New Hybrid Runge-Kutta Methods for Unsteady Reactive Flow Simulation: Applications

The applicability is examined of the new hybrid Runge-Kutta methods derived in the companion paper by specifically analyzing both nonstiff and stiff system of equations that represent multidimensional reactive flows. In a reactive flow simulation, the standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system. The new hybrid Runge-Kutta schemes are suitable for this task because the time-step size is controlled by the Courant condition, whereas the stiffness is treated by an unconditionally stable method. This set of methods also meets the modern computing needs of high-order accuracy and low-storage requirement. A representative scheme is used to simulate a series of combustion problems that include model equations with stiff sources and multidimensional detonations with complex chemical kinetics