Implicit Density Projection for Volume Conserving Liquids.

We propose a novel implicit density projection approach for hybrid Eulerian/Lagrangian methods like FLIP and APIC to enforce volume conservation of incompressible liquids. Our approach is able to robustly recover from highly degenerate configurations and incorporates volume-conserving boundary handling. A problem of the standard divergence-free pressure solver is that it only has a differential view on density changes. Numerical volume errors, which occur due to large time steps and the limited accuracy of pressure projections, are invisible to the solver and cannot be corrected. Moreover, these errors accumulate over time and can lead to drastic volume changes, especially in long-running simulations or interactive scenarios. Therefore, we introduce a novel method that enforces constant density throughout the fluid. The density itself is tracked via the particles of the hybrid Eulerian/Lagrangian simulation algorithm. To achieve constant density, we use the continuous mass conservation law to derive a pressure Poisson equation which also takes density deviations into account. It can be discretized with standard approaches and easily implemented into existing code by extending the regular pressure solver. Our method enables us to relax the strict time step and solver accuracy requirements of a regular solver, leading to significantly higher performance. Moreover, our approach is able to push fluid particles out of solid obstacles without losing volume and generates more uniform particle distributions, which makes frequent particle resampling unnecessary. We compare the proposed method to standard FLIP and APIC and to previous volume correction approaches in several simulations and demonstrate significant improvements in terms of incompressibility, visual realism, and computational performance.

Implicit Frictional Boundary Handling for SPH.

In this article, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. First, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

Turbulent Micropolar SPH Fluids with Foam.

In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). As already investigated in previous works, SPH fluid simulations suffer from numerical diffusion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier-Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids also have a field of microrotation which represents existing vortices and provides a source for new ones. However, classical micropolar materials are viscous and the translational and the rotational motion are coupled in a dissipative way. Since our goal is to simulate turbulent fluids, we introduce a novel modified micropolar material for inviscid fluids with a non-dissipative coupling. Our model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible. Another important visual feature of turbulent liquids is foam. Therefore, we present a post-processing method which considers microrotation in the foam particle generation. It works completely automatic and requires only one user-defined parameter to control the amount of foam.