Mathieu Desbrun

Figure 1: By developing an integration scheme that exhibits zero numerical dissipation, we can achieve more predictable control over viscosity in fluid animation. Dissipation can then be modeled explicitly to taste, allowing for very low (left) or high (right) viscosities. Numerical viscosity has long been a problem in fluid animation. Existing methods suffer from intrinsic artificial dissipation and of-ten apply complicated computational mechanisms to combat such effects. Consequently, dissipative behavior cannot be controlled or modeled explicitly in a manner independent of time step size, complicating the use of coarse previews and adaptive-time step-ping methods. This paper proposes simple, unconditionally stable, fully Eulerian integration schemes with no numerical viscosity that are capable of maintaining the liveliness of fluid motion without recourse to corrective devices. Pressure and fluxes are solved effi-ciently and simultaneously in a time-reversible manner on simpli-cial grids, and the energy is preserved exactly over long time scales in the case of inviscid fluids. These integrators can be viewed as an extension of the classical energy-preserving Harlow-Welch / Crank-Nicolson scheme to simplicial grids