Narrow Band Pressure Computation for Eulerian Fluid Simulation

Aditya Prakash, Parag Chaudhuri

2017

Abstract

An Eulerian fluid simulation for incompressible fluids spends a lot of time in enforcing incompressibility by solving a large Poisson’s equation. This involves solving a large system of equations using a solver like conjugate gradients. We introduce a way of accelerating this computation by dividing the grid domain of the fluid simulation into a narrow band of high resolution grid cells near fluid-solid boundaries and a coarser grid everywhere else. Judiciously reducing the number of high resolution grid cells significantly lowers the cost of the pressure projection step, while not sacrificing the simulation quality. The coarse grid values are upgraded to a finer grid before advecting the fluid surface so that enough degrees of freedom are available to resolve surface detail. We present and analyse two methods to perform this upgradation, namely, velocity interpolation and pressure field smoothing. We discuss the merits and demerits of each and quantify the errors introduced in the simulation as a function of size of the narrow band. Finally, since we are primarily interested in visualizing the fluid animation, we produce rendered fluid simulation output to also validate the visual quality of the simulations.

References

  1. Ando, R., Thuerey, N., and Wojtan, C. (2015). A dimension-reduced pressure solver for liquid simulations. Computer Graphics Forum, 34(2):473-480.
  2. Autodesk. Deep adaptive fluid simulation in Maya 2016. http://www.autodesk.com/products/maya/features/ dynamics-and-effects/deep-adaptive-fluid-simulation. Last accessed on 8/6/2016.
  3. Berger, M. and Oliger, J. (1984). Adaptive mesh refinement for hyperbolic partial differential equations. Journal of Computational Physics, 53:484-512.
  4. Bridson, R. (2008). Fluid Simulation for Computer Graphics. Taylor & Francis.
  5. Bridson, R., Houriham, J., and Nordenstam, M. (2007). Curl-noise for procedural fluid flow. ACM Transactions on Graphics, 26(3).
  6. Chentanez, N. and Müller, M. (2011). Real-time eulerian water simulation using a restricted tall cell grid. In ACM Transactions on Graphics, volume 30, page 82.
  7. Chentanez, N., M üller, M., and Kim, T.-Y. (2014). Coupling 3d eulerian, heightfield and particle methods for interactive simulation of large scale liquid phenomena. In Proceedings of the ACM SIGGRAPH/Eurographics SCA, pages 1-10.
  8. De Witt, T., Lessig, C., and Fiume, E. (2012). Fluid simulation using laplacian eigenfunctions. ACM Transactions on Graphics, 31(1):10:1-10:11.
  9. Enright, D., Marschner, S., and Fedkiw, R. (2002). Animation and rendering of complex water surfaces. ACM Transactions on Graphics, 21(3):736-744.
  10. Ferstl, F., Ando, R., Wojtan, C., Westermann, R., and Thuerey, N. (2016). Narrow band FLIP for liquid simulations. Computer Graphics Forum (Eurographics), 35(2):to appear.
  11. Ferstl, F., Westermann, R., and Dick, C. (2014). Large-scale liquid simulation on adaptive hexahedral grids. IEEE Transactions on Visualization and Computer Graphics, 20(10):1407-1417.
  12. Foster, N. and Fedkiw, R. (2001). Practical animation of liquids. In Proceedings of SIGGRAPH, pages 23-30.
  13. Jung, H. R., Kim, S.-T., Noh, J., and Hong, J.-M. (2013). A heterogeneous CPUGPU parallel approach to a multigrid poisson solver for incompressible fluid simulation. Computer Animation and Virtual Worlds, 24(3- 4):185-193.
  14. Kim, T., Tessendorf, J., and Threy, N. (2013). Closest point turbulence for liquid surfaces. ACM Transactions on Graphics, 32(2):15:1-15:13.
  15. Larmorlette, L. and Foster, N. (2002). Structural modeling of flames for a production environment. ACM Transactions on Graphics, 21(3):729-735.
  16. Lentine, M., Zheng, W., and Fedkiw, R. (2010). A novel algorithm for incompressible flow using only a coarse grid projection. ACM Transactions on Graphics, 29(4).
  17. Losasso, F., Gibou, F., and Fedkiw, R. (2004). Simulating water and smoke with an octree data structure. ACM Transactions on Graphics, 23(3):457-462.
  18. McAdams, A., Sifakis, E., and Teran, J. (2010). A parallel multigrid poisson solver for fluids simulation on large grids. In Proceedings of ACM SIGGRAPH/Eurographics SC, pages 65-74.
  19. Montijn, C., Hundsdorfer, W., and Ebert, U. (2006). An adaptive grid refinement strategy for the simulation of negative streamers. Journal of Computational Physics, 219(2).
  20. Mullen, P., Crane, K., Pavlov, D., Y., T., and Desbrun, M. (2009). Energy-preserving integrators for fluid animation. In Proceedings of SIGGRAPH, pages 1-8.
  21. Prakash, A. and Chaudhuri, P. (2015). Comparing performance of parallelizing frameworks for grid-based fluid simulation on the cpu. In Proceedings of the 8th ACM India Computing Conference, Compute 7815, pages 1-7.
  22. Rasmussen, N., Nguyen, D., Geiger, W., and Fedkiw, R. (2003). Smoke simulation for large scale phenomena. ACM Transactions on Graphics, 22(3):703-707.
  23. Schechter, H. and Bridson, R. (2008). Evolving sub-grid turbulence for smoke animation. In Proceedings of the ACM SIGGRAPH/Eurographics SCA, page 17.
  24. Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac, J. (2008). An unconditionally stable maccormack method. Journal of Scientific Computing , 35(2- 3):350-371.
  25. Stam, J. (1999). Stable fluids. In Proceedings of SIGGRAPH, pages 121-128.
  26. Stomakhin, A., Schroeder, C., Chai, L., Teran, J., and Selle, A. (2013). A material point method for snow simulation. ACM Transactions on Graphics, 32(4):102:1- 102:10.
  27. Threy, N., Wojtan, C., Gross, M., and Turk, G. (2010). A multiscale approach to mesh-based surface tension flows. ACM Transactions on Graphics, 29(4).
  28. Treuille, A., Lewis, A., and Popovi, Z. (2006). Model reduction for real-time fluids. ACM Transactions on Graphics, 25(3):826-834.
  29. Yue, Y., Smith, B., Batty, C., Zheng, C., and Grinspun, E. (2015). Continuum foam: A material point method for shear-dependent flows. ACM Transactions on Graphics, 34(5):160:1-160:20.
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Paper Citation


in Harvard Style

Prakash A. and Chaudhuri P. (2017). Narrow Band Pressure Computation for Eulerian Fluid Simulation . In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2017) ISBN 978-989-758-224-0, pages 17-26. DOI: 10.5220/0006090200170026


in Bibtex Style

@conference{grapp17,
author={Aditya Prakash and Parag Chaudhuri},
title={Narrow Band Pressure Computation for Eulerian Fluid Simulation},
booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2017)},
year={2017},
pages={17-26},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006090200170026},
isbn={978-989-758-224-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2017)
TI - Narrow Band Pressure Computation for Eulerian Fluid Simulation
SN - 978-989-758-224-0
AU - Prakash A.
AU - Chaudhuri P.
PY - 2017
SP - 17
EP - 26
DO - 10.5220/0006090200170026