Two-way coupled SPH and particle level set fluid simulation

Efficient learning representation of noise-reduced foam effects with convolutional denoising networks

This study proposes a neural network framework for modeling the foam effects found in liquid simulation without noise. The position and advection of the foam particles are calculated using the existing screen projection method, and the noise problem that occurs in this process is prevented by using the neural network. A significant problem in the screen projection approach is the noise generated in the projection map during the projecting of momentum onto the discretized screen space. We efficiently solve this problem by utilizing a denoising neural network. Following the selection of the foam generation area using a projection map, the foam particles are generated through the inverse transformation of the 2D space into 3D space. This solves the problem of small-sized foam dissipation that occurs in conventional denoising networks. Furthermore, by integrating the proposed algorithm with the screen-space projection framework, it is able to maintain all the advantages of this approach. In conclusion, the denoising process and clean foam effects enable the proposed network to model the foam effects stably.

Incompressibility Enforcement for Multiple-Fluid SPH Using Deformation Gradient

To maintain incompressibility in SPH fluid simulations is important for visual plausibility. However, it remains an outstanding challenge to enforce incompressibility in such recent multiple-fluid simulators as the mixture-model SPH framework. To tackle this problem, we propose a novel incompressible SPH solver, where the compressibility of fluid is directly measured by the deformation gradient. By disconnecting the incompressibility of fluid from the conditions of constant density and divergence-free velocity, the new incompressible SPH solver is applicable to both single- and multiple-fluid simulations. The proposed algorithm can be readily integrated into existing incompressible SPH frameworks developed for single-fluid, and is fully parallelizable on GPU. Applied to multiple-fluid simulations, the new incompressible SPH scheme significantly improves the visual effects of the mixture-model simulation, and it also allows exploitation for artistic controlling.

Adapted SIMPLE Algorithm for Incompressible SPH Fluids With a Broad Range Viscosity

In simulating viscous incompressible SPH fluids, incompressibility and viscosity are typically solved in two separate stages. However, the interference between pressure and shear forces could cause the missing of behaviors that include preservation of sharp surface details and remarkable viscous behaviors such as buckling and rope coiling. To alleviate this problem, we introduce for the first time the semi-implicit method for pressure linked equations (SIMPLE) into SPH to solve incompressible fluids with a broad range viscosity. We propose to link incompressibility and viscosity solvers, and impose incompressibility and viscosity constraints iteratively to gradually remove the interference between pressure and shear forces. We will also discuss how to solve the particle deficiency problem for both incompressibility and viscosity solvers. Our method is stable at simulating incompressible fluids whose viscosity can range from zero to an extremely high value. Compared to state-of-the-art methods, our method not only produces realistic viscous behaviors, but is also better at preserving sharp surface details.

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.

Fluid Simulation with Adaptive Staggered Power Particles on GPUs

This paper extends the recently proposed power-particle-based fluid simulation method with staggered discretization, GPU implementation, and adaptive sampling, largely enhancing the efficiency and usability of the method. In contrast to the original formulation which uses co-located pressures and velocities, in this paper, a staggered scheme is adapted to the Power Particles to benefit visual details and computing efficiency. Meanwhile, we propose a novel facet-based power diagrams construction algorithm suitable for parallelization and explore its GPU implementation, achieving an order of magnitude boost in performance over the existing code library. In addition, to utilize the potential of Power Particles to control individual cell volume, we apply adaptive particle sampling to improve the detail level with varying resolution. The proposed method can be entirely carried out on GPUs, and our extensive experiments validate our method both in terms of efficiency and visual quality.

