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Solid-Fluid Interaction on Particle Flow Maps

Published: 19 November 2024 Publication History

Abstract

We propose a novel solid-fluid interaction method for coupling elastic solids with impulse flow maps. Our key idea is to unify the representation of fluid and solid components as particle flow maps with different lengths and dynamics. The solid-fluid coupling is enabled by implementing two novel mechanisms: first, we developed an impulse-to-velocity transfer mechanism to unify the exchanged physical quantities; second, we devised a particle path integral mechanism to accumulate coupling forces along each flow-map trajectory. Our framework integrates these two mechanisms into an Eulerian-Lagrangian impulse fluid simulator to accommodate traditional coupling models, exemplified by the Material Point Method (MPM) and Immersed Boundary Method (IBM), within a particle flow map framework. We demonstrate our method's efficacy by simulating solid-fluid interactions exhibiting strong vortical dynamics, including various vortex shedding and interaction examples across swimming, falling, breezing, and combustion.

References

[1]
Muzaffer Akbay, Nicholas Nobles, Victor Zordan, and Tamar Shinar. 2018. An extended partitioned method for conservative solid-fluid coupling. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1--12.
[2]
Nadir Akinci, Jens Cornelis, Gizem Akinci, and Matthias Teschner. 2013. Coupling elastic solids with smoothed particle hydrodynamics fluids. Computer Animation and Virtual Worlds 24, 3--4 (2013), 195--203.
[3]
Christopher Batty, Florence Bertails, and Robert Bridson. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Transactions on Graphics (TOG) 26, 3 (2007), 100--es.
[4]
P Becker, SR Idelsohn, and E Oñate. 2015. A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the particle finite element method with fixed mesh. Computational Mechanics 55 (2015), 1091--1104.
[5]
Jan Bender, Matthias Müller, Miguel A Otaduy, Matthias Teschner, and Miles Macklin. 2014. A survey on position-based simulation methods in computer graphics. In Computer graphics forum, Vol. 33. Wiley Online Library, 228--251.
[6]
I Borazjani and Fotis Sotiropoulos. 2010. On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming. Journal of Experimental Biology 213, 1 (2010), 89--107.
[7]
Landon Boyd and Robert Bridson. 2012. MultiFLIP for energetic two-phase fluid simulation. ACM Transactions on Graphics (TOG) 31, 2 (2012), 1--12.
[8]
TF Buttke. 1992. Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flow. (1992).
[9]
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.
[10]
Thomas F Buttke and Alexandre J Chorin. 1993. Turbulence calculations in magnetization variables. Applied numerical mathematics 12, 1--3 (1993), 47--54.
[11]
Mark Carlson, Peter J Mucha, and Greg Turk. 2004. Rigid fluid: animating the interplay between rigid bodies and fluid. ACM Transactions on Graphics (TOG) 23, 3 (2004), 377--384.
[12]
Pascal Clausen, Martin Wicke, Jonathan R Shewchuk, and James F O'brien. 2013. Simulating liquids and solid-liquid interactions with lagrangian meshes. ACM Transactions on Graphics (TOG) 32, 2 (2013), 1--15.
[13]
Ricardo Cortez. 1996. An impulse-based approximation of fluid motion due to boundary forces. J. Comput. Phys. 123, 2 (1996), 341--353.
[14]
Georges-Henri Cottet, Petros D Koumoutsakos, et al. 2000. Vortex methods: theory and practice. Vol. 313. Cambridge university press Cambridge.
[15]
Massimiliano Cremonesi, Alessandro Franci, Sergio Idelsohn, and Eugenio Oñate. 2020. A state of the art review of the particle finite element method (PFEM). Archives of Computational Methods in Engineering 27, 5 (2020), 1709--1735.
[16]
Zuo Cui, Zixuan Yang, Hong-Zhou Jiang, Wei-Xi Huang, and Lian Shen. 2018. A sharp-interface immersed boundary method for simulating incompressible flows with arbitrarily deforming smooth boundaries. International Journal of Computational Methods 15, 01 (2018), 1750080.
[17]
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.
[18]
Th Dunne. 2006. An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaptation. International journal for numerical methods in fluids 51, 9--10 (2006), 1017--1039.
[19]
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.
[20]
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.
[21]
