Abstract
We present a novel approach for animating incompressible fluids with Eulerian advection-projection solvers on the surface of a sphere by extending the recent work by Hill and Henderson [2016] with a staggered spherical grid discretization. By doing so, we avoid the infamous checkerboard null modes. We additionally introduce new, straightforward polar singularity treatments that avoid the previous need for any spectral filtering of high-frequency noise at the poles. Lastly, we enforce incompressibility with a fast Fourier solution to Poisson's equation for pressure in spherical coordinates. Our high-performance GPU-based framework combines scalability, art-directability, and ease of implementation, and reaches real-time speeds for various practical scenarios.
- G. K. Batchelor. 2000. An introduction to fluid dynamics. Cambridge University Press.Google Scholar
- G. Bradski. 2000. The OpenCV library. J Soft Tools (2000).Google Scholar
- Robert Bridson. 2015. Fluid simulation for computer graphics. CRC Press.Google Scholar
- Robert Bridson, Jim Houriham, and Marcus Nordenstam. 2007. Curl-noise for procedural fluid flow. ACM Trans Graph 26, 3 (2007). Google Scholar
Digital Library
- Maria Francesca Carfora. 2007. Semi-Lagrangian advection on a spherical geodesic grid. 55 (09 2007), 127.Google Scholar
- Leonardo Carvalho, Maria Andrade, and Luiz Velho. 2012. Fluid simulation on surfaces in the GPU. In SIBGRAPI Conf Graph Patt Images. 205--212. Google Scholar
Digital Library
- Sharif Elcott, Yiying Tong, Eva Kanso, Peter Schröder, and Mathieu Desbrun. 2007. Stable, circulation-preserving, simplicial fluids. ACM Trans Graph 26, 1 (2007). Google Scholar
Digital Library
- Ronald Fedkiw, Jos Stam, and Henrik Wann Jensen. 2001. Visual simulation of smoke. In Comp Graph Inter Tech. 15--22. Google Scholar
Digital Library
- Andrew S Glassner. 1999. Andrew Glassner's notebook: Recreational computer graphics. Google Scholar
Digital Library
- Kyle Hegeman, Michael Ashikhmin, Hongyu Wang, and Hong Qin. 2009. GPU-based conformal flow on surfaces.Google Scholar
- David J. Hill and Ronald D. Henderson. 2016. Efficient fluid simulation on the surface of a sphere. ACM Trans Graph 35, 2 (2016), 16:1--16:9. Google Scholar
Digital Library
- Zhanpeng Huang, Ladislav Kavan, Weikai Li, Pan Hui, and Guanghong Gong. 2015. Reducing numerical dissipation in smoke simulation. Graph. Models 78, C (2015), 10--25. Google Scholar
Digital Library
- Gergely Klár, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran. 2016. Drucker-prager elastoplasticity for sand animation. ACM Trans Graph 35, 4 (2016), 103. Google Scholar
Digital Library
- Ming-Chih Lai and Wei-Cheng Wang. 2002. Fast direct solvers for Poisson equation on 2D polar and spherical geometries. Num Meth Part Diff Eq 18, 1 (2002), 18:56--18:68.Google Scholar
- Huan Mei, Faming Wang, Zhong Zeng, Zhouhua Qiu, Linmao Yin, and Liang Li. 2016. A global spectral element model for Poisson equations and advective flow over a sphere. Adv Atom Sci 33, 3 (2016), 377--390.Google Scholar
Cross Ref
- Ken Museth, Jeff Lait, John Johanson, Jeff Budsberg, Ron Henderson, Mihai Alden, Peter Cucka, David Hill, and Andrew Pearce. 2013. OpenVDB: an open-source data structure and toolkit for high-resolution volumes. In SIGGRAPH Courses. 19. Google Scholar
Digital Library
- Ramachandran D. Nair, Stephen J. Thomas, and Richard D. Loft. 2005. A discontinuous Galerkin transport scheme on the cubed sphere. Mon Weather Rev 133, 4 (2005), 814--828.Google Scholar
Cross Ref
- Azencot Omri, Weiçmann Steffen, Ovsjanikov Maks, Wardetzky Max, and BenâĂŘChen Mirela. 2014. Functional fluids on surfaces. Comp Graph Forum 33, 5 (2014), 237--246.Google Scholar
Digital Library
- William M. Putman and Shian-Jiann Lin. 2007. Finite-volume transport on various cubed-sphere grids. J Comp Phys 227, 1 (2007), 55--78. Google Scholar
Digital Library
- Dave Randall. 2011. An introduction to numerical modeling of the atmosphere.Google Scholar
- David A. Randall, Todd D. Ringler, Ross P. Heikes, Phil Jones, and John Baumgardner. 2002. Climate modeling with spherical geodesic grids. Comp Sci Eng 4, 5 (2002), 32--41. Google Scholar
Digital Library
- C. Ronchi, R. Iacono, and P.S. Paolucci. 1996. The "cubed sphere". J Comp Phys 124, 1 (1996), 93--114. Google Scholar
Digital Library
- Lin Shi and Yizhou Yu. 2004. Inviscid and incompressible fluid simulation on triangle meshes: Research articles. Comp Anim Virt Worlds 15, 3-4 (2004), 173--181. Google Scholar
Digital Library
- Jos Stam. 1999. Stable fluids. In Comp Graph Inter Tech. 121--128. Google Scholar
Digital Library
- Jos Stam. 2003. Flows on surfaces of arbitrary topology. ACM Trans Graph 22, 3 (2003), 724--731. Google Scholar
Digital Library
- Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. 2013. A material point method for snow simulation. ACM Trans Graph 32, 4 (2013), 102. Google Scholar
Digital Library
- J. B. White, III and J. J. Dongarra. 2011. High-performance high-resolution semi-Lagrangian tracer transport on a sphere. J Comp Phys 230, 17 (2011), 6778--6799. Google Scholar
Digital Library
- J. Zehnder, R. Narain, and B. Thomaszewski. 2018. An advection-reflection solver for detail-preserving fluid simulation. ACM Trans Graph 37, 4 (2018). Google Scholar
Digital Library
- Yao Zhang, Jonathan Cohen, and John D. Owens. 2010. Fast tridiagonal solvers on the GPU. SIGPLAN Not 45, 5 (2010), 127--136. Google Scholar
Digital Library
- Yongning Zhu and Robert Bridson. 2005. Animating sand as a fluid. ACM Trans Graph 24, 3 (2005), 965--972. Google Scholar
Digital Library
Index Terms
Real-Time Fluid Simulation on the Surface of a Sphere
Recommendations
A novel surface tension formulation for SPH fluid simulation
Surface tension plays a significant role in fluid simulation, especially small-scale fluid. In this paper, we present a novel surface tension formulation for smoothed particle hydrodynamics (SPH) to simulate interfacial fluid flow. The surface tension ...
Vortical Inviscid Flows with Two-Way Solid-Fluid Coupling
Vortex methods increasingly receive attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. The coupling between free-form solids, represented by arbitrary surface meshes, and fluids ...
Multiple-Fluid SPH Simulation Using a Mixture Model
This article presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is ...






Comments