“Efficient and conservative fluids using bidirectional mapping” by Qu, Zhang, Gao, Jiang and Chen
Conference:
Type:
Title:
- Efficient and conservative fluids using bidirectional mapping
Session/Category Title: Fluids II
Presenter(s)/Author(s):
Abstract:
In this paper, we introduce BiMocq2, an unconditionally stable, pure Eulerianbased advection scheme to efficiently preserve the advection accuracy of all physical quantities for long-term fluid simulations. Our approach is built upon the method of characteristic mapping (MCM). Instead of the costly evaluation of the temporal characteristic integral, we evolve the mapping function itself by solving an advection equation for the mappings. Dual mesh characteristics (DMC) method is adopted to more accurately update the mapping. Furthermore, to avoid visual artifacts like instant blur and temporal inconsistency introduced by re-initialization, we introduce multi-level mapping and back and forth error compensation. We conduct comprehensive 2D and 3D benchmark experiments to compare against alternative advection schemes. In particular, for the vortical flow and level set experiments, our method outperforms almost all state-of-art hybrid schemes, including FLIP, PolyPic and Particle-Level-Set, at the cost of only two Semi-Lagrangian advections. Additionally, our method does not rely on the particle-grid transfer operations, leading to a highly parallelizable pipeline. As a result, more than 45× performance acceleration can be achieved via even a straightforward porting of the code from CPU to GPU.
References:
1. Mridul Aanjaneya, Ming Gao, Haixiang Liu, Christopher Batty, and Eftychios Sifakis. 2017. Power diagrams and sparse paged grids for high resolution adaptive liquids. ACM Transactions on Graphics (TOG) 36, 4 (2017), 140. Google ScholarDigital Library
2. Ryoichi Ando, Nils Thuerey, and Chris Wojtan. 2015. A stream function solver for liquid simulations. ACM Transactions on Graphics (TOG) 34, 4 (2015), 53. Google ScholarDigital Library
3. Alexis Angelidis. 2017. Multi-scale Vorticle Fluids. ACM Trans. Graph. 36, 4, Article 104 (July 2017), 12 pages. Google ScholarDigital Library
4. R. Bridson. 2008. Fluid Simulation for Computer Graphics. Taylor & Francis.Google ScholarDigital Library
5. Tyson Brochu, Todd Keeler, and Robert Bridson. 2012. Linear-time smoke animation with vortex sheet meshes. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Eurographics Association, 87–95. Google ScholarDigital Library
6. Chung-Ki Cho, Byungjoon Lee, and Seongjai Kim. 2018. Dual-Mesh Characteristics for Particle-Mesh Methods for the Simulation of Convection-Dominated Flows. SIAM Journal on Scientific Computing 40, 3 (2018), A1763–A1783.Google ScholarDigital Library
7. Georges-Henri Cottet, Petros D Koumoutsakos, D Petros, et al. 2000. Vortex methods: theory and practice. Cambridge university press.Google Scholar
8. Roger A Crawfis and Nelson Max. 1993. Texture splats for 3D scalar and vector field visualization. In Proceedings of the 4th conference on Visualization’93. IEEE Computer Society, 261–266. Google ScholarDigital Library
9. S. Elcott, Y. Tong, E. Kanso, P. Schröder, and M. Desbrun. 2007. Stable, Circulation-preserving, Simplicial Fluids. ACM Trans. Graph. 26, 1, Article 4 (2007). Google ScholarDigital Library
10. Douglas Enright, Ronald Fedkiw, Joel Ferziger, and Ian Mitchell. 2002a. A hybrid particle level set method for improved interface capturing. Journal of Computational physics 183, 1 (2002), 83–116. Google ScholarDigital Library
11. Douglas Enright, Stephen Marschner, and Ronald Fedkiw. 2002b. Animation and rendering of complex water surfaces. In ACM Trans. Graph., Vol. 21. 736–744. Google ScholarDigital Library