Yun Fei, Christopher Batty, Eitan Grinspun, and Changxi Zheng. 2019. A multi-scale model for coupling strands with shear-dependent liquid. ACM Transactions on Graphics (TOG) 38, 6 (2019), 1--20.
[22]
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.
[23]
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).
[24]
Mattia Gazzola, Philippe Chatelain, Wim M Van Rees, and Petros Koumoutsakos. 2011. Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230, 19 (2011), 7093--7114.
[25]
Olivier Génevaux, Arash Habibi, and Jean-Michel Dischler. 2003. Simulating Fluid-Solid Interaction. In Graphics Interface, Vol. 2003. 31--38.
[26]
Eran Guendelman, Andrew Selle, Frank Losasso, and Ronald Fedkiw. 2005. Coupling water and smoke to thin deformable and rigid shells. ACM Transactions on Graphics (TOG) 24, 3 (2005), 973--981.
[27]
Jean-Luc Guermond, Peter Minev, and Jie Shen. 2006. An overview of projection methods for incompressible flows. Computer methods in applied mechanics and engineering 195, 44--47 (2006), 6011--6045.
[28]
Toshiya Hachisuka. 2005. Combined Lagrangian-Eulerian approach for accurate advection. In ACM SIGGRAPH 2005 Posters. 114--es.
[29]
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.
[30]
Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Frédo Durand. 2019. Taichi: a language for high-performance computation on spatially sparse data structures. ACM Transactions on Graphics (TOG) 38, 6 (2019), 201.
[31]
Libo Huang, Ziyin Qu, Xun Tan, Xinxin Zhang, Dominik L Michels, and Chenfanfu Jiang. 2021. Ships, splashes, and waves on a vast ocean. ACM Transactions on Graphics (TOG) 40, 6 (2021), 1--15.
[32]
Wei-Xi Huang and Hyung Jin Sung. 2009. An immersed boundary method for fluid-flexible structure interaction. Computer methods in applied mechanics and engineering 198, 33--36 (2009), 2650--2661.
[33]
Wei-Xi Huang and Fang-Bao Tian. 2019. Recent trends and progress in the immersed boundary method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, 23--24 (2019), 7617--7636.
[34]
Sergio R Idelsohn, Julio Marti, A Limache, and Eugenio Oñate. 2008. Unified Lagrangian formulation for elastic solids and incompressible fluids: application to fluid-structure interaction problems via the PFEM. Computer Methods in Applied Mechanics and Engineering 197, 19--20 (2008), 1762--1776.
[35]
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.
[36]
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.
[37]
Ken Kamrin and Jean-Christophe Nave. 2009. An Eulerian approach to the simulation of deformable solids: Application to finite-strain elasticity. arXiv preprint arXiv:0901.3799 (2009).
[38]
Ken Kamrin, Chris H Rycroft, and Jean-Christophe Nave. 2012. Reference map technique for finite-strain elasticity and fluid-solid interaction. Journal of the Mechanics and Physics of Solids 60, 11 (2012), 1952--1969.
[39]
Richard Keiser, Bart Adams, Dominique Gasser, Paolo Bazzi, Philip Dutré, and Markus Gross. 2005. A unified lagrangian approach to solid-fluid animation. In Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, 2005. IEEE, 125--148.
[40]
Bryan M Klingner, Bryan E Feldman, Nuttapong Chentanez, and James F O'brien. 2006. Fluid animation with dynamic meshes. In ACM SIGGRAPH 2006 Papers. 820--825.
[41]
EH Lee and DT Liu. 1967. Finite stain elastic-plastic theory particularly for plane wave analysis. J. Appl. Phys 38 (1967), t9.
[42]
Erastus H Lee. 1969. Elastic-plastic deformation at finite strains. (1969).
[43]
Zhiqi Li, Barnabás Börcsök, Duowen Chen, Yutong Sun, Bo Zhu, and Greg Turk. 2024. Lagrangian Covector Fluid with Free Surface. In ACM SIGGRAPH 2024 Conference Papers. 1--10.
[44]
YP Lian, X Zhang, and Y Liu. 2011a. Coupling of finite element method with material point method by local multi-mesh contact method. Computer Methods in Applied Mechanics and Engineering 200, 47--48 (2011), 3482--3494.
[45]
YP Lian, X Zhang, and Y Liu. 2012. An adaptive finite element material point method and its application in extreme deformation problems. Computer methods in applied mechanics and engineering 241 (2012), 275--285.
[46]
YP Lian, X Zhang, X Zhou, and ZT Ma. 2011b. A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading. Computer Methods in Applied Mechanics and Engineering 200, 17--20 (2011), 1659--1670.
[47]
Yan-Ping Lian, Yan Liu, and Xiong Zhang. 2014. Coupling of membrane element with material point method for fluid-membrane interaction problems. International Journal of Mechanics and Materials in Design 10 (2014), 199--211.
