6 ms·

Fluid Simulation (2007) [pdf]

54 points by strangecasts 8y ago

mishurov 8y ago
They wrote a book based on that course and notes. https://www.cs.ubc.ca/~rbridson/fluidsimulation/ https://www.cs.ubc.ca/~rbridson/fluidsimulation/ It's for computer graphics. Fluid simulation for, for example, simulating air pressure on an aircraft in development is more precise and numerical methods are more complex.
- slavik81 8y ago
  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? What does the CFD community do? Something like the Finite Element Method? I sat in on a grad course on continuum mechanics from the mech eng. department, but we never strayed from abstract mathematics.
  - lasagnaphil 8y ago
    In CG fluid simulations, one either use grid-based Eulerian methods (Bridson’s book uses a thing called a MAC grid), or use particled-based Lagrangian methods such as SPH (smoothed particle hydrodynamics). They all use the Navier-Stokes equations and the incompressibility condition; the difference is how you approximate it (with tradeoff between realism/performance). Each method has its own quirks (such as the PIC method suffering from unwanted viscosity, and FLIP suffering from numerical instability.) Nowadays the grid-based people use APIC a lot, because it seems to solve both the disadvantages of the two (you can see the links in the comment above)
    - pilooch 8y ago
      There's a new trend of using deeplearning to replace and mix the solvers. Some ongoing research looks at tackling the compressible flows. Accelerating lattice boltzman methods with DL is also under study at various labs. See https://github.com/jolibrain/fluidnet_cxx https://github.com/jolibrain/fluidnet_cxx for a reimplementation of fluidnet with aten/Pytorch tensors. The literature on DL + cfd is growing steadily with some interesting papers at machine learning conferences. We are seeing the first set of applications in industry as well, very exciting !
      - btrettel 8y ago
        Fluid dynamicist here. I wasn't aware of the machine learning work you've mentioned. They're addressing an important problem, but I'm disappointed in the paper based on a brief look. I see no comparison against experimental data (validation). Indeed, the cases the authors compute most likely have no corresponding experiments, but do look cool. I'd recommend that the authors learn more about verification, validation, and uncertainty quantification for fluid dynamics. And I'd encourage all machine learning folks approaching CFD to present your work at both fluids and machine learning conferences. I think problems like this would be reduced or fixed entirely by more interactions with fluid dynamicists. Another smaller recommendation. What they call a "MAC grid" is called a staggered grid or mesh by CFD folks in my experience, so it might be better to use this terminology instead. The reference they cite is also out of date. I'd recommend something like this instead: https://www.sciencedirect.com/science/article/pii/S0021999198959629 https://www.sciencedirect.com/science/article/pii/S002199919... This newer paper has higher order extensions of the method the 1965 paper uses and as I recall goes into much more detail about the properties of the schemes.
        pilooch 8y ago
        There are many recent works originating from the CFD community now. Too many to list here, you can PM me if you don't find them easily online for some reason.
    - deleted 8y ago
      [deleted]
  - proginthebox 8y ago
    In short, the two fields just look similar, but are actually extremely different fields. Physical simulations need to preserve entropy, maximum principle, energy conservation and other kinds of conservation, preservation of consistent states, convergence in case of finer mesh. There are multiple equations which model different forms of fluid: 1. Incompressible Euler (For liquid) 2. Compressible Euler (For non-viscous gases) 3. Navier Stokes Equations (For viscous liquids) There are multiple solver methods: 1. Finite Difference 2. Finite Element 3. Discontiguous Galerkin Finite Element 4. Finite Volume Method There are multiple equation methods: 1. equation splitting is just one of the many methods possible. Just because the equation is unique does not mean that the solution is unique. Single equation provably have multiple and even infinite solution for the same initial condition. Computer graphics fluid simulation does not care (with a good reason) about this and hence, often their simulations even though they look kind of nice, are often incorrect since they do not demonstrate various physical characteristics that must be preserved. In contrast, the qualitative/quantitative constraint in physical simulations are very strict. You need to know a lot of theoretical math to even understand if you are even computing the correct solution.
