Implicit-explicit Runge-Kutta method for combustion simulation
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Abstract
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. The resulting nonlinear systems in each stage are solved by Newtons method. If only the chemistry is treated implicitly, the linear systems in each Newton iteration are simple and solved directly. If in addition certain convection or diffusion terms are treated implicitly as well, the sparse linear systems in each Newton iteration are solved by preconditioned GMRES. Numerical simulations of deflagration-to-detonation transition (DDT) show the potential of the new time integration for computaional combustion.