by Julius Donnert

Bug fixing the 2d and 3d code versions, I recently ran the famous Orszag-Tang Vortex test. This is a small simulation that showcases the transition of a flow to 2d MHD turbulence. Here is a screen shot of the simulation after some time with WENO5 (left) and TVD (right) :

It is a challenge to find differences between the two simulations (there are few though). However the WENO5 simulations has only half the resolution of the TVD run !

This nicely showcases the impact of increased algorithmic fidelity on fluid simulations. Even though a WENO5 timestep is nearly 4 times more expensive to compute than a TVD step (exact numbers to come, but likely 1 Million zones/sec/node on Broadwell), similar effective resolution is obtained at double the zone size.

In 3d this means that WENO5 is actually faster than TVD, if the quality of the solution is the only concern. TVD has a factor 8 more zones to compute, with twice as many time steps. The error introduced by finite precision reduces as well. Additionally, the data size goes down by a factor of 8, which makes post-processing simulations much easier.

We will argue in our paper that WENO5 represents an efficiency optimum for our type of simulations. Nonetheless one is usually bound by memory and runs the largest simulation that fits on the machine at hand. This is where scalability and vectorization come into play, but that is another blog entry ...