“Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps”
Conference:
Type(s):
Title:
- Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps
Presenter(s)/Author(s):
Abstract:
We introduce Particle Flow Maps (PFM), a fluid simulation method outperforming Neural Flow Maps (NFM) in efficiency and maintaining high accuracy. By leveraging particle trajectories and an Eulerian-Lagrangian framework, PFM achieves up to 49 times faster computation and 41\% less memory usage while better preserving vorticity in complex fluid dynamics.
References:
[1]
Ryoichi Ando and Reiji Tsuruno. 2011. A particle-based method for preserving fluid sheets. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics symposium on computer animation. 7–16.
[2]
Jeremiah U Brackbill and Hans M Ruppel. 1986. FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. Journal of Computational physics 65, 2 (1986), 314–343.
[3]
TF Buttke. 1992. Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flow. (1992).
[4]
Tomas F Buttke. 1993. Velicity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flow. In Vortex flows and related numerical methods. Springer, 39–57.
[5]
Thomas F Buttke and Alexandre J Chorin. 1993. Turbulence calculations in magnetization variables. Applied numerical mathematics 12, 1–3 (1993), 47–54.
[6]
A. Chern, F. Kn?ppel, U. Pinkall, P. Schr?der, and S. Wei?mann. 2016. Schr?dinger’s smoke. ACM Trans. Graph. 35 (2016), 77.
[7]
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.
[8]
Ricardo Cortez. 1996. An impulse-based approximation of fluid motion due to boundary forces. J. Comput. Phys. 123, 2 (1996), 341–353.
[9]
Jean M D?lery. 2001. Robert Legendre and Henri Werl?: toward the elucidation of three-dimensional separation. Annual review of fluid mechanics 33, 1 (2001), 129–154.
[10]
Yitong Deng, Mengdi Wang, Xiangxin Kong, Shiying Xiong, Zangyueyang Xian, and Bo Zhu. 2022. A moving eulerian-lagrangian particle method for thin film and foam simulation. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1–17.
[11]
Yitong Deng, Hong-Xing Yu, Diyang Zhang, Jiajun Wu, and Bo Zhu. 2023. Fluid Simulation on Neural Flow Maps. ACM Transactions on Graphics (TOG) 42, 6 (2023), 1–21.
[12]
Yu Fang, Ziyin Qu, Minchen Li, Xinxin Zhang, Yixin Zhu, Mridul Aanjaneya, and Chenfanfu Jiang. 2020. IQ-MPM: an interface quadrature material point method for non-sticky strongly two-way coupled nonlinear solids and fluids. ACM Transactions on Graphics (TOG) 39, 4 (2020), 51–1.
[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. 15–22.
[14]
Yun Fei, Christopher Batty, Eitan Grinspun, and Changxi Zheng. 2018. A multi-scale model for simulating liquid-fabric interactions. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1–16.
[15]
Yun Fei, Qi Guo, Rundong Wu, Li Huang, and Ming Gao. 2021. Revisiting integration in the material point method: a scheme for easier separation and less dissipation. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1–16.
[16]
Yun Fei, Henrique Teles Maia, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2017. A multi-scale model for simulating liquid-hair interactions. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–17.
[17]
Fan Feng, Jinyuan Liu, Shiying Xiong, Shuqi Yang, Yaorui Zhang, and Bo Zhu. 2022. Impulse fluid simulation. IEEE Transactions on Visualization and Computer Graphics (2022).
[18]
Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A polynomial particle-in-cell method. ACM Transactions on Graphics (TOG) 36, 6 (2017), 1–12.
[19]
Ming Gao, Andre Pradhana, Xuchen Han, Qi Guo, Grant Kot, Eftychios Sifakis, and Chenfanfu Jiang. 2018. Animating fluid sediment mixture in particle-laden flows. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1–11.
[20]
Yue Gao, Chen-Feng Li, Shi-Min Hu, and Brian A Barsky. 2009. Simulating gaseous fluids with low and high speeds. In Computer Graphics Forum, Vol. 28. Wiley Online Library, 1845–1852.
