by Julius Donnert

I have been experimenting with CT schemes in our new WENO5 implementation into WOMBAT. We already had the simple CT implementation from Ryu et al 1998, which is second order and not computationally very intensive. In second order codes, a high order upwinded CT scheme is essential to get magnetic field advection right. So I implemented the Lee 2013 scheme, which is an upwinded version of his excellent high order scheme. Given that cosmological simulations are all about advection and isotropy at insane density contrasts, it is a good idea to make sure the code handles this situation accurately.

Here is a video of the magnetic field loop advection in 2d with TVD (Mendygral+ 2017), WOMBAT WENO5 with second order CT and WOMBAT WENO5 with upwinded high order CT like Lee 2013.

As you can see the simple CT scheme performs as well as the high order scheme that costs significantly more flops. There certainly is room for improvement, but the code outperforms Lee's implementation in FLASH already with the low order scheme.

We are running the CT scheme at every sub-step of the RK4 time integrator, so my guess is the simple estimate from Ryu's scheme is just good enough to get a non-diffusive field. With these results I won't even test 3D leave a higher order CT scheme for a future paper. We would have the flops to spare, but at the moment its just not worth it.