Figure 1: Multiple fluids with different viscosity coefficients and surface tension densities splashing on the bottom of a cylindrical container. Observe that the simulation has no problem dealing with thin sheets. AbstractIn this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method.

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Smoke animations are hard to art-direct because simple changes in parameters such as simulation resolution often lead to unpredictable changes in the final result. Previous work has addressed this problem with a guiding approach which couples low-resolution simulations -that exhibit the desired flow and behaviour -to the final, high-resolution simulation. This is done in such a way that the desired low frequency features are to some extent preserved in the high-resolution simulation. However, the steady (i.e. constant) guiding used often leads to a lack of sufficiently high detail, and employing time-dependent guiding is expensive because the matrix of the resulting set of equations needs to be recomputed at every iteration. We propose an improved mathematical model for Eulerianbased simulations which is better suited for dynamic, time-dependent guiding of smoke animations through a novel variational coupling of the low-and high-resolution simulations. Our model results in a matrix that does not require re-computation when the guiding changes over time, and hence we can employ time-dependent guiding more efficiently both in terms of storage and computational requirements. We demonstrate that time-dependent guiding allows for more high frequency detail to develop without losing correspondence to the low resolution simulation. Furthermore, we explore various artistic effects made possible by time-dependent guiding.

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