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. AbstractWe 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 introduced by the SPH pressure solver to counteract density deviations. The target gradient ensures that pressure and viscosity computation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eulerian 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.

We present a strong fluid-rigid coupling for Smoothed Particle Hydrodynamics (SPH) fluids and rigid bodies with particle-sampled surfaces. The approach interlinks the iterative pressure update at fluid particles with a second SPH solver that computes artificial pressure at rigid-body particles. The introduced SPH rigid-body solver models rigid-rigid contacts as artificial density deviations at rigid-body particles. The corresponding pressure is iteratively computed by solving a global formulation that is particularly useful for large numbers of rigid-rigid contacts. Compared to previous SPH coupling methods, the proposed concept stabilizes the fluid-rigid interface handling. It significantly reduces the computation times of SPH fluid simulations by enabling larger time steps. Performance gain factors of up to 58 compared to previous methods are presented. We illustrate the flexibility of the presented fluid-rigid coupling by integrating it into DFSPH, IISPH, and a recent SPH solver for highly viscous fluids. We further show its applicability to a recent SPH solver for elastic objects. Large scenarios with up to 90 M particles of various interacting materials and complex contact geometries with up to 90 k rigid-rigid contacts are shown. We demonstrate the competitiveness of our proposed rigid-body solver by comparing it to Bullet.

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Figure 1: Scene with 160 million FLIP particles. Particles are color coded with respect to velocity. AbstractWe propose to use Implicit Incompressible Smoothed Particle Hydrodynamics (IISPH) for pressure projection and boundary handling in Fluid-Implicit-Particle (FLIP) solvers for the simulation of incompressible fluids. This novel combination addresses two issues of existing SPH and FLIP solvers, namely mass preservation in FLIP and efficiency and memory consumption in SPH. First, the SPH component enables the simulation of incompressible fluids with perfect mass preservation. Second, the FLIP component efficiently enriches the SPH component with detail that is comparable to a standard SPH simulation with the same number of particles, while improving the performance by a factor of 7 and significantly reducing the memory consumption. We demonstrate that the proposed IISPH-FLIP solver can simulate incompressible fluids with a quantifiable, imperceptible density deviation below 0.1%. We show large-scale scenarios with up to 160 million particles that have been processed on a single desktop PC using only 15GB of memory. One-and two-way coupled solids are illustrated.

Implicit incompressible SPH (IISPH) solves a pressure Poisson equation (PPE). While the solution of the PPE provides pressure at fluid samples, the embedded boundary handling does not compute pressure at boundary samples. Instead, IISPH uses various approximations to remedy this deficiency. In this article, we illustrate the issues of these IISPH approximations. We particularly derive Pressure Boundaries, a novel boundary handling that overcomes previous IISPH issues by the computation of physically meaningful pressure values at boundary samples. This is basically achieved with an extended PPE. We provide a detailed description of the approach that focuses on additional technical challenges due to the incorporation of boundary samples into the PPE. We therefore use volume-centric SPH discretizations instead of typically used density-centric ones. We further analyze the properties of the proposed boundary handling and compare it to the previous IISPH boundary handling. In addition to the fact that the proposed boundary handling provides physically meaningful pressure and pressure gradients at boundary samples, we show further benefits, such as reduced pressure oscillations, improved solver convergence, and larger possible time steps. The memory footprint of fluid samples is reduced and performance gain factors of up to five compared to IISPH are presented.

We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.

Working with prescribed velocity gradients is a promising approach to efficiently and robustly simulate highly viscous SPH fluids. Such approaches allow to explicitly and independently process shear rate, spin, and expansion rate. This can be used to, e.g., avoid interferences between pressure and viscosity solvers. Another interesting aspect is the possibility to explicitly process the vorticity, e.g., to preserve the vorticity. In this context, this paper proposes a novel variant of the prescribed-gradient idea that handles vorticity in a physically motivated way. In contrast to a less appropriate vorticity preservation that has been used in a previous approach, vorticity is diffused. The paper illustrates the utility of the vorticity diffusion. Therefore, comparisons of the proposed vorticity diffusion with vorticity preservation and additionally with vorticity damping are presented. The paper further discusses the relation between prescribed velocity gradients and prescribed velocity Laplacians which improves the intuition behind the prescribed-gradient method for highly viscous SPH fluids. Finally, the paper discusses the relation of the proposed method to a physically correct implicit viscosity formulation.

Snow is a complex material. It resists elastic normal and shear deformations, while some deformations are plastic. Snow can deform and break. It can be significantly compressed and gets harder under compression. Existing snow solvers produce impressive results. E.g., hybrid Lagrangian/Eulerian techniques have been used to capture all material properties of snow. The auxiliary grid, however, makes it challenging to handle small volumes. In particular, snow fall and accumulation on surfaces have not been demonstrated with these solvers yet. Existing particle-based snow solvers, on the other hand, can naturally handle small snow volumes. However, existing solutions consider simplified material properties. In particular, shear deformation and the hardening effect are typically omitted. We present a novel Lagrangian snow approach based on Smoothed Particle Hydrodynamics (SPH). Snow is modeled as an elastoplastic continuous material that captures all above-mentioned effects. The compression of snow is handled by a novel compressible pressure solver, where the typically employed state equation is replaced by an implicit formulation. Acceleration due to shear stress is computed using a second implicit formulation. The linear solvers of the two implicit formulations for accelerations due to shear and normal stress are realized with matrix-free implementations. Using implicit formulations and solving them with matrix-free solvers allows to couple the snow to other phases and is beneficial to the stability and the time step size, i.e., performance of the approach. Solid boundaries are represented with particles and a novel implicit formulation is used to handle friction at solid boundaries. We show that our approach can simulate accumulation, deformation, breaking, compression and hardening of snow. Furthermore, we demonstrate two-way coupling with rigid bodies, interaction with incompressible and highly viscous fluids and phase change from fluid to snow.