Researches: Nuria Suarez, Antonio Susín.

The complexity of fluid behaviour is well known. Generally, all the methods used in Fluid Animation have their advantages and their disadvantages and the use of only one of such methods is not enough to catch the realism of the scene maintaining, at the same time, an acceptable performance and some animation control to modify the behaviour of a fluid when its real simulation does not fit the artistic requirements. These are the main challenges when simulating fluids for video-games, virtual environments or other interactive applications.

In the Fluid Simulation world, the reference equations for modelling ordinary events (like liquid streams, liquids moving inside containers and even low speed smoke) are the
Navier-Stokes Equations for Incompressible Viscous Flows, (1) expressed in terms of velocity and pressure, and including fluid parameters like the Reynolds Number, directly related with the Kinematic Viscosity, and other body external forces, like Gravity, etc.




From the wide range of approaches to the numeric solution of these equations different methods of Fluid Simulation have arisen, each one, as we said, with its advantages and its disadvantages. Among all of them, we can stand out the following two:

Marker and Cell (MAC). Simulation method with an Eulerian approach, in which the unknowns are calculated over a mesh of the domain and the fluid position is determined, at every time step, by marker particles. These particles do not have any mass and are moved through the simulation area according to the velocity field. It has very good simulation times when the scene does not require high-level details [FM96].


Fig 2. Marker and Cell formulation.

Smoothed Particle Hydrodynamics (SPH). It is a Lagrangian method in which the fluid is represented by particles, each of them with its own values and associated characteristics, that determine the movement of the fluid. This method can achieve high-level detail but means a
very important computational effort since the behaviour of each particle depends on the behaviour of the surrounding particles at every time step [Mon92].

Nowadays, MAC and SPH coexist with other important and interesting methods, like the semi-lagrangian one of J. Stam [Sta99]. Unfortunately, this method is very suitable for dealing with smoke but has some troubles when it is directly applied to liquid simulation (it suffers from mass dissipation) and needs some special techniques to be used on the surface


Fig. 3. Velocity Field. Blue SPH simulation model. Orange MAC simulation model. The transition zone in between

[FF01]. We are interested in the animation and control of big volumes of fluid, but considering the possibility of having different level of detail simulation. Thus, we are planning to build hybrid methods using MAC and SPH taking advantage of their combination.  



Fig. 4. Hybrid simulation of two square falling fluid drops.



Suarez de la Torre, Nuria
PhD Dissertation: Coupling Marker and Cell and Smoothed Particle Hydrodynamics for Fluid Animation.
Dept. Matemàtica Aplicada 1, Univ. Politècnica de Catalunya. 22/12/2006

Example image - aligned to the right

Suárez N., A. Susín. A Mesh-Particle Model for Fluid Animation.
3th Ibero-American Symposium in Computer Graphics (SIACG-2006). Editors Brunet P., Correia N., Baranoski G. Proc. SIACG-06, pp 13-20 (2006).(PDF 5.7Mb)

Example image - aligned to the right

Suárez N.,  A. Susín
A Mesh-Particle Model for the Animation of Large-Volume Fluids
Proceedings of the International Conference on Engineering and Mathematics 2006 (ENMA06),  pp 169—176 (2006)

Example image - aligned to the right

Suárez N., A. Susin. Desarrollo de un mètodo mixto malla-partícula para la animación de fluidos. Actas XV Congreso Español de Informática Gráfica (CEIG'2005). Editores J. Regincós, D. Martín. Ed. Thomson- Paraninfo, pp 233-236, 2005 (ISBN: 84-9732-431-5).(PDF 374Kb)



[DC99] Desbrun, M., Cani, M., Space-Time Adaptive Simulation of Highly Deformable Substances, Technical Report 3839, INRIA, 1999.
[FF01] Foster, N., Fedkiw, R., Practical Animation of Liquids, ACM SIGGRAPH 2001, 15-22, 2001.
[FM96] Foster, N., Metaxas, D., Realistic Animation of Liquids, Graphical Models and Image Processing 58, 471-483, 1996.
[FM97] Foster, N., Metaxas, D., Controlling Fluid Animation, Computer Graphics international 97, 178-188, 1997.
[Mon92] Monaghan, J., Smoothed Particle Hydrodynamics, Annu. Rev. Astron. Astrophys. 30, 543-74, 1992.
[MK00] Monaghan, J., Kos, A., Scott Russell’s Wave Generator, Physics of Fluids, vol 12, num 3, 2000.
[MCG03] Müller, M., Charypar, D., Gross, M., Particle-Based Fluid Simulation for Interactive Applications, Proc. Eurographics/ SIGGRAPH Sym., 154-159, 2003.
[MST04] Müller, M. et al., Interaction of Fluids with Deformable Solids, Journal of Computer Animation and Virtual Worlds, vol 15, num 3-4, 159-171, 2004.
[SS06] Suárez N.,  A. Susín. A Mesh-Particle Model for Fluid Animation. In Proc. 3th Ibero-American Symposium in Computer Graphics (SIACG-2006), Brunet P., Correia N., Baranoski G Ed,  pp 13--20 (2006)
[Sta99] Stam, J., Stable Fluids, ACM SIGGRAPH 99, 121-128, 1999.
[Sta03] Stam, J., Real-Time Fluid Dynamics for Games, Proceedings of the Game Developer Conference, 2003.
[TFK*03] Takahashi, T. et al., Realistic Animation of Fluid with Splash and Foam, Proc. Eurographics 2003, vol 22, num 3, 2003.

Toni Susin