“Incompressible flow simulation on vortex segment clouds” by Xiong, Tao, Zhang, Feng and Zhu

We propose a novel Lagrangian geometric representation using segment clouds to simulate incompressible fluid exhibiting strong anisotropic vortical features. The central component of our approach is a cloud of discrete segments enhanced by a set of local segment reseeding operations to facilitate both the geometrical evolution and the topological updates of vortical flow. We build a vortex dynamics solver with the support for dynamic solid boundaries based on discrete segment primitives. We demonstrate the efficacy of our approach by simulating a broad range of challenging flow phenomena, such as reconnection of non-closed vortex tubes and vortex shedding behind a rotating object.

1. A. S. Almgren, T. Buttke, and P. Colella. 1994. A fast adaptive vortex method in three dimensions. J. Comput. Phys. 113 (1994), 177–200.Google ScholarDigital Library
2. R. Ando, N. Thurey, and R. Tsuruno. 2012. Preserving fluid sheets with adaptively sampled anisotropic particles. IEEE T. Vis. Comput. Gr. 18 (2012), 1202–1214.Google ScholarDigital Library
3. A. Angelidis. 2017. Multi-scale vorticle fluids. ACM Trans. Graph. 36 (2017), 1–12.Google ScholarDigital Library
4. A. Angelidis and F. Neyret. 2005. Simulation of smoke based on vortex filament primitives. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 87–96.Google Scholar
5. H. Aref and E. Flinchem. 1985. Dynamics of a vortex filament in a shear flow. J. Fluid Mech. 148 (1985), 477–497.Google ScholarCross Ref
6. G. Barill, N. G. Dickson, R. Schmidt, D. I. W. Levin, and A. Jacobson. 2018. Fast winding numbers for soups and clouds. ACM Trans. Graph. 37 (2018), 43.Google ScholarDigital Library
7. A. Barnat and N. S. Pollard. 2012. Smoke sheets for graph-structured vortex filaments. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 77–86.Google Scholar
8. G. Beardsell, L. Dufresne, and G. Dumas. 2016a. Investigation of the viscous reconnection phenomenon of two vortex tubes through spectral simulations. Phys. Fluids 28 (2016), 095103.Google ScholarCross Ref
9. G. Beardsell, L. Dufresne, and G. Dumas. 2016b. Investigation of the viscous reconnection phenomenon of two vortex tubes through spectral simulations. Phys. Fluids 28 (2016), 095103.Google ScholarCross Ref
10. P. S. Bernard. 2009. Vortex filament simulation of the turbulent coflowing jet. Phys. Fluids 21 (2009), 025107.Google ScholarCross Ref
11. T. Brochu, T. Keeler, and R. Bridson. 2012. Linear-time smoke animation with vortex sheet meshes. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 87–95.Google Scholar
12. A. Chern, F. Knöppel, U. Pinkall, and P. Schröder. 2017. Inside fluids: Clebsch maps for visualization and processing. ACM Trans. Graph. 36 (2017), 142.Google ScholarDigital Library
13. A. Chern, F. Knöppel, U. Pinkall, P. Schröder, and S. Weißmann. 2016. Schrödinger’s smoke. ACM Trans. Graph. 35 (2016), 77.Google ScholarDigital Library
14. J. P. Choquin and S. Huberson. 1990. Computational experiments on interactions between numerical and physical instabilities. Int. J. Numer. Meth. Fl. 11 (1990), 541–553.Google ScholarCross Ref
15. A. J. Chorin. 1973. Numerical study of slightly viscous flow. J. Fluid Mech. 57 (1973), 785–796.Google ScholarCross Ref
16. A. J. Chorin. 1990. Hairpin removal in vortex interactions. J. Comput. Phys. 91 (1990), 1–21.Google ScholarDigital Library
17. A. J. Chorin. 1993. Hairpin removal in vortex interactions II. J. Comput. Phys. 107 (1993), 1–9.Google ScholarDigital Library
18. R. Cortez. 1996. An impulse-based approximation of fluid motion due to boundary forces. J. Comput. Phys. 123, 2 (1996), 341–353.Google ScholarDigital Library
19. G. H. Cottet and P. Koumoutsakos. 2000. Vortex Methods: Theory and Practice. Cambridge University Press.Google ScholarCross Ref
