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.

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.

We propose a novel method to predict pressure values at boundary particles in incompressible divergence-free SPH simulations (DFSPH). Our approach employs Moving Least Squares (MLS) to predict the pressure at boundary particles. Therefore, MLS computes hyperplanes that approximate the pressure field at the interface between fluid and boundary particles. We compare this approach with two previous techniques. One previous technique mirrors the pressure from fluid to boundary particles. The other one extrapolates the pressure from fluid to boundary particles, but uses a gradient that is computed with Smoothed Particle Hydrodynamics (SPH). We motivate that gradient-based extrapolation is more accurate than mirroring. We further motivate that our proposed MLS gradient is less error prone than the SPH gradient at the boundary. In our experiments, we indicate artifacts in previous approaches. We show that these artifacts are significantly reduced with our approach resulting in simulation steps that can be twice as large compared to previous methods. We further present challenging and complex scenarios to illustrate the capabilities of the proposed boundary handling. CCS Concepts •Computing methodologies → Physical simulation; Massively parallel and high-performance simulations;

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 thatin contrast to previous workallows 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.

In this paper we present a novel method to predict pressure values at boundary particles in incompressible divergence-free SPH simulations (DFSPH). Our approach employs Moving Least Squares (MLS) to predict the pressure at boundary particles. Therefore, MLS computes hyperplanes that approximate the pressure field at the interface between fluid and boundary particles. We compare this approach with three previous techniques. One previous technique mirrors the pressure from fluid to boundary particles. Another one extrapolates the pressure from fluid to boundary particles, but uses a gradient that is computed with Smoothed Particle Hydrodynamics (SPH). The third one solves a pressure Poisson equation (PPE) for boundary particles. In our experiments, we indicate artifacts in the three previous approaches. We show that these artifacts are significantly reduced with our approach resulting in simulation steps that can be twice as large. We motivate that gradient-based extrapolation is more accurate than mirroring. We further motivate that, due to particle deficiency at the boundary, the SPH gradient is error prone. This is less the case for our proposed MLS gradient. Moreover, our approach is computationally less expensive as solving a PPE for the boundary particles. We present challenging and complex scenarios to illustrate the capabilities of our method. In addition, we demonstrate that the proposed boundary handling is applicable to highly viscous fluids. (C) 2018 Elsevier Ltd. All rights reserved.

Computing the forces acting from a surrounding air phase onto a particle-based fluid or rigid object is challenging. Simulating the air phase and modeling the interactions using a multiphase approach is computationally expensive. Furthermore, stability issues may arise in such multiphase simulations. In contrast, the effects from the air can be approximated efficiently by employing a drag equation. Here, for plausible effects, the parameterization is important but challenging. We present a drag force discretization based on the drag equation that acts on each particle separately. It is used to compute the effects of air onto particle-based fluids and rigid objects. Our presented approach calculates the exposed surface area and drag coefficient of each particle. For fluid particles, we approximate their deformation to improve the drag coefficient estimation. The resulting effects are validated by comparing them to the results of multiphase SPH simulations. We further show the practicality of our approach by combining it with different types of SPH fluid solvers and by simulating multiple, complex scenes. (C) 2017 Elsevier Ltd. All rights reserved.

Computing the forces acting from a surrounding air phase onto an SPH free-surface fluid is challenging. For full multiphase simulations the computational overhead is significant and stability issues due to the high density ratio may arise. In contrast, the air-fluid interactions can be approximated efficiently by employing a drag equation. Here, for plausible effects, the parameterization is important but challenging. We present an approach to calculate the parameters of the used drag equation in a physically motivated way. We approximate the deformation and occlusion of particles to determine their drag coefficient and exposed surface area. The resulting effects are validated by comparing them to the results of a multiphase SPH simulation. We further show the practicality of our approach by combining it with different types of SPH solvers and by simulating multiple, complex scenes.

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.

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 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 propose a novel unified particle representation for fluids and solid boundaries in Implicit Incompressible SPH (IISPH). In contrast to existing particle representations, the proposed concept does not require a separate processing of fluid and boundary particles. On one hand, this results in a simplified solver implementation with improved efficiency. On the other hand, the unified fluid and boundary representation adds flexibility to IISPH which enables versatile effects. In particular, particles can now dynamically interchange their role between fluid and boundary which we therefore refer to as liquid boundary. The paper mainly focuses on the description of the unified representation and on the application of the concept to visual effects such as solidification and liquefaction. To support the realization of these effects, the concept of unified fluid and liquid boundary particles is extended to a third particle type, so-called candidate particles that are used in a transition phase between fluid and liquid boundaries.

We 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.