[21]
Toshiya Hachisuka. 2005. Combined Lagrangian-Eulerian approach for accurate advection. In ACM SIGGRAPH 2005 Posters. 114–es.
[22]
George Haller and Guocheng Yuan. 2000. Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D: Nonlinear Phenomena 147, 3–4 (2000), 352–370.
[23]
Xuchen Han, Theodore F Gast, Qi Guo, Stephanie Wang, Chenfanfu Jiang, and Joseph Teran. 2019. A hybrid material point method for frictional contact with diverse materials. Proceedings of the ACM on Computer Graphics and Interactive Techniques 2, 2 (2019), 1–24.
[24]
Francis H Harlow. 1962. The particle-in-cell method for numerical solution of problems in fluid dynamics. Technical Report. Los Alamos National Lab.(LANL), Los Alamos, NM (United States).
[25]
Woosuck Hong, Donald H House, and John Keyser. 2008. Adaptive particles for incompressible fluid simulation. The Visual Computer 24 (2008), 535–543.
[26]
Yuanming Hu, Yu Fang, Ziheng Ge, Ziyin Qu, Yixin Zhu, Andre Pradhana, and Chenfanfu Jiang. 2018. A moving least squares material point method with displacement discontinuity and two-way rigid body coupling. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1–14.
[27]
Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Fr?do Durand. 2019. Taichi: a language for high-performance computation on spatially sparse data structures. ACM Transactions on Graphics (TOG) 38, 6 (2019), 1–16.
[28]
Antony Jameson, Wolfgang Schmidt, and Eli Turkel. 1981. Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes. In 14th fluid and plasma dynamics conference. 1259.
[29]
Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The affine particle-in-cell method. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–10.
[30]
Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle. 2016. The material point method for simulating continuum materials. In Acm siggraph 2016 courses. 1–52.
[31]
Bernhard Kerbl, Georgios Kopanas, Thomas Leimk?hler, and George Drettakis. 2023. 3D Gaussian Splatting for Real-Time Radiance Field Rendering. ACM Transactions on Graphics 42, 4 (2023).
[32]
ByungMoon Kim, Yingjie Liu, Ignacio Llamas, and Jarek Rossignac. 2006. Advections with significantly reduced dissipation and diffusion. IEEE transactions on visualization and computer graphics 13, 1 (2006), 135–144.
[33]
Dustin Kleckner and William TM Irvine. 2013. Creation and dynamics of knotted vortices. Nature physics 9, 4 (2013), 253–258.
[34]
Sahil Kommalapati. 2021. Machine Learning for Coherent Structure Identification and Super Resolution in Turbulent flows. University of Washington.
[35]
Petros D Koumoutsakos, Georges-Henri Cottet, and Diego Rossinelli. 2008. Flow simulations using particles-Bridging Computer Graphics and CFD. In SIGGRAPH 2008-35th International Conference on Computer Graphics and Interactive Techniques. ACM, 1–73.
[36]
Shingyu Leung. 2011. An Eulerian approach for computing the finite time Lyapunov exponent. Journal of computational physics 230, 9 (2011), 3500–3524.
[37]
Shingyu Leung. 2013. The backward phase flow method for the Eulerian finite time Lyapunov exponent computations. Chaos: An Interdisciplinary Journal of Nonlinear Science 23, 4 (2013).
[38]
TT Lim and TB Nickels. 1992. Instability and reconnection in the head-on collision of two vortex rings. Nature 357, 6375 (1992), 225–227.
[39]
Frank Losasso, Ronald Fedkiw, and Stanley Osher. 2006. Spatially adaptive techniques for level set methods and incompressible flow. Computers & Fluids 35, 10 (2006), 995–1010.
[40]
Theodore MacMillan and David H Richter. 2021. The most robust representations of flow trajectories are Lagrangian coherent structures. Journal of Fluid Mechanics 927 (2021), A26.
