Model-reduced variational fluid simulation

ACM Transactions on Graphics

Volumn 34, Issue 6, 2015, Pages

  Liu, Beibei ^a   Mason, Gemma ^b,c   Hodgson, Julian ^d   Tong, Yiying ^a   Desbrun, Mathieu ^b,e  

^a MSU   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

^d UNIVERSITY COLLEGE LONDON   (United Kingdom)

^e INRIA   (France)

Author keywords

Computational fluid dynamics; Energy preservation; Eulerian simulation; Model reduction; Sub grid resolution geometry

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL GEOMETRY; EIGENVALUES AND EIGENFUNCTIONS; MAGNETOHYDRODYNAMICS; MATHEMATICAL OPERATORS; VARIATIONAL TECHNIQUES;

ACCURATE BOUNDARY CONDITIONS; EIGENFUNCTIONS OF THE LAPLACIAN; EULERIAN SIMULATIONS; GEOMETRIC INTEGRATORS; MODEL REDUCTION; SPATIAL AND TEMPORAL RESOLUTIONS; SUB-GRIDS; VARIATIONAL INTEGRATORS;

NUMERICAL METHODS;

EID: 84995748168     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/2816795.2818130     Document Type: Conference Paper

References (49)

1. AN, S., KIM, T., AND JAMES, D. 2008. Optimizing cubature for efficient integration of subspace deformations. ACM Trans. Graph. 27, 5, Art. 165.
2. ARNOLD, D. N., FALK, R. S., AND WINTHER, R. 2006. Finite element exterior calculus, homological techniques, and applications. Acta Numerica 15, 1-155.
3. AZENCOT, O., WEISSMANN, S., OVSJANIKOV, M., WARDETZKY, M., AND BEN-CHEN, M. 2014. Functional fluids on surfaces. Comput. Graph. Forum 33, 5, 237-246.
4. BATTY, C., BERTAILS, F., AND BRIDSON, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. 26, 3, Art. 100.
5. BELL, N., AND HIRANI, A. N., 2008. PyDEC: A Python library for Discrete Exterior Calculus. Google Code project at: http://code.google.com/p/pydec/.
6. CHORIN, A., AND MARSDEN, J. 1979. A Mathematical Introduction to Fluid Mechanics, 3rd edition ed. Springer-Verlag.
7. COHEN, J. M., TARIQ, S., AND GREEN, S. 2010. Interactive fluid-particle simulation using translating Eulerian grids. In ACM Symp. on Interactive 3D Graphics and Games, 15-22.
8. DE WITT, T., LESSIG, C., AND FIUME, E. 2012. Fluid simulation using Laplacian eigenfunctions. ACM Trans. Graph. 31, 1, Art. 10.
9. DESBRUN, M., KANSO, E., AND TONG, Y. 2008. Discrete differential forms for computational modeling. In Discrete Differential Geometry, A. I. Bobenko et al., Ed., vol. 38 of Oberwolfach Seminars. Birkhäuser Basel, 287-324.
10. DESBRUN, M., GAWLIK, E. S., GAY-BALMAZ, F., AND ZEITLIN, V. 2013. Variational discretization for rotating stratified fluids. Disc. Cont. Dyn. S. 34, 2, 477-509.
11. ELCOTT, S., AND SCHRÖDER, P. 2006. Building your own DEC at home. In Discrete Differential Geometry, ACM SIGGRAPH Courses, 55-59.
12. ELCOTT, S., TONG, Y., KANSO, E., SCHRÖDER, P., AND DESBRUN, M. 2007. Stable, circulation-preserving, simplicial fluids. ACM Trans. Graph. 26, 1, Art. 4.
13. FELDMAN, B. E., O'BRIEN, J. F., AND KLINGNER, B. M. 2005. Animating gases with hybrid meshes. ACM Trans. Graph. 24, 3, 904-909.
14. FOIAS, C., HOLM, D. D., AND TITI, E. S. 2002. The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Dyn. Differ. Equ. 14, 1, 1-35.
15. FOSTER, N., AND METAXAS, D. 1997. Modeling the motion of a hot, turbulent gas. In Proc. ACM SIGGRAPH, 181-188.
16. GAO, Y., LI, C.-F., REN, B., AND HU, S.-M. 2013. View-dependent multiscale fluid simulation. IEEE Trans. Vis. Comput. Graph. 19, 2, 178-188.
17. GAWLIK, E., MULLEN, P., PAVLOV, D., MARSDEN, J., AND DESBRUN, M. 2011. Geometric, variational discretization of continuum theories. Physica D: Nonlinear Phenomena 240, 21, 1724-1760.
18. 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, Art. 148.
19. GUPTA, M., AND NARASIMHAN, S. G. 2007. Legendre fluids: A unified framework for analytic reduced space modeling and rendering of participating media. In Symp. on Computer Animation, 17-25.
20. HARLOW, F. H., AND WELCH, J. E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids 8, 12, 2182-2189.
21. HOWES, R., SCHROEDER, C., AND TERAN, J. M. 2013. A virtual node algorithm for Hodge decompositions of inviscid flow problems with irregular domains. Methods Appl. Anal. 20, 4, 439-455.