  - btrettel 8y ago
    > 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.
    - slavik81 8y ago
      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. [1]: https://royalsocietypublishing.org/doi/abs/10.1098/rspl.1883.0018 https://royalsocietypublishing.org/doi/abs/10.1098/rspl.1883...
slavik81 8y ago
I worked through these course notes with my lab last year. As someone else commented, Bridson expanded these notes into a book, "Fluid Simulation for Computer Graphics." The first edition is basically the free PDF with fixes for things like typos (e.g. the unlabeled variable, rho, in the Conjugate Gradient algorithm). Robert Bridson does a great job on explaining fluid concepts, and there's a useful appendix on the basics of vector math, but it's definitely still a lot of work to build up a good understanding of the equations. I own the second edition of the book, released in 2015, though I haven't read too much of it, as I already went through the first in detail. However, I did notice that the second edition emphasizes some important points that were a little subtle in the first edition. That would have made implementing it easier [1]. The other thing about the second edition is that fluid simulation has advanced since 2007. The foundations are still the same, and the pressure solve remains unchanged, but advection has been made both simpler to implement and more accurate by using a particle representation for that portion of the algorithm. IIRC, the 2nd edition covers FLIP, which is one of those newer techniques, though not the most current. The APIC paper[2] was also released in 2015 (with a video [3]), and it was a bit of a breakthrough. APIC is pretty much better in every way. Fortunately, Bridson's book prepares you well for reading the APIC paper (which assumes you know the standard fluid simulation techniques already). In short: this free material is a great introduction to fluid simulation. If you want to implement your own simulation, read the second edition of the book, then read the APIC paper. [1]: The greatest weakness of the notes/book IMO, was the lack of a reference implementation. I never got around to cleaning up the code after I got it working, but here's my implementation. Please forgive the mess: https://github.com/cgmb/euler https://github.com/cgmb/euler [2]: The affine particle-in-cell method (2015) - https://disney-animation.s3.amazonaws.com/uploads/production/publication_asset/104/asset/apic-aselle-final.pdf https://disney-animation.s3.amazonaws.com/uploads/production... [3]: https://youtu.be/rPPW_1M8nRA https://youtu.be/rPPW_1M8nRA
fallingfrog 8y ago
I created a fluid simulation in unity last year, with the goal being to use it to simulate flowing flames. I had to write my own fft on the gpu to get it to work. You can see the results here: https://m.youtube.com/watch?v=KcLz3yAqqyI https://m.youtube.com/watch?v=KcLz3yAqqyI https://m.youtube.com/watch?v=jWu7yWw_jBQ https://m.youtube.com/watch?v=jWu7yWw_jBQ https://m.youtube.com/watch?v=G9l1PP0-rDY https://m.youtube.com/watch?v=G9l1PP0-rDY It’s up on the unity asset store too under “physics based flames”. I was thinking about doing a writeup on it for hn since it was a pretty interesting journey making it..
VRay 8y ago
I slogged through implementing this for a game earlier this year. Man oh man, I bit off way more than I could chew comfortably.. I know this is well known among scientists and a lot of software engineers, and I should have remembered it from my math classes in college, but: It was new to me that just because you have a set of differential equations, a computer, and (relatively) unlimited time to evaluate them doesn't mean you can get a useful or stable solution I eventually got it working thanks to the book by Bridson and Müller-Fischer and a few other papers I read through, but it took about 5 times as long to implement as I expected. Also I couldn't use it in my game, since I couldn't figure out how to handle my special boundary conditions and ran out of time, so there were a lot of situations where the water in the game would explode and fly everywhere. Hoo whee
- lasagnaphil 8y ago
  Yep, Eulerian fluid simulations are pretty hard to control. I’ve also tried implementing a fluid sim for my undergraduate thesis (mainly looking at the Bridson book), but you have to play around with the parameters a lot to get a smooth result. Fiddling with timestep size, handling numerical instability, etc... I think that is why games use particle-based methods a lot more, because it is less finicky and works better in extreme conditions (well, the players seem to really love doing extreme things in the game...)

