We currently do the solid lines for horizontal diffusion of vorticity and divergence which change shape with higher resolution (hence the time scale is adapted to compensate that somehow)
I believe a more scale-selective diffusion just via a spectral filter might avoid overly diffusive simulations while efficiently taking out power at high wavenumbers, like the dashed lines above, which were created with
with parameters $k = 0$ (the shift, for k=-5 the 5th highest wavenumbers is dampened like the highest wavenumber with $k=0$) and the stretch $s = 0.12$ which controls the scale-selectiveness, ($s=0.7$ is more like a biharmonic Laplacian, etc.)
Coded like
using SpecialFunctions
T = 31
l = 0:T
s = 0.05
k = 0
1/2 * (erfc(s*(l - T - k)))
We currently do the solid lines for horizontal diffusion of vorticity and divergence which change shape with higher resolution (hence the time scale is adapted to compensate that somehow)
I believe a more scale-selective diffusion just via a spectral filter might avoid overly diffusive simulations while efficiently taking out power at high wavenumbers, like the dashed lines above, which were created with
$$ K(l) = \frac{1}{2} (1 - \text{erf}(s(l - T - k)))$$
with parameters $k = 0$ (the shift, for k=-5 the 5th highest wavenumbers is dampened like the highest wavenumber with $k=0$) and the stretch $s = 0.12$ which controls the scale-selectiveness, ($s=0.7$ is more like a biharmonic Laplacian, etc.)
Coded like
(
erfc = 1 - erf)