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Level Set Advection of Free Fluid Surface Modified by Surface Tension

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초록

Fluids appear in innumerable phenomena; therefore, it is interesting to reproduce those phenomena by computer graphics techniques. However, this process is not trivial. We work with a fluid simulation that uses Navier-Stokes equations to model the fluid, a semi-Lagrangian approach to solve it and the level set method to track the surface of the fluid. Modified versions of the Navier-Stokes equations for computer graphics allow us to create a wide diversity of effects. In this paper, we propose a technique that allows us to integrate a force inspired by surface tension into the model. We describe which information we need and how to modify the model with this new approach. We end up with a modified simulation that has additional effects that might be suitable for computer graphics purposes. The effects that we are able to recreate are small waves and droplet-like formations close to the surface of the fluid. This model preserves the overall behavior governed by the Navier-Stokes equations.

Abstract

Fluids appear in innumerable phenomena; therefore, it is interesting to reproduce those phenomena by computer graphics techniques. However, this process is not trivial. We work with a fluid simulation that uses Navier-Stokes equations to model the fluid, a semi-Lagrangian approach to solve it and the level set method to track the surface of the fluid. Modified versions of the Navier-Stokes equations for computer graphics allow us to create a wide diversity of effects. In this paper, we propose a technique that allows us to integrate a force inspired by surface tension into the model. We describe which information we need and how to modify the model with this new approach. We end up with a modified simulation that has additional effects that might be suitable for computer graphics purposes. The effects that we are able to recreate are small waves and droplet-like formations close to the surface of the fluid. This model preserves the overall behavior governed by the Navier-Stokes equations.

참고문헌 (15)

  1. Israel Pineda, "Surface Tension Approximation in Semi-Lagrangian Level Set Based Fluid Simulations for Computer Graphics", CGMIP 2014 The International Conference on Computer Graphics, Multimedia and Image Processing (2014)
  2. Huamin Wang, "Water Drops on Surfaces", ACM SIGGRAPH 2005 Papers, pp.921~929 (2005)
  3. Myungjoo Kang, "A Level Set Approach for the Motion of Soap Bubbles with Curvature Dependent Velocity Or Acceleration", ~ (1996)
  4. A. Albadawi, "Influence of surface tension implementation in Volume of Fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment", International Journal of Multiphase Flow, 53, pp.11~28 (2013)
  5. Douglas Enright, "A Hybrid Particle Level Set Method for Improved Interface Capturing", Journal of Computational Physics, 183(1), pp.83~116 (2002)
  6. Frank Losasso, "Multiple Interacting Liquids", ACM SIGGRAPH 2006 Papers, pp.812~819 (2006), ACM
  7. Christopher Batty, "A Fast Variational Framework for Accurate Solid-fluid Coupling", ACM SIGGRAPH 2007 Papers (2007), ACM
  8. Ronald Fedkiw, "A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)", Journal of Computational Physics, 152(2), pp.457~492 (1999)
  9. Jie Tan, "Physically-based fluid animation: A survey", Science in China Series F: Information Sciences, 52(5), pp.723~740 (2009)
  10. Francis Harlow, "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface", Phys. Fluids, 8, pp.2182~2189 (1965)
  11. Jos Stam, "Stable Fluids", Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp.121~128 (1999), ACM Press[DOI]
  12. Nick Foster, "Realistic Animation of Liquids", Graphical Models and Image Processing, pp.23~30 (1996)
  13. C. W. Hirt, "Volume of fluid (VOF) method for the dynamics of free boundaries", Journal of Computational Physics, 39(1), pp.201~225 (1981)
  14. Stanley Osher, "Level Set Methods and Dynamic Implicit Surfaces 2003 edition" (2002), Springer
  15. Raanan Fattal, "Target-driven Smoke Animation", ACM SIGGRAPH 2004 Papers, pp.441~448 (2004), ACM

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