Is my equation stiff????

Mehdi Asghari

Hi all;

I want to solve following problem by a numerical method.

In a one-dimentional problem, particle velocity equation for particulated flows is given as follows:

D(Up)/Dt=Fd(Up-U);U =10+x;Up=dx/dt;

That Fd=18mu/ (dp*dp*ro_p*Cc) Cc=1+2l/dp*(1.257+0.4exp-(1.1dp/(2l)) Dp(particle diameter) is equal to 10 (micro meter) and 0.01(micro meter), respectively. Also, mu=0.001003,l=3e-10,ro_p=3900.

I used forth-order Runge-kutta method for solution. dt was suitable for dp=10(micro meter), but required dt for stability in dp=0.01(micro meter) was very small. This dt was so small that solution became impossible. Is his equation stiff? Is there a logical numerical method instead of forth-order runge-kutta method to be solved this problem?

Thanx in advance for any suggestion.