54 points by strangecasts 8y ago

They wrote a book based on that course and notes. https://www.cs.ubc.ca/~rbridson/fluidsimulation/ https://www.cs.ubc.ca/~rbridson/fluidsimulation/ It's for computer graphics. Fluid simulation for, for example, simulating air pressure on an aircraft in development is more precise and numerical methods are more complex.

slavik81 8y ago
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? What does the CFD community do? Something like the Finite Element Method? I sat in on a grad course on continuum mechanics from the mech eng. department, but we never strayed from abstract mathematics.
- lasagnaphil 8y ago
  In CG fluid simulations, one either use grid-based Eulerian methods (Bridson’s book uses a thing called a MAC grid), or use particled-based Lagrangian methods such as SPH (smoothed particle hydrodynamics). They all use the Navier-Stokes equations and the incompressibility condition; the difference is how you approximate it (with tradeoff between realism/performance). Each method has its own quirks (such as the PIC method suffering from unwanted viscosity, and FLIP suffering from numerical instability.) Nowadays the grid-based people use APIC a lot, because it seems to solve both the disadvantages of the two (you can see the links in the comment above)
  - pilooch 8y ago
    There's a new trend of using deeplearning to replace and mix the solvers. Some ongoing research looks at tackling the compressible flows. Accelerating lattice boltzman methods with DL is also under study at various labs. See https://github.com/jolibrain/fluidnet_cxx https://github.com/jolibrain/fluidnet_cxx for a reimplementation of fluidnet with aten/Pytorch tensors. The literature on DL + cfd is growing steadily with some interesting papers at machine learning conferences. We are seeing the first set of applications in industry as well, very exciting !
    - btrettel 8y ago
      Fluid dynamicist here. I wasn't aware of the machine learning work you've mentioned. They're addressing an important problem, but I'm disappointed in the paper based on a brief look. I see no comparison against experimental data (validation). Indeed, the cases the authors compute most likely have no corresponding experiments, but do look cool. I'd recommend that the authors learn more about verification, validation, and uncertainty quantification for fluid dynamics. And I'd encourage all machine learning folks approaching CFD to present your work at both fluids and machine learning conferences. I think problems like this would be reduced or fixed entirely by more interactions with fluid dynamicists. Another smaller recommendation. What they call a "MAC grid" is called a staggered grid or mesh by CFD folks in my experience, so it might be better to use this terminology instead. The reference they cite is also out of date. I'd recommend something like this instead: https://www.sciencedirect.com/science/article/pii/S0021999198959629 https://www.sciencedirect.com/science/article/pii/S002199919... This newer paper has higher order extensions of the method the 1965 paper uses and as I recall goes into much more detail about the properties of the schemes.
      - pilooch 8y ago
        There are many recent works originating from the CFD community now. Too many to list here, you can PM me if you don't find them easily online for some reason.
  - deleted 8y ago
    [deleted]
- proginthebox 8y ago
  In short, the two fields just look similar, but are actually extremely different fields. Physical simulations need to preserve entropy, maximum principle, energy conservation and other kinds of conservation, preservation of consistent states, convergence in case of finer mesh. There are multiple equations which model different forms of fluid: 1. Incompressible Euler (For liquid) 2. Compressible Euler (For non-viscous gases) 3. Navier Stokes Equations (For viscous liquids) There are multiple solver methods: 1. Finite Difference 2. Finite Element 3. Discontiguous Galerkin Finite Element 4. Finite Volume Method There are multiple equation methods: 1. equation splitting is just one of the many methods possible. Just because the equation is unique does not mean that the solution is unique. Single equation provably have multiple and even infinite solution for the same initial condition. Computer graphics fluid simulation does not care (with a good reason) about this and hence, often their simulations even though they look kind of nice, are often incorrect since they do not demonstrate various physical characteristics that must be preserved. In contrast, the qualitative/quantitative constraint in physical simulations are very strict. You need to know a lot of theoretical math to even understand if you are even computing the correct solution.
- btrettel 8y ago
  > 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.
  - slavik81 8y ago
    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. [1]: https://royalsocietypublishing.org/doi/abs/10.1098/rspl.1883.0018 https://royalsocietypublishing.org/doi/abs/10.1098/rspl.1883...