[41]
Takumi Matsuzawa, Noah P. Mitchell, St?phane Perrard, and William T.M. Irvine. 2022. Video: Turbulence through sustained vortex ring collisions. 75th Annual Meeting of the APS Division of Fluid Dynamics – Gallery of Fluid Motion (2022). https://api.semanticscholar.org/CorpusID:252974545
[42]
Aleka McAdams, Eftychios Sifakis, and Joseph Teran. 2010. A Parallel Multigrid Poisson Solver for Fluids Simulation on Large Grids. In Symposium on Computer Animation, Vol. 65. 74.
[43]
Alexander George McKenzie. 2007. HOLA: a high-order Lie advection of discrete differential forms with applications in Fluid Dynamics. Ph. D. Dissertation. California Institute of Technology.
[44]
Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. 2021. Nerf: Representing scenes as neural radiance fields for view synthesis. Commun. ACM 65, 1 (2021), 99–106.
[45]
Patrick Mullen, Keenan Crane, Dmitry Pavlov, Yiying Tong, and Mathieu Desbrun. 2009. Energy-preserving integrators for fluid animation. ACM Transactions on Graphics (TOG) 28, 3 (2009), 1–8.
[46]
Mohammad Sina Nabizadeh, Stephanie Wang, Ravi Ramamoorthi, and Albert Chern. 2022. Covector fluids. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1–16.
[47]
Keita Nakamura, Satoshi Matsumura, and Takaaki Mizutani. 2023. Taylor particle-in-cell transfer and kernel correction for material point method. Computer Methods in Applied Mechanics and Engineering 403 (2023), 115720.
[48]
Rahul Narain, Jonas Zehnder, and Bernhard Thomaszewski. 2019. A second-order advection-reflection solver. Proceedings of the ACM on Computer Graphics and Interactive Techniques 2, 2 (2019), 1–14.
[49]
Jean-Christophe Nave, Rodolfo Ruben Rosales, and Benjamin Seibold. 2010. A gradient-augmented level set method with an optimally local, coherent advection scheme. J. Comput. Phys. 229, 10 (2010), 3802–3827.
[50]
Valery Iustinovich Oseledets. 1989. On a new way of writing the Navier-Stokes equation. The Hamiltonian formalism. Russ. Math. Surveys 44 (1989), 210–211.
[51]
Ziyin Qu, Minchen Li, Fernando De Goes, and Chenfanfu Jiang. 2022. The power particle-in-cell method. ACM Transactions on Graphics 41, 4 (2022).
[52]
Ziyin Qu, Xinxin Zhang, Ming Gao, Chenfanfu Jiang, and Baoquan Chen. 2019. Efficient and conservative fluids using bidirectional mapping. ACM Transactions on Graphics (TOG) 38, 4 (2019), 1–12.
[53]
Daniel Ram, Theodore Gast, Chenfanfu Jiang, Craig Schroeder, Alexey Stomakhin, Joseph Teran, and Pirouz Kavehpour. 2015. A material point method for viscoelastic fluids, foams and sponges. In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 157–163.
[54]
Karthik Raveendran, Chris Wojtan, and Greg Turk. 2011. Hybrid smoothed particle hydrodynamics. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics symposium on computer animation. 33–42.
[55]
PH Roberts. 1972. A Hamiltonian theory for weakly interacting vortices. Mathematika 19, 2 (1972), 169–179.
[56]
Avi Robinson-Mosher, Tamar Shinar, Jon Gretarsson, Jonathan Su, and Ronald Fedkiw. 2008. Two-way coupling of fluids to rigid and deformable solids and shells. ACM Transactions on Graphics (TOG) 27, 3 (2008), 1–9.
[57]
Takahiro Sato, Christopher Batty, Takeo Igarashi, and Ryoichi Ando. 2018. Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection. Computational Visual Media 4, 3 (2018), 6.
[58]
Takahiro Sato, Takeo Igarashi, Christopher Batty, and Ryoichi Ando. 2017. A long-term semi-lagrangian method for accurate velocity advection. In SIGGRAPH Asia 2017 Technical Briefs. 1–4.
