Max time step for semi-implicit mtd

zonexo

hello,

I've coded a 2d structured FVM fractional step NS solver. It's fully implicit (using CN2). It worked fine. Now I've modified it to be semi implicit (using CN2 for diffusive, AB2 for convective).

I know max CFL <=1 for semi-implicit mtd. In the mtd I've used, it was given CFL = max(|u(i)|(delta_t/delta_x(i)) ~ 1. However, it was given for cartesian grids. I've tried to use replace delta_x(i) with the quadrilateral's edge length.

The prob is for very small time step (CFL<<1), both give pretty similar results. However, for reasonable time step (CFL~1) and long duration, errors start appearing for the semi-implicit mtd.

Btw, I'm simulating flow past an airfoil at 0deg AOA at Re=10. So is this an inherent limitation of the semi-implicit mtd or it's due to my own errors?

Thanks