Modeling Several Fluids with Preserved Volume on an Octree Data Structure

Abstract

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 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 equations on the octree grid yielding to a symmetric positive definite linear system. 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 track the fluid surface and integrate it into the multi phase-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. Values of VOF are actually used to tract the fluid surface for visualization purposes and to calculate the surface tension forces acting on the fluid interfaces.