12. Ye Fan, Joshua Litven, David IW Levin, and Dinesh K Pai. 2013. Eulerian-on-lagrangian simulation. ACM Transactions on Graphics (TOG) 32, 3 (2013), 22. Google ScholarDigital Library
13. Ronald Fedkiw, Jos Stam, and Henrik Wann Jensen. 2001. Visual Simulation of Smoke. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). ACM, New York, NY, USA, 15–22. Google ScholarDigital Library
14. Bryan E Feldman, James F O’brien, and Okan Arikan. 2003. Animating suspended particle explosions. In ACM Transactions on Graphics (TOG), Vol. 22. ACM, 708–715. Google ScholarDigital Library
15. Florian Ferstl, Ryoichi Ando, Chris Wojtan, Rüdiger Westermann, and Nils Thuerey. 2016. Narrow band FLIP for liquid simulations. In Computer Graphics Forum, Vol. 35. Wiley Online Library, 225–232.Google Scholar
16. Nick Foster and Ronald Fedkiw. 2001. Practical Animation of Liquids. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). ACM, New York, NY, USA, 23–30. Google ScholarDigital Library
17. C. Fu, Q. Guo, T. Gast, C. Jiang, and J. Teran. 2017. A Polynomial Particle-in-cell Method. ACM Trans. Graph. 36, 6, Article 222 (2017), 222:1–222:12 pages. Google ScholarDigital Library
18. M. Gao. 2018. Sparse Paged Grid and its Applications to Adaptivity and Material Point Method in Physics Based Simulations. Ph.D. Dissertation. University of Wisconsin, Madison.Google Scholar
19. Ming Gao, Andre Pradhana Tampubolon, Chenfanfu Jiang, and Eftychios Sifakis. 2017. An Adaptive Generalized Interpolation Material Point Method for Simulating Elastoplastic Materials. ACM Trans. Graph. 36, 6, Article 223 (Nov. 2017), 12 pages. Google ScholarDigital Library
20. Ming Gao, Xinlei Wang, Kui Wu, Andre Pradhana, Eftychios Sifakis, Cem Yuksel, and Chenfanfu Jiang. 2018. GPU Optimization of Material Point Methods. In SIGGRAPH Asia 2018 Technical Papers (SIGGRAPH Asia ’18). ACM, New York, NY, USA, Article 254, 12 pages. Google ScholarDigital Library
21. C. Jiang, C. Schroeder, A. Selle, J. Teran, and A. Stomakhin. 2015. The Affine Particle-in-cell Method. ACM Trans. Graph. 34, 4 (July 2015), 51:1–51:10. Google ScholarDigital Library
22. B. Kim, Y. Liu, I. Llamas, and J. Rossignac. 2005. FlowFixer: Using BFECC for Fluid Simulation. In Eurographics Conference on Natural Phenomena. 51–56. Google ScholarDigital Library
23. Theodore Kim, Nils Thürey, Doug James, and Markus Gross. 2008. Wavelet Turbulence for Fluid Simulation. In ACM SIGGRAPH 2008 Papers (SIGGRAPH ’08). ACM, New York, NY, USA, Article 50, 6 pages. Google ScholarDigital Library
24. David I. W. Levin, Joshua Litven, Garrett L. Jones, Shinjiro Sueda, and Dinesh K. Pai. 2011. Eulerian Solid Simulation with Contact. In ACM SIGGRAPH 2011 Papers (SIGGRAPH ’11). Article 36, 36:1–36:10 pages. Google ScholarDigital Library
25. T. T. Lim and T. B. Nickels. 1992. Instability and reconnection in the head-on collision of two vortex rings. Nature 357 (05 1992), 225–227.Google Scholar
26. Nelson Max, Roger Crawfis, and Dean Williams. 1992. Visualizing wind velocities by advecting cloud textures. In Proceedings Visualization’92. IEEE, 179–184. Google ScholarDigital Library
27. A. McKenzie. 2007. HOLA: a High-Order Lie Advection of discrete differential forms, with applications in fluid dynamics. Ph.D. Dissertation. Caltech.Google Scholar
28. Patrick Mullen, Keenan Crane, Dmitry Pavlov, Yiying Tong, and Mathieu Desbrun. 2009. Energy-preserving Integrators for Fluid Animation. In ACM SIGGRAPH 2009 Papers (SIGGRAPH ’09). Article 38, 38:1–38:8 pages. Google ScholarDigital Library
