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ABSTRACT

We have developed a novel approach to open-boundaries for fluid animations. More specifically we present a highly efficient energy absorbing boundary condition for the incompressible Navier-Stokes equations in the prescence of a free surface. Our work extends and adapts a Perfectly Matched Layer (PML) approach [Berenger 1994; Johnson 2007], recently developed for the Navier-Stokes equations, to free surfaces in the context fluid animations. We show how our PML boundary condition is able to effectively eliminate reflections generated by the presence of solid boundaries in the simulation domain, and that our method is far superior to simpler approaches for reducing wave reflection. Furthermore, we have adapted our theoretical PML model to work with the Stable-Fluids Eulerian Navier-Stokes solver commonly used in computer graphics. Finally, we show that the cost of deploying our method in terms of memory and additional computations is small, and for a given quality significantly less than other known methods.

REFERENCES

• 1: Berenger, J.-P. 1994. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 114, 2, 185--200.
• 2: Johnson, S. G., 2007. Notes on perfectly matched layers. online MIT course notes (Aug. 2007).

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Boundary representations

Additional Classification:
  A. General Literature
  A.m MISCELLANEOUS

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.m Miscellaneous