# 2009 Research Summary

## Simultaneous Coupling of Fluids and Deformable Bodies

View Current Project Information

Nuttapong Chentanez, Bryan Eric Feldman, Tolga Gokce Goktekin and James O'Brien

UC MICRO, Apple Computer, Intel, Sony, AT&T, Pixar, Autodesk and Alfred P. Sloan Foundation

This project presents a method for simulating the two-way interaction between fluids and deformable solids. The fluids are simulated using an incompressible Eulerian formulation where a linear pressure projection on the fluid velocities enforces mass conservation. Similarly, elastic solids are simulated using a semi-implicit integrator implemented as a linear operator applied to the forces acting on the nodes in Lagrangian formulation. The proposed method enforces coupling constraints between the fluid and the elastic systems by combining both the pressure projection and implicit integration steps into one set of simultaneous equations. Because these equations are solved simultaneously, the resulting combined system treats closed regions in a physically correct fashion and has good stability characteristics allowing relatively large time steps. This general approach is not tied to any particular volume discretization of fluid or solid, and we present results implemented using both grid-based and tetrahedral simulations.

Figure 1: A deformable bowl filled with liquid falls on shallow water contained in an invisible water tank, hits the bottom of the tank, and squirts the liquid out.

Figure 2: A deformable paddle blown by a jet of smoke rotates and bounces against the floor.

- [1]
- N. Chentanez, T. G. Goktekin, B. E. Feldman, and J. F. O'Brien, "Simultaneous Coupling of Fluids and Deformable Bodies,"
*Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation,*Vienna, Austria, September 2006. - [2]
- N. Chentanez, T. G. Goktekin, B. E. Feldman, and J. F. O'Brien, "Simultaneous Coupling of Fluids and Deformable Bodies,"
*ACM SIGGRAPH,*Boston, MA, July-August 2006 (technical sketch).