[ Fluid Simulation Internship ]
During my six-month NII International Internship Program 2020, supervised by Ryoichi Ando, I studied research papers on fluid simulation and implemented a Navier-Stokes fluid solver from scratch in C++ and OpenGL. I started with smoke simulation and gradually evolved it toward liquid simulation.
Here's a summary of what I worked on:
- Advection: Semi-Lagrangian scheme and MacCormack method
- Projection: Pressure solver with Neumann boundary condition
- Linear solvers: Gauss-Seidel relaxation and conjugate gradient method with modified incomplete Cholesky zero-level preconditioning
- Grid structure: basic and staggered
- Level set: with reinitialization
- Parallelization: use of OpenMP and SSH remote compilation/execution of simulations on remote computing servers
- Rendering: GLSL implementation of the Volume Ray Marching algorithm, exporting Marching Cubes meshes to .ply files to be read by Mitsuba 2
Code available on GitHub or download ZIP.
[ Early live demo ]
This is a rough translation from C++ to JavaScript of my early work on fluid simulation. It is intentionally approximate so it can be rendered in real time in the browser.
[ Final Mitsuba renderings ]
Here are some renderings of my own simulations using the Mitsuba renderer. Each image took several seconds or even minutes to calculate and render.
[ Timeline of my progress ]
[ References ]
- Stable fluids - Jos Stam. 1999. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH'99. ACM Press. doi.org/10.1145/311535.311548
- Fluid simulation for computer graphics - Robert Bridson. 2016. CRC Press, Taylor & Francis Group, Boca Raton. doi.org/10.1201/9781315266008
- Fluid simulation - Robert Bridson and Matthias Müller-Fischer. 2007. In ACM SIGGRAPH 2007 courses on SIGGRAPH'07. ACM Press. doi.org/10.1145/1281500.1281681
- Practical animation of liquids - Nick Foster and Ronald Fedkiw. 2001. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH'01. ACM Press. doi.org/10.1145/383259.383261
- Adventures in Fluid Simulation - Miles Macklin. 2010. blog.mmacklin.com/2010/11/01/adventures-in-fluid-simulation
- An Unconditionally Stable MacCormack Method - Andrew Selle, Ronald Fedkiw, ByungMoon Kim, Yingjie Liu, and Jarek Rossignac. 2007. Journal of Scientific Computing 35, 2-3 (Nov. 2007), 350-371. doi.org/10.1007/s10915-007-9166-4
- Real-Time Fluid Dynamics for Games - Jos Stam. 2003. graphics.cs.cmu.edu/nsp/course/15-464/Spring11/papers/StamFluidforGames.pdf
- Real-Time Simulation and Rendering of 3D Fluids - Keenan Crane, Ignacio Llamas, and Sarah Tariq. 2007. in GPU Gems 3. Chapter 30. dl.acm.org/doi/10.5555/1407436
- Visual simulation of smoke - Ronald Fedkiw, Jos Stam, and Henrik Wann Jensen. 2001. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH'01. ACM Press. doi.org/10.1145/383259.383260
- Realistic Animation of Liquids - Nick Foster and Dimitri Metaxas. 1996. Graphical Models and Image Processing 58, 5 (Sept. 1996), 471-483. doi.org/10.1006/gmip.1996.0039
- Mitsuba 2 - mitsuba-renderer.org
- OpenMP - openmp.org