[aerosayan]

Taking a rocket's combustion chamber as an example : the scale of different fluid phenomenons happening inside the chamber are orders of magnitude different from each other. The whole combustion chamber + nozzle itself can be 1 m long, while the combustion and viscous effects are extremely small.

My question is, how do we represent this whole domain with a standard 64 bit floating point number? IIRC, In some astrophysics codes the scientists just use 128 bit floating point numbers because the scale is too large. But can't we do anything better?

If we take a quadtree grid to represent the whole domain, we can subdivide as much as we want but the cells will be so small that the physical properties like position, cell area, cell volume, cell surface areas, etc. will be less than machine epsilon for a 64 bit floating point number.

Can't we logically scale the smaller cells up (and make them 100, 1000, 10000 times larger), so we can do our simulation and then "somehow" combine the data back to the real values?

I think we can do that, since electrons are significantly small and quantum chemistry codes scale them up so the simulation can use a 64 bit floating point number. I'm not 100% sure how they do it, but it involves some form of non-dimensionalization and different scaling factors with which they multiply their different parameters.


Can we do something like this in CFD too? I don't know if someone already did this.