22. KHAREVYCH, L., YANG, W., TONG, Y., KANSO, E., MARSDEN, J. E., SCHRÖDER, P., AND DESBRUN, M. 2006. Geometric, variational integrators for computer animation. In Symp. on Computer Animation, 43-51.
23. KIM, T., AND DELANEY, J. 2013. Subspace fluid re-simulation. ACM Trans. Graph. 32, 4, 62.
24. KIM, T., THÜREY, N., JAMES, D., AND GROSS, M. 2008. Wavelet turbulence for fluid simulation. In ACM Trans. Graph., vol. 27, ACM, 50.
25. LI, S., HUANG, J., DE GOES, F., JIN, X., BAO, H., AND DESBRUN, M. 2014. Space-time editing of elastic motion through material optimization and reduction. ACM Trans. Graph. 33, 4, Art. 108.
26. LONG, B., AND REINHARD, E. 2009. Real-time fluid simulation using discrete sine/cosine transforms. In Symp. on Interactive 3D Graphics and Games, 99-106.
27. LOSASSO, F., TALTON, J., KWATRA, N., AND FEDKIW, R. 2008. Two-way coupled SPH and Particle Level Set fluid simulation. IEEE Trans. Vis. Comput. Graph. 14, 4, 797-804.
28. MARSDEN, J. E., AND WEST, M. 2001. Discrete mechanics and variational integrators. Acta Numerica 2001 10, 357-514.
29. MULLEN, P., CRANE, K., PAVLOV, D., TONG, Y., AND DESBRUN, M. 2009. Energy-preserving integrators for fluid animation. ACM Trans. Graph. 28, 3, Art. 38.
30. NARAIN, R., SEWALL, J., CARLSON, M., AND LIN, M. C. 2008. Fast animation of turbulence using energy transport and procedural synthesis. ACM Trans. Graph. 27, 5, 166.
31. NG, Y. T., MIN, C., AND GIBOU, F. 2009. An efficient fluid-solid coupling algorithm for single-phase flows. J. Comput. Phys. 228, 23, 8807-8829.
32. ORSZAG, S. A. 1969. Numerical methods for the simulation of turbulence. Physics of Fluids 12, II 250-257.
33. PAVLOV, D., MULLEN, P., TONG, Y., KANSO, E., MARSDEN, J., AND DESBRUN, M. 2011. Structure-preserving discretization of incompressible fluids. Physica D: Nonlinear Phenomena 240, 6, 443-458.
34. SCHECHTER, H., AND BRIDSON, R. 2008. Evolving sub-grid turbulence for smoke animation. In Symp. on Computer Animation, 1-7.
35. SELLE, A., RASMUSSEN, N., AND FEDKIW, R. 2005. A vortex particle method for smoke, water and explosions. ACM Trans. Graph. 24, 3, 910-914.
36. SILBERMAN, I. 1954. Planetary waves in the atmosphere. J. Meteor. 11, 27-34.
37. STAM, J., AND FIUME, E. 1993. Turbulent wind fields for gaseous phenomena. In Proc. ACM SIGGRAPH, 369-376.
38. STAM, J. 1999. Stable fluids. In Proc. ACM SIGGRAPH, 121-128.
39. STAM, J. 2002. A simple fluid solver based on the FFT. J. Graph. Tools 6, 2, 43-52.
40. STAM, J. 2003. Flows on surfaces of arbitrary topology. ACM Trans. Graph. 22, 3, 724-731.
41. STANTON, M., SHENG, Y., WICKE, M., PERAZZI, F., YUEN, A., NARASIMHAN, S., AND TREUILLE, A. 2013. Non-polynomial Galerkin projection on deforming meshes. ACM Trans. Graph. 32, 4, Art. 86.
42. STEINHOFF, J., AND UNDERHILL, D. 1994. Modification of the Euler equations for Vorticity Confinement. Physics of Fluids 6, 8, 2738-2744.
43. TONG, Y., ALLIEZ, P., COHEN-STEINER, D., AND DESBRUN, M. 2006. Designing quadrangulations with discrete harmonic forms. In Symp. on Geometry Processing, 201-210.
44. TREUILLE, A., LEWIS, A., AND POPOVIĆ, Z. 2006. Model reduction for real-time fluids. ACM Trans. Graph. 25, 3, 826-834.
45. URBAN, K. 2002. Wavelet bases for H(div) and H(curl). In Wavelets in Numerical Simulation, vol. 22 of Lecture Notes in Computational Science and Engineering. 83-107.
46. VON TYCOWICZ, C., SCHULZ, C., SEIDEL, H.-P., AND HILDEBRANDT, K. 2013. An efficient construction of reduced deformable objects. ACM Trans. Graph. 32, 6, Art. 213.
47. YUAN, Z., CHEN, F., AND ZHAO, Y. 2011. Pattern-guided smoke animation with Lagrangian Coherent Structure. ACM Trans. Graph. 30, 6, Art. 136.
48. YUDOVICH, V. 1963. Non-stationary flow of an ideal incompressible liquid. USSR Computational Mathematics and Mathematical Physics 3, 6, 1407-1456.
49. ZHANG, X., BRIDSON, R., AND GREIF, C. 2015. Restoring the missing vorticity in advection-projection fluid solvers. ACM Trans. Graph. 34, 4, Art. 52.