20. S. Eberhardt, S. Weissmann, U. Pinkall, and N. Thuerey. 2017. Hierarchical vorticity skeletons. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 6.Google Scholar
21. L. L. Erickson. 1990. Panel methods: An introduction. Vol. 2995. National Aeronautics and Space Administration.Google Scholar
22. V. M. Fernandez, N. J. Zabusky, P. Liu, S. Bhatt, and A. Gerasoulis. 1996. Filament surgery and temporal grid adaptivity extensions to a parallel tree code for simulation and diagnosis in 3D vortex dynamics. In ESAIM: Proceedings, Vol. 1. 197–211.Google ScholarCross Ref
23. F. Ferstl, R. Ando, C. Wojtan, R. Westermann, and N. Thuerey. 2016. Narrow band fLIP for liquid simulations. In Computer Graphics Forum, Vol. 35. 225–232.Google ScholarCross Ref
24. L. Greengard and V. Rokhlin. 1987. A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987), 325–348.Google ScholarDigital Library
25. O. Hald. 1979. Convergence of vortex methods for Euler’s equations. II. SIAM J. Numer. Anal. 16 (1979), 726–755.Google ScholarDigital Library
26. O. Hald and V. M. Del Prete. 1978. Convergence of vortex methods for Euler’s equations. Math. Comput. 32 (1978), 791–809.Google Scholar
27. H. Hasimoto. 1972. A soliton on a vortex filament. J. Fluid Mech. 854 (1972), 477–485.Google ScholarCross Ref
28. E. Hopfinger, F. Browand, and Y. Gagne. 1982. Turbulence and waves in a rotating tank. J. Fluid Mech. 125 (1982), 505–534.Google ScholarCross Ref
29. L. Hu, M. Chen, P. X. Liu, and S. Xu. 2020. A vortex method of 3D smoke simulation for virtual surgery. Comput. Meth. Prog. Bio. 198 (2020), 105813.Google ScholarCross Ref
30. Y. Hu, X. Zhang, M. Gao, and C. Jiang. 2019. On hybrid lagrangian-eulerian simulation methods: practical notes and high-performance aspects. In ACM SIGGRAPH 2019 Courses. 1–246.Google Scholar
31. S. C. Hung and R. B. Kinney. 1988. Unsteady viscous flow over a grooved wall: A comparison of two numerical methods. Int. J. Numer. Meth. Fl. 8 (1988), 1403–1437.Google ScholarCross Ref
32. S. Kida and M. Takaoka. 1994. Vortex reconnection. Annu. Rev. Fluid Mech. 26 (1994), 169–189.Google ScholarCross Ref
33. D. Kleckner, L. H. Kauffman, and W. T. M. Irvine. 2016. How superfluid vortex knots untie. Nat. Phys. 12 (2016), 650–655.Google ScholarCross Ref
34. P. Koumoutsakos. 1993. Direct numerical simulations of unsteady separated flows using vortex methods. Ph.D. Dissertation.Google Scholar
35. R. Krasny. 1988. Numerical simulation of vortex sheet evolution. Fluid Dyn. Res. 3 (1988), 93–97.Google ScholarCross Ref
36. K. Kuzmina and I. Marchevsky. 2021. Flow simulation around circular cylinder at low Reynolds numbers using vortex particle method. In Journal of Physics: Conference Series, Vol. 1715. 012067.Google ScholarCross Ref
37. S. Leibovich. 1978. The structure of vortex breakdown. Ann. Rev. Fluid Mech. 10 (1978), 221–246.Google ScholarCross Ref
38. M. J. Lighthill. 1963. Introduction: Boundary Layer Theory: Laminar Boundary Layer. Oxford University Press.Google Scholar
39. T. Loiseleux, J. M. Chomaz, and P. Huerre. 1998. The effect of swirl on jets and wakes: Linear instability of the Rankine vortex with axial flow. Phys. Fluids 10 (1998), 1120–1134.Google ScholarCross Ref
40. Y. M. Marzouk and A. F. Ghoniem. 2007. Vorticity structure and evolution in a transverse jet. J. Fluid Mech. 575 (2007), 267–305.Google ScholarCross Ref
41. A. G. McKenzie. 2007. HOLA: a high-order Lie advection of discrete differential forms with applications in Fluid Dynamics. Ph.D. Dissertation. California Institute of Technology.Google Scholar
42. R. Mehra, N. Raghuvanshi, L. Antani, A. Chandak, S. Curtis, and D. Manocha. 2013. Wave-based sound propagation in large open scenes using an equivalent source formulation. ACM Trans. Graph. 32 (2013), 1–13.Google ScholarDigital Library
43. M. Padilla, A. Chern, F. Knöppel, U. Pinkall, and P. Schröder. 2019. On bubble rings and ink chandeliers. ACM Trans. Graph. 38, 4 (2019).Google ScholarDigital Library