slavik81 8y ago

I worked through these course notes with my lab last year. As someone else commented, Bridson expanded these notes into a book, "Fluid Simulation for Computer Graphics." The first edition is basically the free PDF with fixes for things like typos (e.g. the unlabeled variable, rho, in the Conjugate Gradient algorithm). Robert Bridson does a great job on explaining fluid concepts, and there's a useful appendix on the basics of vector math, but it's definitely still a lot of work to build up a good understanding of the equations. I own the second edition of the book, released in 2015, though I haven't read too much of it, as I already went through the first in detail. However, I did notice that the second edition emphasizes some important points that were a little subtle in the first edition. That would have made implementing it easier [1]. The other thing about the second edition is that fluid simulation has advanced since 2007. The foundations are still the same, and the pressure solve remains unchanged, but advection has been made both simpler to implement and more accurate by using a particle representation for that portion of the algorithm. IIRC, the 2nd edition covers FLIP, which is one of those newer techniques, though not the most current. The APIC paper[2] was also released in 2015 (with a video [3]), and it was a bit of a breakthrough. APIC is pretty much better in every way. Fortunately, Bridson's book prepares you well for reading the APIC paper (which assumes you know the standard fluid simulation techniques already). In short: this free material is a great introduction to fluid simulation. If you want to implement your own simulation, read the second edition of the book, then read the APIC paper. [1]: The greatest weakness of the notes/book IMO, was the lack of a reference implementation. I never got around to cleaning up the code after I got it working, but here's my implementation. Please forgive the mess: https://github.com/cgmb/euler https://github.com/cgmb/euler [2]: The affine particle-in-cell method (2015) - https://disney-animation.s3.amazonaws.com/uploads/production/publication_asset/104/asset/apic-aselle-final.pdf https://disney-animation.s3.amazonaws.com/uploads/production... [3]: https://youtu.be/rPPW_1M8nRA https://youtu.be/rPPW_1M8nRA

fallingfrog 8y ago

I created a fluid simulation in unity last year, with the goal being to use it to simulate flowing flames. I had to write my own fft on the gpu to get it to work. You can see the results here: https://m.youtube.com/watch?v=KcLz3yAqqyI https://m.youtube.com/watch?v=KcLz3yAqqyI https://m.youtube.com/watch?v=jWu7yWw_jBQ https://m.youtube.com/watch?v=jWu7yWw_jBQ https://m.youtube.com/watch?v=G9l1PP0-rDY https://m.youtube.com/watch?v=G9l1PP0-rDY It’s up on the unity asset store too under “physics based flames”. I was thinking about doing a writeup on it for hn since it was a pretty interesting journey making it..

VRay 8y ago

I slogged through implementing this for a game earlier this year. Man oh man, I bit off way more than I could chew comfortably.. I know this is well known among scientists and a lot of software engineers, and I should have remembered it from my math classes in college, but: It was new to me that just because you have a set of differential equations, a computer, and (relatively) unlimited time to evaluate them doesn't mean you can get a useful or stable solution I eventually got it working thanks to the book by Bridson and Müller-Fischer and a few other papers I read through, but it took about 5 times as long to implement as I expected. Also I couldn't use it in my game, since I couldn't figure out how to handle my special boundary conditions and ran out of time, so there were a lot of situations where the water in the game would explode and fly everywhere. Hoo whee

lasagnaphil 8y ago
Yep, Eulerian fluid simulations are pretty hard to control. I’ve also tried implementing a fluid sim for my undergraduate thesis (mainly looking at the Bridson book), but you have to play around with the parameters a lot to get a smooth result. Fiddling with timestep size, handling numerical instability, etc... I think that is why games use particle-based methods a lot more, because it is less finicky and works better in extreme conditions (well, the players seem to really love doing extreme things in the game...)