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Smoke rings from smoke

Published: 27 July 2014 Publication History

Abstract

We give an algorithm which extracts vortex filaments ("smoke rings") from a given 3D velocity field. Given a filament strength h > 0, an optimal number of vortex filaments, together with their extent and placement, is given by the zero set of a complex valued function over the domain. This function is the global minimizer of a quadratic energy based on a Schrödinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix.
Turning traditional vector field representations of flows, for example, on a regular grid, into a corresponding set of vortex filaments is useful for visualization, analysis of measured flows, hybrid simulation methods, and sparse representations. To demonstrate our method we give examples from each of these.

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References

[1]
Angelidis, A., and Neyret, F. 2005. Simulation of Smoke based on Vortex Filament Primitives. In Proc. Symp. Comp. Anim., 87--96.
[2]
Bernard, P. S. 2006. Turbulent Flow Properties of Large-scale Vortex Systems. PNAS 103, 27, 10174--10179.
[3]
Bernard, P. S. 2009. Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21, 2.
[4]
Brochu, T., Keeler T., and Bridson, R. 2012. Linear-Time Smoke Animation with Vortex Sheet Meshes. In Proc. Symp. Comp. Anim., 87--95.
[5]
Chatelain, P., Curioni, A., Bergdorf, M., Rossinelli, D., Andreoni, W., and Koumoutsakos, P. 2008. Billion Vortex Particle Direct Numerical Simulations of Aircraft Wakes. Comp. Meth. Appl. Mech. & Eng. 197, 13--16, 1296--1304.
[6]
Chorin, A. J. 1990. Hairpin Removal in Vortex Interactions. J. Comput. Phys. 91, 1, 1--21.
[7]
Chorin, A. J. 1993. Hairpin Removal in Vortex Interactions II. J. Comput. Phys. 107, 1, 1--9.
[8]
Christiansen, S. H., and Halvorsen, T. G. 2011. A Gauge Invariant Discretization on Simplicial Grids of the Schrödinger Eigenvalue Problem in an Electromagnetic Field. SIAM J. Numer. Anal. 49, 1, 331--345.
[9]
Crane, K., de Goes, F., Desbrun, M., and Schröder, P. 2013. Digital Geometry Processing with Discrete Exterior Calculus. In ACM SIGGRAPH 2013 Courses, 7:1--7:126.
[10]
Desbrun, M., Kanso, E., and Tong, Y. 2008. Discrete Differential Forms for Computational Modeling. In Discrete Differential Geometry, A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, Eds., Vol. 38 of Oberwolfach Seminars. Birkhäuser Verlag, 287--324.
[11]
Golas, A., Narain, R., Sewall, J., Krajcevski, P., Dubey, P., and Lin, M. 2012. Large-Scale Fluid Simulation using Velocity-Vorticity Domain Decomposition. ACM Trans. Graph. 31, 6.
[12]
Governale, M., and Ungarelli, C. 1998. Gauge Invariant Grid Discretization of the Schrödinger Equation. Phys. Rev. B 58, 12, 7816--7821.
[13]
Halvorsen, T. G., and Kvaal, S. 2012. Manifestly Gauge Invariant Discretizations of the Schrödinger Operator. Phys. Lett. A 376, 12--13, 1107--1114.
[14]
Jiang, M., Machiraju, R., and Thompson, D. 2005. Detection and Visualization of Vortices. In The Visualization Handbook, C. D. Hansen and C. R. Johnson, Eds. Elsevier, 295--309.
[15]
Kim, D., young Song, O., and Ko, H.-S. 2009. Stretching and Wiggling Liquids. ACM Trans. Graph. 28, 5.
[16]
Kleckner, D., and Irvine, W. T. M. 2013. Creation and Dynamics of Knotted Vortices. Nat. Phys. 9, 4, 253--258.
[17]
Knöppel, F., Crane, K., Pinkall, U., and Schröder, P. 2013. Globally Optimal Direction Fields. ACM Trans. Graph. 32, 4.
[18]
Le, T. B., Borazjani, I., Kang, S., and Sotiropoulos, F. 2011. On the Structure of Vortex Rings from Inclined Nozzles. J. Fluid Mech. 686, 451--483.
[19]
Museth, K. 2013. VDB: High-resolution Sparse Volumes with Dynamic Topology. ACM Trans. Graph. 32, 3, 27:1--27:22.
[20]
Pfaff, T., Thuerey, N., and Gross, M. 2012. Lagrangian Vortex Sheets for Animating Fluids. ACM Trans. Graph. 31, 4.
[21]
Saad, Y. 2005. ILUT: A Dual Threshold Incomplete LU Factorization. Num. Lin. Alg. Appl. 1, 4, 387--402.
[22]
Side Effects Software Inc., 2013. Houdini#8482; FX.
[23]
Stathopoulos, A., and McCombs, J. R. 2010. PRIMME: PRe-conditioned Iterative MultiMethod Eigensolver: Methods and Software Description. ACM Trans. Math. Softw. 37, 2, 21:1--21:30.
[24]
Stock, M. J., Dahm, W. J. A., and Tryggvason, G. 2008. Impact of a Vortex Ring on a Density Interface using a Regularized Inviscid Vortex Sheet Method. J. Comput. Phys. 227, 21, 9021--9043.
[25]
Troolin, D. R., and Longmire, E. K. 2010. Volumetric Velocity Measurements of Vortex Rings from Inclined Exits. Exp. Fluids 48, 3, 409--420.
[26]
Weißmann, S., and Pinkall, U. 2010. Filament-based Smoke with Vortex Shedding and Variational Reconnection. ACM Trans. Graph. 29, 4.
[27]
Wikipedia, 2014. Hamiltonian (quantum mechanics) --- Wikipedia, The Free Encyclopedia.
[28]
Wikipedia, 2014. Winding Number --- Wikipedia, The Free Encyclopedia.
[29]
Wilson, K. G. 1974. Confinement of Quarks. Phys. Rev. D 10, 8, 2445--2459.

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    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 33, Issue 4
    July 2014
    1366 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/2601097
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 27 July 2014
    Published in TOG Volume 33, Issue 4

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    Author Tags

    1. DEC
    2. Schrödinger operator
    3. fluid simulation
    4. hairpin removal
    5. hybrid methods
    6. vortex filaments
    7. vortex reconnection

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