Sweden 2 Materials Science and Engineering, KTH, 100 44 Stockholm, Sweden 3 Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes vei 2, 7491 Trondheim, Norway 4 UPPMAX, Uppsala University, Box 337, 751 05 Uppsala, Sweden 5 Department of Physics, Uppsala University, Box 530, 751 21 Uppsala, Sweden Summary. New high order implicit-explicit Runge-Kutta methods have been developed and implemented into a finite volume code to solve the Navier-Stokes equations for reacting gas mixtures. If only the stiff chemistry is treated implicitly, the linear systems in each Newton iteration are simple and solved directly. Numerical simulations of deflagration-to-detonation transition (DDT) show the potential of the new time integration for computational combustion. 1 Introduction The present work is aimed at gaining further understanding of the basic mechanisms controlling deflagration-to-detonation transition (DDT). The understanding of DDT is not only a major challenge of combustion theory, but also important for safety problems and for detonation propulsion engines. The Landau-Darrieus hydrodynamic flame insta- bility plays an important role. Friction and roughness of the tube walls make the flow ahead of the flame nonuniform and result in bending the flame front, which leads to flame acceleration. The accelerating reaction front acts as semitransparent piston, generating a pressure wave ahead. However, the acceleration is too weak to generate strong enough shock waves for triggering detonation. For a flame propagating from the closed end of a semi-infinite tube, it was recently shown that the formation of a preheat zone ahead of the flame is the basic physical mechanism of the deflagration-to-detonation transition, if the preheat zone is extended enough to provide a positive feedback for considerable enhancement of the flame acceleration [1]. Recent 2D studies [2, 3] of a flame propagating from the closed to the open end of a tube show that DDT occurs for a fast flame either due to preheat zone formed within the flame fold developed due to the Landau-Darrieus instability, when the influx of heat from the folded reaction zone increases temperature inside the fold or near the tube wall due to hydraulic resistance caused by the friction or roughness at the tube walls. The simulations [2] were performed using a parallel version of a general code developed by L.-E. Eriksson [4]. This code solves the Navier-Stokes equations for reacting gas mixtures using a third-order upwind-biased finite volume method for the inviscid fluxes and a second-order central discretization of the viscous fluxes with an explicit second order Runge-Kutta time integrator. Future additions include simulations in 3D, complex chemistry and the influence of turbulence. These additions increase the stiffness of the governing equations and therefore the time stepping method must be improved.