44. S. I. Park and M. J. Kim. 2005. Vortex fluid for gaseous phenomena. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 261–270.Google Scholar
45. F. Pepin. 1990. Simulation of the flow past an impulsively started cylinder using a discrete vortex method. Ph.D. Dissertation.Google Scholar
46. T. Pfaff, N. Thuerey, and M. Gross. 2012a. Lagrangian vortex sheets for animating fluids. ACM Trans. Graph. 31 (2012).Google Scholar
47. T. Pfaff, N. Thuerey, and M. Gross. 2012b. Lagrangian vortex sheets for animating fluids. ACM Trans. Graph. 31 (2012), 1–8.Google ScholarDigital Library
48. Z. Qu, X. Zhang, M. Gao, C. Jiang, and B. Chen. 2019. Efficient and conservative fluids using bidirectional mapping. ACM Trans. Graph. 38, 4 (2019).Google ScholarDigital Library
49. L. Rosenhead. 1931. The formation of vortices from a surface of discontinuity. Proc. Roy. Soc. A 134 (1931), 170–192.Google Scholar
50. P. Roushan and X. L. Wu. 2005. Universal wake structures of Kármán vortex streets in two-dimensional flows. Phys. Fluids 17 (2005), 073601.Google ScholarCross Ref
51. M. W. Scheeler, D. Kleckner, D. Proment, G. L. Kindlmann, and W. T. M. Irvine. 2014. Helicity conservation by flow across scales in reconnecting vortex links and knots. Proc. Natl. Acad. Sci. 111 (2014), 15350–15355.Google ScholarCross Ref
52. C. Schreck, C. Hafner, and C. Wojtan. 2019. Fundamental solutions for water wave animation. ACM Trans. Graph. 38 (2019), 1–14.Google ScholarDigital Library
53. Z.-S. She, E. Jackson, and S. A. Orszag. 1990. Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344 (1990), 226–228.Google ScholarCross Ref
54. H. Takami. 1964. A numerical experiment with disecrete vortex approximation, with reference to the rolling up of a vortex sheet. Technical Report. Stanford Univ. Calif.Google Scholar
55. W. M. van Rees, F. Hussain, and P. Koumoutsakos. 2012. Vortex tube reconnection at Re = 104. Phys. Fluids 24 (2012), 075105.Google ScholarCross Ref
56. M. Vines, B. Houston, J. Lang, and W. Lee. 2013. Vortical inviscid flows with two-way solid-fluid coupling. IEEE T. Vis. Comput. Gr. 20 (2013), 303–315.Google ScholarDigital Library
57. H. Wang, Y. Jin, A. Luo, X. Yang, and B. Zhu. 2020. Codimensional surface tension flow using moving-least-squares particles. ACM Trans. Graph. 39, 4 (2020).Google ScholarDigital Library
58. S. Weißmann and U. Pinkall. 2009. Real-time interactive simulation of smoke using discrete integrable vortex filaments. Proc. Vir. Real., Inter. and Phys. Sim., 1–10.Google Scholar
59. S. Weißmann and U. Pinkall. 2010. Filament-based smoke with vortex shedding and variational reconnection. ACM Trans. Graph. 29 (2010), 115.Google ScholarDigital Library
60. S. Weißmann, U. Pinkall, and P. Schröder. 2014. Smoke Rings from Smoke. ACM Trans. Graph. 33 (2014), 140.Google ScholarDigital Library
61. J. C. Wu. 1976. Numerical boundary conditions for viscous flow problems. AIAA J. 14 (1976), 1042–1049.Google ScholarCross Ref
62. J. Z. Wu, H. Y. Ma, and M. D. Zhou. 2015. Vortical Flows. Springer.Google Scholar
63. S. Xiong and Y. Yang. 2017. The boundary-constraint method for constructing vortex-surface fields. J. Comput. Phys. 339 (2017), 31–45.Google ScholarDigital Library
64. S. Xiong and Y. Yang. 2019a. Construction of knotted vortex tubes with the writhe-dependent helicity. Phys. Fluids 31 (2019), 047101.Google ScholarCross Ref
65. S. Xiong and Y. Yang. 2019b. Identifying the tangle of vortex tubes in homogeneous isotropic turbulence. J. Fluid Mech. 874 (2019), 952–978.Google ScholarCross Ref
66. X. Zhang and R. Bridson. 2014. A PPPM fast summation method for fluids and beyond. ACM Trans. Graph. 33 (2014), 1–11.Google ScholarDigital Library
67. Y. Zhu and R. Bridson. 2005. Animating sand as a fluid. ACM Trans. Graph. 24 (2005), 965–972.Google ScholarDigital Library