Usually the time discretation scheme in SIMPLE-like algorithms is the first-order implicit Euler method.

Could you recommend some time discretation schemes with the second or higher-order accuracy that can be used in SIMPLE-like algorithms?

Thanks!

STAR-CD uses Crank-Nicholson with SIMPLE for second order time accuracy.

I have seen two schemes with high-order accuracy in SIMPLE, the Crank-Nicholson, which you have refered to, and three time level method.

Could some more schemes be introduced except the two mentioned above?

Thanks!