A Unified Multiple-Phase Fluids Framework Using Asymmetric Surface Extraction and the Modified Density Model

Multiple-phase fluids’ simulation and 3D visualization comprise an important cooperative visualization subject between fluid dynamics and computer animation. Interactions between different fluids have been widely studied in both physics and computer graphics. To further the study in both areas, cooperative research has been carried out; hence, a more authentic fluid simulation method is required. The key to a better multiphase fluid simulation result is surface extraction. Previous works usually have problems in extracting surfaces with unnatural fluctuations or detail missing. Gaps between different phases also hinder the reality of simulation. In this paper, we propose a unified surface extraction approach integrated with a modified density model for the particle-based multiphase fluid simulation. We refine the original asymmetric smoothing kernel used in the color field and address a binary tree scheme for surface extraction. Besides, we employ a multiphase fluid framework with modified density to eliminate density deviation between different fluids. With the methods mentioned above, our approach can effectively reconstruct the fluid surface for particle-based multiphase fluid simulation. It can also resolve the issue of overlaps and gaps between different fluids, which has widely existed in former methods for a long time. The experiments carried out in this paper show that our approach is able to have an ideal fluid surface condition and have good interaction effects.

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.

A New Deformation Model of Biological Tissue for Surgery Simulation

A novel meshless deformation model of biological soft tissue, which is mainly based on the radial basis function point interpolation, is presented for interactive simulation applications such as virtual surgery simulators. Compared with conventional mesh models, the proposed model is particularly suitable for simulating large deformation, sucking and cutting tasks since there is no need to maintain grid information. Kelvin viscoelasticity, which represents relaxation, creep, and hysteresis of soft tissue, is integrated into the proposed model, making the simulation much more realistic than many existing meshless models. To verify the validity of the proposed model, a biomechanical test was performed on real-life biological tissue and the results show that the maximum relative error between the forces from the biomechanical test and those obtained from the model is less than 5.8%. The proposed model was also implemented on a neurosurgery simulator, which showed that the deformation of the brain tumor can be simulated in a high degree of accuracy with real-time performance. In particular, the error and distortion from the remeshing process inherited in conventional mesh models when deformation is large are avoided.

Efficient Representation of Detailed Foam Waves by Incorporating Projective Space

We propose an efficient framework to realistically simulate foam effects in which 3D water particles from a base water solver are first projected onto 2D screen space in order to reduce computational complexity of finding foam particles. Because foam effects are often created primarily in fast and complicated water flows, we analyze acceleration and curvature values to identify the areas exhibiting such flow patterns. Identified foam particles are emitted in 3D simulation space, and each foam particle is advected by its classified type based on its velocity, thereby capturing the essential characteristics of foam wave motions (e.g., floating waves or scattering bubbles). In addition, we provide an intuitive and flexible mechanism (e.g., user sketch or image) to customize parameters and control the appearance of foam effects while minimizing the occurrence of popping artifacts. Experiments convincingly demonstrate that the proposed approach is efficient and easy to use while delivering high-quality results.

Divergence-Free SPH for Incompressible and Viscous Fluids

In this paper we present a novel Smoothed Particle Hydrodynamics (SPH) method for the efficient and stable simulation of incompressible fluids. The most efficient SPH-based approaches enforce incompressibility either on position or velocity level. However, the continuity equation for incompressible flow demands to maintain a constant density and a divergence-free velocity field. We propose a combination of two novel implicit pressure solvers enforcing both a low volume compression as well as a divergence-free velocity field. While a compression-free fluid is essential for realistic physical behavior, a divergence-free velocity field drastically reduces the number of required solver iterations and increases the stability of the simulation significantly. Thanks to the improved stability, our method can handle larger time steps than previous approaches. This results in a substantial performance gain since the computationally expensive neighborhood search has to be performed less frequently. Moreover, we introduce a third optional implicit solver to simulate highly viscous fluids which seamlessly integrates into our solver framework. Our implicit viscosity solver produces realistic results while introducing almost no numerical damping. We demonstrate the efficiency, robustness and scalability of our method in a variety of complex simulations including scenarios with millions of turbulent particles or highly viscous materials.

