An Implicit Viscosity Formulation for SPH Fluids

Figure 1: Interaction of a highly viscous fluid with complex moving solids. Up to 780k particles are used. The computation time is 30s per frame. We present a novel implicit formulation for highly viscous fluids simulated with Smoothed Particle Hydrodynamics SPH. Compared to explicit methods, our formulation is significantly more efficient and handles a larger range of viscosities. Differing from existing implicit formulations, our approach reconstructs the velocity field from a target velocity gradient. This gradient encodes a desired shear-rate damping and preserves the velocity divergence that is in-troduced by the SPH pressure solver to counteract density devia-tions. The target gradient ensures that pressure and viscosity com-putation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eu-lerian formulations. While our model differs from true viscosity in that vorticity diffusion is not encoded in the target gradient, it nevertheless captures many of the qualitative behaviors of viscous liquids. Our formulation can easily be incorporated into complex scenarios with one- and two-way coupled solids and multiple fluid phases with different densities and viscosities