29. Ken Museth. 2013. VDB: High-resolution Sparse Volumes with Dynamic Topology. ACM Trans. Graph. 32, 3, Article 27 (July 2013), 22 pages. Google ScholarDigital Library
30. Duc Quang Nguyen, Ronald Fedkiw, and Henrik Wann Jensen. 2002. Physically Based Modeling and Animation of Fire. In Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques. 721–728. Google ScholarDigital Library
31. Tobias Pfaff, Nils Thuerey, and Markus Gross. 2012. Lagrangian Vortex Sheets for Animating Fluids. ACM Trans. Graph. 31, 4, Article 112 (2012), 112:1–112:8 pages. Google ScholarDigital Library
32. N. Rasmussen, D. Nguyen, W. Geiger, and R. Fedkiw. 2003. Smoke simulation for large scale phenomena. In ACM Trans Graph, Vol. 22. ACM, 703–707. Google ScholarDigital Library
33. Takahiro Sato, Christopher Batty, Takeo Igarashi, and Ryoichi Ando. 2017. A Long-term Semi-lagrangian Method for Accurate Velocity Advection. In SIGGRAPH Asia 2017 Technical Briefs (SA ’17). ACM, New York, NY, USA, Article 5, 4 pages. Google ScholarDigital Library
34. Andrew Selle, Ronald Fedkiw, Byungmoon Kim, Yingjie Liu, and Jarek Rossignac. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing 35, 2–3 (2008), 350–371. Google ScholarDigital Library
35. Rajsekhar Setaluri, Mridul Aanjaneya, Sean Bauer, and Eftychios Sifakis. 2014. SPGrid: A Sparse Paged Grid Structure Applied to Adaptive Smoke Simulation. ACM Trans. Graph. 33, 6, Article 205 (Nov. 2014), 12 pages. Google ScholarDigital Library
36. Karl Sims. 1992. Choreographed image flow. The Journal Of Visualization And Computer Animation 3, 1 (1992), 31–43.Google ScholarCross Ref
37. Jos Stam. 1999. Stable Fluids. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 121–128. Google ScholarDigital Library
38. Jos Stam and Eugene Fiume. 1995. Depicting fire and other gaseous phenomena using diffusion processes. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM, 129–136. Google ScholarDigital Library
39. Yun Teng, David I. W. Levin, and Theodore Kim. 2016. Eulerian Solid-fluid Coupling. ACM Trans. Graph. 35, 6, Article 200 (2016), 200:1–200:8 pages. Google ScholarDigital Library
40. Jerry Tessendorf. 2015. Advection Solver Performance with Long Time Steps, and Strategies for Fast and Accurate Numerical Implementation.Google Scholar
41. Jerry Tessendorf and Brandon Pelfrey. 2011. The characteristic map for fast and efficient vfx fluid simulations. In Computer Graphics International Workshop on VFX, Computer Animation, and Stereo Movies. Ottawa, Canada.Google Scholar
42. Steffen Weißmann and Ulrich Pinkall. 2010. Filament-based smoke with vortex shedding and variational reconnection. In ACM Trans. Graph., Vol. 29. 115. Google ScholarDigital Library
43. D. C. Wiggert and E. B. Wylie. 1976. Numerical predictions of two-dimensional transient groundwater flow by the method of characteristics. Water Resources Research 12, 5 (1976), 971–977.Google ScholarCross Ref
44. You Xie, Erik Franz, Mengyu Chu, and Nils Thuerey. 2018. tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow. ACM Trans. Graph. 37, 4, Article 95 (July 2018), 15 pages. Google ScholarDigital Library
45. Jonas Zehnder, Rahul Narain, and Bernhard Thomaszewski. 2018. An Advection-reflection Solver for Detail-preserving Fluid Simulation. ACM Trans. Graph. 37, 4, Article 85 (July 2018), 8 pages. Google ScholarDigital Library
46. Xinxin Zhang, Robert Bridson, and Chen Greif. 2015. Restoring the Missing Vorticity in Advection-projection Fluid Solvers. ACM Trans. Graph. 34, 4, Article 52 (2015), 52:1–52:8 pages. Google ScholarDigital Library
47. Yongning Zhu and Robert Bridson. 2005. Animating Sand As a Fluid. In ACM SIGGRAPH 2005 Papers (SIGGRAPH ’05). ACM, New York, NY, USA, 965–972. Google ScholarDigital Library
