If rotational symmetry is important to the dynamics, you're likely to do much better on coarse grids with a hex layout, because it has a finer rotational symmetry.
Of course, with a small-enough grid rotational symmetry should be restored (or you've chosen a poor discretization!). One might rephrase your statement as: the lattice artifacts / discretization errors vanish faster on a hex grid. Could be.
When I worked on fire-spreading models [0] the grids we used were square. I would wager that this is because it makes thinking significantly easier. In my current field[1], square lattices are chosen because of the underlying supercomputing architecture. The communication mesh in tera- and petascale computers tend to be rectangular [2]. At these scales, having a nice rectangular layout of the local subvolumes simplifies communication algorithms and can provide a dramatic speedup---in this case having fewer neighbors is better.
[0]: In high school I implemented the fact that fires burn faster uphill while working for David Keyes on http://www.cs.cmu.edu/~caliente/
Of course, with a small-enough grid rotational symmetry should be restored (or you've chosen a poor discretization!). One might rephrase your statement as: the lattice artifacts / discretization errors vanish faster on a hex grid. Could be.
When I worked on fire-spreading models [0] the grids we used were square. I would wager that this is because it makes thinking significantly easier. In my current field[1], square lattices are chosen because of the underlying supercomputing architecture. The communication mesh in tera- and petascale computers tend to be rectangular [2]. At these scales, having a nice rectangular layout of the local subvolumes simplifies communication algorithms and can provide a dramatic speedup---in this case having fewer neighbors is better.
[0]: In high school I implemented the fact that fires burn faster uphill while working for David Keyes on http://www.cs.cmu.edu/~caliente/
[1]: Lattice QCD codes use a (4D spacetime) rectangular lattice https://usqcd-software.github.io/
[2]: The BlueGene/Q, for example, is a 5-dimensional rectangular torus.