[59]
Robert Saye. 2016. Interfacial gauge methods for incompressible fluid dynamics. Science advances 2, 6 (2016), e1501869.
[60]
Robert Saye. 2017. Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part I. J. Comput. Phys. 344 (2017), 647–682.
[61]
Andrew Selle, Ronald Fedkiw, Byungmoon Kim, Yingjie Liu, and Jarek Rossignac. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing 35 (2008), 350–371.
[62]
Jos Stam. 1999. Stable fluids. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques. 121–128.
[63]
Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. 2013. A material point method for snow simulation. ACM Transactions on Graphics (TOG) 32, 4 (2013), 1–10.
[64]
Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Transactions on Graphics (TOG) 33, 4 (2014), 1–11.
[65]
DM Summers. 2000. A representation of bounded viscous flow based on Hodge decomposition of wall impulse. J. Comput. Phys. 158, 1 (2000), 28–50.
[66]
PN Sun, A Colagrossi, S Marrone, and AM Zhang. 2016. Detection of Lagrangian coherent structures in the SPH framework. Computer Methods in Applied Mechanics and Engineering 305 (2016), 849–868.
[67]
Yuchen Sun, Xingyu Ni, Bo Zhu, Bin Wang, and Baoquan Chen. 2021. A material point method for nonlinearly magnetized materials. ACM Transactions on Graphics (TOG) 40, 6 (2021), 1–13.
[68]
Andre Pradhana Tampubolon, Theodore Gast, Gergely Kl?r, Chuyuan Fu, Joseph Teran, Chenfanfu Jiang, and Ken Museth. 2017. Multi-species simulation of porous sand and water mixtures. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–11.
[69]
Jerry Tessendorf. 2015. Advection Solver Performance with Long Time Steps, and Strategies for Fast and Accurate Numerical Implementation. (2015).
[70]
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.
[71]
E Weinan and Jian-Guo Liu. 2003. Gauge method for viscous incompressible flows. Communications in Mathematical Sciences 1, 2 (2003), 317–332.
[72]
DC Wiggert and EB Wylie. 1976. Numerical predictions of two-dimensional transient groundwater flow by the method of characteristics. Water Resources Research 12, 5 (1976), 971–977.
[73]
S. Xiong, R. Tao, Y. Zhang, F. Feng, and B. Zhu. 2021. Incompressible flow simulation on vortex segment clouds. ACM Trans. Graph. 40, 4 (2021).
[74]
S. Xiong, Z. Wang, M. Wang, and B. Zhu. 2022. A Clebsch method for free-surface vortical flow simulation. ACM Trans. Graph. 41, 4 (2022).
[75]
Xiao Yan, C-F Li, X-S Chen, and S-M Hu. 2018. MPM simulation of interacting fluids and solids. In Computer Graphics Forum, Vol. 37. Wiley Online Library, 183–193.
[76]
Shuqi Yang, Shiying Xiong, Yaorui Zhang, Fan Feng, Jinyuan Liu, and Bo Zhu. 2021. Clebsch gauge fluid. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1–11.
[77]
Yonghao Yue, Breannan Smith, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2015. Continuum foam: A material point method for shear-dependent flows. ACM Transactions on Graphics (TOG) 34, 5 (2015), 1–20.
[78]
Jonas Zehnder, Rahul Narain, and Bernhard Thomaszewski. 2018. An advection-reflection solver for detail-preserving fluid simulation. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1–8.
[79]
Xinxin Zhang, Robert Bridson, and Chen Greif. 2015. Restoring the missing vorticity in advection-projection fluid solvers. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–8.
[80]
Bo Zhu, Xubo Yang, and Ye Fan. 2010. Creating and preserving vortical details in sph fluid. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 2207–2214.
[81]
Yongning Zhu and Robert Bridson. 2005. Animating sand as a fluid. ACM Transactions on Graphics (TOG) 24, 3 (2005), 965–972.