How to solve 1st step of semi implicit mtd
 

I'm trying to write a ns code using fractional step. I've read that most people use semi-implicit method ie CN2+AB2. AB2 requires info at 2 time steps. But in the beginning, how is the answer to the 1st step obtained?

Thank you

Re: How to solve 1st step of semi implicit mtd
 

In my very humble opinion...

You can use a 1st order method (forward Euler) in step 1 and then switch over to CN/AB2 in the following steps.

But,

maybe a better way is to just use an RK method for the whole simulation, (like TVD RK2) which doesn't rely on old time step info, is 2nd order accurate and has better stability properties.

Hope this helps

Re: How to solve 1st step of semi implicit mtd
 

Crank-Nicolson (CN) is for diffusion terms and better numerical statbility. TVD RK2 has worse stability, I do not recommend it for diffusion problems.

Re: How to solve 1st step of semi implicit mtd
 

Sorry, I didn't make it very clear in my first post.

You can do an operator split and treat the non-linear terms with TVD RK2 and the viscous terms with CN, because as Versi said you need to treat diffusion implicitly to get accetable stability.

There are loads of ways to do the time stepping though, so I'm not trying to say this is the "best" or anything although I would be interested to hear what other people do.

Darren

Re: How to solve 1st step of semi implicit mtd
 

Forward Euler is sufficient for starting a second order multistep method, because local error is second order.