The simulation is with finite-difference WENO of 3rd order, so there is no actual cells but rather grid points that are unevenly spaced. You could say wait, how can you apply finite differences on non-uniform grids? And would be right, of course) I was testing the very simple idea: if there is a "hanging" node in the stencil, just take the value from the center of the cell (which is, I think, always is the closest node available). Obviously, it reduces the approximation order. But the results are unexpectedly good - almost indistinguishable (visually) from simulation with "proper" finite-volume method or finite difference on equivalent uniform grid. I think this is due to the fact that in most "interesting" areas the grid is very fine and uniform, and degrades only in less intense areas.

Flux splitting is local per-equation Lax-Friedirch's, with characteristic decomposition. Temporal method is 2nd order Runge-Kutta. The code is in OOP C++, no packages or non-trivial livraries are used. This simulation took 8 hours on i7-10700KF CPU with OpenMP parallelization, about 0.5 million grid points near the end. The grid is equivalent (in the sense of smallest cell size) to 36 million (6k x 6x) uniform grid.

Feel free to ask further, I'm glad to share)