Semi-implicit Runge-Kutta

Bobby

Hi, everyone,

I am doing LES of jet diffusion flames. The problem I face now is the reaction terms in the energy equation (finite rate chemistry is adopted in my code), which make the equation a stiff system. Because the low-storage third-order Runge-Kutta method developed by Williamson has been used, it's preferrable for me to stick with higher-order Runge-Kutta method, but perhaps to fully solve this problem, I need to use some semi-implicit Runge-Kutta method, the implicit algorithm to handle the stiff reaction term. Now, I can find some references on semi-implicit RK methods, but cannot find any practical applications. The first thing I am worrying about is the feasibility of such semi-implicit RK method in practical LES, i.e. the additional simulation time needed in comparison with the fully explicit RK methods. For example, my current grid system looks like 40*90*150 (100*100*200 would be expected in future simulations), compact FD schemes are used in spatial discretization. To reach nondimensional time t=100 with 32 processors of a modern pc cluster, I need about 24 hours, which is not bad for me. So how about the situation with the semi-implicit RK method? Do I need 2 days, 1 week or even longer ... , to finish one case? Any experienced statements on this respect is very welcome. And if you have other ideas to handle the reaction term, please also give some advice. Thanks a lot.