VOF Method for Fluids and Solids on Octree Structure

Fluid simulation, proposed here, runs on an unrestricted octree data structure which uses mesh refinement techniques to enable higher level of detail and solves Navier Stokes equations for multiple fluids. We also show our solution for floating objects and unmoving obstacles by setting up the boundry conditions and solving the velocity of objects using a simple rigid body solver.We propose technique for discretizing the Poisson equation on octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods. The standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging. To solve the advection of fluid we use the semi-Lagrangian characteristic tracing technique. To track the fluid surface we use Volume of Fluid (VOF) method.