Two-dimensional circulation-preserving fluid simulation with discrete exterior calculus

The development of efficient and stable fluid simulations is a challenging task in computer graphics. Elcott et al. [6] describe an approach, based on Discrete Exterior Calculus for simulating the fluid flow. A vorticity based formulation of the incompressible Navier-Stokes equations is used, resulting in a mass-conserving representation of the velocity field by definition. This approach preserves vorticity at a discrete level, resulting in a visually more realistic fluid flow. We extend this approach to regular grids in two dimensions. So, we avoid computationally expensive mesh constructions. We discuss non-trivial boundary conditions and arbitrary topologies. The vorticity conservation properties are compared with the classical mesh based approach of Elcott et. al. We especially analyze the corresponding pressure fields near the boundaries of inner objects.