[48]
Zhaowu Lin, Andrew Hess, Zhaosheng Yu, Shengqiang Cai, and Tong Gao. 2019. A fluid-structure interaction study of soft robotic swimmer using a fictitious domain/active-strain method. J. Comput. Phys. 376 (2019), 1138--1155.
[49]
Chun Liu and Noel J Walkington. 2001. An Eulerian description of fluids containing visco-elastic particles. Archive for rational mechanics and analysis 159 (2001), 229--252.
[50]
Wing Kam Liu, Do Wan Kim, and Shaoqiang Tang. 2007. Mathematical foundations of the immersed finite element method. Computational Mechanics 39 (2007), 211--222.
[51]
Wing Kam Liu, Yaling Liu, David Farrell, Lucy Zhang, X Sheldon Wang, Yoshio Fukui, Neelesh Patankar, Yongjie Zhang, Chandrajit Bajaj, Junghoon Lee, et al. 2006. Immersed finite element method and its applications to biological systems. Computer methods in applied mechanics and engineering 195, 13--16 (2006), 1722--1749.
[52]
Frank Losasso, Geoffrey Irving, Eran Guendelman, and Ronald Fedkiw. 2006. Melting and burning solids into liquids and gases. IEEE Transactions on Visualization and Computer Graphics 12, 3 (2006), 343--352.
[53]
Yoichiro Mori and Charles S Peskin. 2008. Implicit second-order immersed boundary methods with boundary mass. Computer methods in applied mechanics and engineering 197, 25--28 (2008), 2049--2067.
[54]
Matthias Müller, Richard Keiser, Andrew Nealen, Mark Pauly, Markus Gross, and Marc Alexa. 2004. Point based animation of elastic, plastic and melting objects. In Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation. 141--151.
[55]
Mohammad Sina Nabizadeh, Stephanie Wang, Ravi Ramamoorthi, and Albert Chern. 2022. Covector fluids. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1--16.
[56]
Yen Ting Ng, Chohong Min, and Frédéric Gibou. 2009. An efficient fluid-solid coupling algorithm for single-phase flows. J. Comput. Phys. 228, 23 (2009), 8807--8829.
[57]
Valery Iustinovich Oseledets. 1989. On a new way of writing the Navier-Stokes equation. The Hamiltonian formalism. Russ. Math. Surveys 44 (1989), 210--211.
[58]
Charles S Peskin. 1972. Flow patterns around heart valves: a numerical method. Journal of computational physics 10, 2 (1972), 252--271.
[59]
Charles S Peskin. 2002. The immersed boundary method. Acta numerica 11 (2002), 479--517.
[60]
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.
[61]
PH Roberts. 1972. A Hamiltonian theory for weakly interacting vortices. Mathematika 19, 2 (1972), 169--179.
[62]
Avi Robinson-Mosher, R Elliot English, and Ronald Fedkiw. 2009. Accurate tangential velocities for solid fluid coupling. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 227--236.
[63]
Avi Robinson-Mosher, Craig Schroeder, and Ronald Fedkiw. 2011. A symmetric positive definite formulation for monolithic fluid structure interaction. J. Comput. Phys. 230, 4 (2011), 1547--1566.
[64]
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.
[65]
Chris H Rycroft, Chen-Hung Wu, Yue Yu, and Ken Kamrin. 2020. Reference map technique for incompressible fluid-structure interaction. Journal of Fluid Mechanics 898 (2020), A9.
[66]
Sergio Sancho, Jingwei Tang, Christopher Batty, and Vinicius C Azevedo. 2024. The Impulse Particle-In-Cell Method. In Computer Graphics Forum. Wiley Online Library, e15022.
[67]
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.
[68]
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.
[69]
Robert Saye. 2016. Interfacial gauge methods for incompressible fluid dynamics. Science advances 2, 6 (2016), e1501869.
[70]
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.
[71]
Tokimasa Shimada, Koji Nishiguchi, Rahul Bale, Shigenobu Okazawa, and Makoto Tsubokura. 2022. Eulerian finite volume formulation using Lagrangian marker particles for incompressible fluid-structure interaction problems. Internat. J. Numer. Methods Engrg. 123, 5 (2022), 1294--1328.
[72]
TOKIMASA Shimada, KOJI Nishiguchi, Christian Peco, Shigenobu Okazawa, and Makoto Tsubokura. 2021. Eulerian formulation using lagrangian marker particles with reference map technique for fluid-structure interaction problem. In of the International Conference on Computational Methods for Coupled Problems in Science and Engineering. 1--7.
[73]
Barbara Solenthaler, Jürg Schläfli, and Renato Pajarola. 2007. A unified particle model for fluid-solid interactions. Computer Animation and Virtual Worlds 18, 1 (2007), 69--82.
