Handling Several Fluids in Computer Graphics Simulations

Fluid dynamics governed by Navier-Stokes equations is already solved for decades but the recent trend in computer graphics is to modify the simulation such that it easily controllable for the purpose of computer animation or real time fluid animation. In Eulerian approach, fields must be discretized in space, making these techniques inherently mesh-based. Each mesh cell represents an approximation of the infinitesimal volume at a fixed position in space and during the simulation monitors the evaluation of state variables at that location. Our approach is an extension of a well known Marker-and-Cell (MAC) fluid simulation method, within each cell we define density and pressure in center and fluid velocities on the walls separately in each 6 directions. To simulate several fluids, we propose the modification of Volume-of-Fluid (VOF) method enabling us to tract the fluid surface and integrate it into the multiphase-fluid approach. A mixture of fluids is treated as a single fluid having variable density and viscosity. This scheme allows two or more fluids having different densities and viscosities to be simulated simultaneously. We simulate a one-way solid fluid interaction (either solid influences the velocity of the fluid or fluid moves the solid) that requires having fine details in the colliding areas. To cope with this problem we use an unrestricted octree data structure with adaptive mesh refinement technique to enable higher level of detail and solve Navier Stokes equations for multiple fluids. We propose the technique for discretizing the Poisson equation on octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods, while the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging. Finally, we show several fluid flow animations with static obstacles, floating objects colliding each other. Mathematics Subject Classification 2000: I.3.5, I.3.7 Additional