> I'm kind of curious about those models. Are there any major differences aside from the assumption of incompresssibility? I suppose they probably don't do equation splitting either?
Other folks have already discussed differences in numerical methods, so I'll discuss the other major difference: turbulence modeling.
I don't think that turbulence modeling is addressed in computer graphics, as physical accuracy does not seem to be a major priority. The word "turbulence" or variants of it does not seem to be in the linked notes.
From an equations perspective, the "raw" Navier-Stokes equations are used for "direct numerical simulation" (DNS). The resolution requirements (e.g., grid size and time step) to accurately simulate turbulent flows makes the computational cost very high for all but the most trivial flows. Using a larger grids and time steps reduces the accuracy far too much. So instead of solving the Navier-Stokes equations, typically one of two different sets of equations that are derived from the Navier-Stokes equations are solved. These are the Reynolds-averaged Navier-Stokes equations (RANS equations; a statistical approach) dating back to the 19th century and the Large eddy simulation (LES; applying spatial filters instead of averages) equations, dating back to the 1960s. The RANS equations compute time or "ensemble" averaged quantities typically. The LES equations compute a filtered version of the fields, including only the large scales on the grid. These equations have lower computational requirements, but include new "unclosed" terms that require modeling. LES is typically viewed as more credible, though in my experience RANS computes the quantities you typically want. Well designed LES schemes will converge to DNS as the grid is refined; this is not true for RANS.
Turbulence modeling unfortunately has not proved to be as successful as it needs to be. Turbulence modeling might be impossible in some sense, as there's no reason to believe that the information one has available can be used to estimate the information one needs to accurately model turbulence. I view these models as requiring empirical data and not generalizing well.
Thank you very much for this response. I found it helpful.
I've been reading some of the research papers on waves and fluids from the late-1800s. One I went through a couple weeks ago was Reynold's 1883 paper on turbulent flow [1]. It's interesting going through old papers. They're a lot more casual and meandering than modern ones, and I feel like I get more insight into how the sausage is made that way.
I still wonder about some things, though. I'm familiar with the main CG fluid techniques, and it seems that they are used in real scientific simulations on occasion. For example, Smoothed-Particle Hydrodynamics have been used in ocean wave simulations, and they appear to validate against wave tank experiments. I actually was going to use them myself for simulations of wave-swept environments.
But, aside from bumping into Bridson at a conference, I haven't gotten many chances to speak to someone who really knows fluids well. I was wondering if you'd be willing to answer some more questions of mine about how the CG methods compare to DNS, LES and RANS. If so, send me an email and maybe we can chat about it. My address is just my HN username at gmail.com.
Other folks have already discussed differences in numerical methods, so I'll discuss the other major difference: turbulence modeling.
I don't think that turbulence modeling is addressed in computer graphics, as physical accuracy does not seem to be a major priority. The word "turbulence" or variants of it does not seem to be in the linked notes.
From an equations perspective, the "raw" Navier-Stokes equations are used for "direct numerical simulation" (DNS). The resolution requirements (e.g., grid size and time step) to accurately simulate turbulent flows makes the computational cost very high for all but the most trivial flows. Using a larger grids and time steps reduces the accuracy far too much. So instead of solving the Navier-Stokes equations, typically one of two different sets of equations that are derived from the Navier-Stokes equations are solved. These are the Reynolds-averaged Navier-Stokes equations (RANS equations; a statistical approach) dating back to the 19th century and the Large eddy simulation (LES; applying spatial filters instead of averages) equations, dating back to the 1960s. The RANS equations compute time or "ensemble" averaged quantities typically. The LES equations compute a filtered version of the fields, including only the large scales on the grid. These equations have lower computational requirements, but include new "unclosed" terms that require modeling. LES is typically viewed as more credible, though in my experience RANS computes the quantities you typically want. Well designed LES schemes will converge to DNS as the grid is refined; this is not true for RANS.
Turbulence modeling unfortunately has not proved to be as successful as it needs to be. Turbulence modeling might be impossible in some sense, as there's no reason to believe that the information one has available can be used to estimate the information one needs to accurately model turbulence. I view these models as requiring empirical data and not generalizing well.