Narrow Band Pressure Computation for Eulerian Fluid Simulation

An Eulerian fluid simulation for incompressible fluids spends a lot of time in enforcing incompressibility by solving a large Poisson’s equation. This involves solving a large system of equations using a solver like conjugate gradients. We introduce a way of accelerating this computation by dividing the grid domain of the fluid simulation into a narrow band of high resolution grid cells near fluid-solid boundaries and a coarser grid everywhere else. Judiciously reducing the number of high resolution grid cells significantly lowers the cost of the pressure projection step, while not sacrificing the simulation quality. The coarse grid values are upgraded to a finer grid before advecting the fluid surface so that enough degrees of freedom are available to resolve surface detail. We present and analyse two methods to perform this upgradation, namely, velocity interpolation and pressure field smoothing. We discuss the merits and demerits of each and quantify the errors introduced in the simulation as a function of size of the narrow band. Finally, since we are primarily interested in visualizing the fluid animation, we produce rendered fluid simulation output to also validate the visual quality of the simulations.