Stability Condition for Immersed Boundary Method

Dave Rudolf

Hey all,

I have a very naive forward-Euler implementation of the Peskin's immersed boundary (IB) method. I would like to be able to use adaptive time steps with this system. However, the standard Courant stability condition seems to over-estimate the step size that I can use. This makes sense, since apparently the IB formulation is much more stiff than regular grid-based Navier-Stokes solvers.

So, I'm trying to find information about what kind of stability condition to use. I have looked around the research literature, and found a lot of info about how certain time-stepping schemes are better than others, and plots of the stability regions, etc. However, I haven't seen a formula (like the Courant condition) for computing an acceptable step size.

So, can anyone nudge me in the right direction?

Thanks.