Optimisation of numerical conditioning
Numerical conditioning is very important, especially when using single precision. There are several cases that have been shown in the literature where this plays an important role. First storing only the deviation from the equilibrium of the particle distributions of a lattice Boltzmann simulation instead of storing the equilibrium. Second in the advanced lattice Boltzmann methods like the cumulant LBM where it was shown that numerical conditioning is an extremely important task to get a stable simulation.
This task is very tedious and complicated. However, a starting point could be to look at pyinterval and investigate the error which comes from certain operations. This could lead to knowledge on minimizing errors arising from numerical methods.