Tristan Marrec

### Fluid Simulation Internship - 2021-09-24 ###

During my 6-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. Starting with smoke simulation and gradually evolving towards liquid simulation.

Here’s a summary of what I’ve been working 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, export Marching Cube meshes to a .ply file 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 highly inaccurate so it can be easily rendered in real time in the browser.

### Final Mitsuba renderings ###

Here are some renderings of my own simulations using the Mitsuba renderer, each image requiring several seconds or even minutes to calculate and render.

### Timeline of my progress ###

### References ###

1. 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

2. Fluid simulation for computer graphics - Robert Bridson. 2016. CRC Press, Taylor & Francis Group, CRC Pressis an imprint of the Taylor & Francis Group, an informa Business, Boca Raton. doi.org/10.1201/9781315266008

3. 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

4. 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

5. Adventures in Fluid Simulation - Miles Macklin. 2010. blog.mmacklin.com/2010/11/01/adventures-in-fluid-simulation

6. 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), 350–37. doi.org/10.1007/s10915-007-9166-4

7. Real-Time Fluid Dynamics for Games - Jos Stam. 2003. graphics.cs.cmu.edu/nsp/course/15-464/Spring11/papers/StamFluidforGames.pdf

8. 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

9. 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

10. 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

11. Mitsuba 2 - mitsuba-renderer.org

12. OpenMP - openmp.org