[74]
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.
[75]
DM Summers. 2000. A representation of bounded viscous flow based on Hodge decomposition of wall impulse. J. Comput. Phys. 158, 1 (2000), 28--50.
[76]
Kunihiko Taira and Tim Colonius. 2007. The immersed boundary method: a projection approach. J. Comput. Phys. 225, 2 (2007), 2118--2137.
[77]
Tetsuya Takahashi and Christopher Batty. 2020. Monolith: a monolithic pressure-viscosity-contact solver for strong two-way rigid-rigid rigid-fluid coupling. (2020).
[78]
Tetsuya Takahashi and Christopher Batty. 2022. ElastoMonolith: A monolithic optimization-based liquid solver for contact-aware elastic-solid coupling. ACM Transactions on Graphics (TOG) 41, 6 (2022), 1--19.
[79]
Yun Teng, David IW Levin, and Theodore Kim. 2016. Eulerian solid-fluid coupling. ACM Transactions on Graphics (TOG) 35, 6 (2016), 1--8.
[80]
Jerry Tessendorf. 2015. Advection Solver Performance with Long Time Steps, and Strategies for Fast and Accurate Numerical Implementation. (2015).
[81]
Fang-Bao Tian, Hu Dai, Haoxiang Luo, James F Doyle, and Bernard Rousseau. 2014. Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems. Journal of computational physics 258 (2014), 451--469.
[82]
Emad Uddin, Wei-Xi Huang, and Hyung Jin Sung. 2013. Interaction modes of multiple flexible flags in a uniform flow. Journal of Fluid Mechanics 729 (2013), 563--583.
[83]
Chengjie Wang and Jeff D Eldredge. 2015. Strongly coupled dynamics of fluids and rigid-body systems with the immersed boundary projection method. J. Comput. Phys. 295 (2015), 87--113.
[84]
Li Wang and Fang-bao Tian. 2019. Numerical simulation of flow over a parallel cantilevered flag in the vicinity of a rigid wall. Physical Review E 99, 5 (2019), 053111.
[85]
Luohao Wang, Chunmei Xie, and Weixi Huang. 2020. A monolithic projection framework for constrained FSI problems with the immersed boundary method. Computer methods in applied mechanics and engineering 371 (2020), 113332.
[86]
Sheldon Wang. 2006. From immersed boundary method to immersed continuum methods. International Journal for Multiscale Computational Engineering 4, 1 (2006).
[87]
Xiaolin Wang, Ken Kamrin, and Chris H Rycroft. 2022. An incompressible Eulerian method for fluid-structure interaction with mixed soft and rigid solids. Physics of Fluids 34, 3 (2022).
[88]
X Sheldon Wang. 2007. An iterative matrix-free method in implicit immersed boundary/continuum methods. Computers & structures 85, 11--14 (2007), 739--748.
[89]
E Weinan and Jian-Guo Liu. 2003. Gauge method for viscous incompressible flows. Communications in Mathematical Sciences 1, 2 (2003), 317--332.
[90]
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.
[91]
Joel Wretborn, Sean Flynn, and Alexey Stomakhin. 2022. Guided bubbles and wet foam for realistic whitewater simulation. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1--16.
[92]
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).
[93]
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.
[94]
Omar Zarifi and Christopher Batty. 2017. A positive-definite cut-cell method for strong two-way coupling between fluids and deformable bodies. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 1--11.
[95]
Hong Zhao, Jonathan B Freund, and Robert D Moser. 2008. A fixed-mesh method for incompressible flow-structure systems with finite solid deformations. J. Comput. Phys. 227, 6 (2008), 3114--3140.
[96]
Junwei Zhou, Duowen Chen, Molin Deng, Yitong Deng, Yuchen Sun, Sinan Wang, Shiying Xiong, and Bo Zhu. 2024. Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps. ACM Transactions on Graphics (TOG) 43, 4 (2024), 1--20.

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    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 43, Issue 6
    December 2024
    1828 pages
    EISSN:1557-7368
    DOI:10.1145/3702969
    Issue’s Table of Contents
    This work is licensed under a Creative Commons Attribution International 4.0 License.

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    Publication History

    Published: 19 November 2024
    Published in TOG Volume 43, Issue 6

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    Author Tags

    1. solid-fluid interaction
    2. particle flow map
    3. impulse gauge fluid
    4. vortex dynamics
    5. path integral

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