Coupling 3D Eulerian, Heightfield and Particle Methods for Interactive Simulation of Large Scale Liquid Phenomena

We propose a new method to simulate large scale water phenomena by combining particle, 3D grid and height field methods. In contrast to most hybrid approaches that use particles to simulate foam and spray only, we also represent the bulk of water near the surface with both particles and a grid depending on the regions of interest and switch between those two representations during the course of the simulation. For the coupling we leverage the recent idea of tracking the water surface with a density field in grid based methods. Combining particles and a grid simulation then amounts to adding the density field of the particles and the one stored on the grid. For open scenes, we simulate the water outside of the 3D grid domain by solving the Shallow Water Equations on a height field. We propose new methods to couple these two domains such that waves travel naturally across the border. We demonstrate the effectiveness of our approach in various scenarios including a whale breaching simulation, all running in real-time or at interactive rates.

Multi-resolution level sets with shape priors: a validation report for 2D segmentation of prostate gland in T2W MR images

The level set approach to segmentation of medical images has received considerable attention in recent years. Evolving an initial contour to converge to anatomical boundaries of an organ or tumor is a very appealing method, especially when it is based on a well-defined mathematical foundation. However, one drawback of such evolving method is its high computation time. It is desirable to design and implement algorithms that are not only accurate and robust but also fast in execution. Bresson et al. have proposed a variational model using both boundary and region information as well as shape priors. The latter can be a significant factor in medical image analysis. In this work, we combine the variational model of level set with a multi-resolution approach to accelerate the processing. The question is whether a multi-resolution context can make the segmentation faster without affecting the accuracy. As well, we investigate the question whether a premature convergence, which happens in a much shorter time, would reduce accuracy. We examine multiple semiautomated configurations to segment the prostate gland in T2W MR images. Comprehensive experimentation is conducted using a data set of a 100 patients (1,235 images) to verify the effectiveness of the multi-resolution level set with shape priors. The results show that the convergence speed can be increased by a factor of ≈ 2.5 without affecting the segmentation accuracy. Furthermore, a premature convergence approach drastically increases the segmentation speed by a factor of ≈ 17.9.

Implicit incompressible SPH

We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01 percent can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

A deformable surface model for real-time water drop animation

A water drop behaves differently from a large water body because of its strong viscosity and surface tension under the small scale. Surface tension causes the motion of a water drop to be largely determined by its boundary surface. Meanwhile, viscosity makes the interior of a water drop less relevant to its motion, as the smooth velocity field can be well approximated by an interpolation of the velocity on the boundary. Consequently, we propose a fast deformable surface model to realistically animate water drops and their flowing behaviors on solid surfaces. Our system efficiently simulates water drop motions in a Lagrangian fashion, by reducing 3D fluid dynamics over the whole liquid volume to a deformable surface model. In each time step, the model uses an implicit mean curvature flow operator to produce surface tension effects, a contact angle operator to change droplet shapes on solid surfaces, and a set of mesh connectivity updates to handle topological changes and improve mesh quality over time. Our numerical experiments demonstrate a variety of physically plausible water drop phenomena at a real-time rate, including capillary waves when water drops collide, pinch-off of water jets, and droplets flowing over solid materials. The whole system performs orders-of-magnitude faster than existing simulation approaches that generate comparable water drop effects.

Preserving fluid sheets with adaptively sampled anisotropic particles

This paper presents a particle-based model for preserving fluid sheets of animated liquids with an adaptively sampled Fluid-Implicit-Particle (FLIP) method. In our method, we preserve fluid sheets by filling the breaking sheets with particle splitting in the thin regions, and by collapsing them in the deep water. To identify the critically thin parts, we compute the anisotropy of the particle neighborhoods, and use this information as a resampling criterion to reconstruct thin liquid surfaces. Unlike previous approaches, our method does not suffer from diffusive surfaces or complex remeshing operations, and robustly handles topology changes with the use of a meshless representation. We extend the underlying FLIP model with an anisotropic position correction to improve the particle spacing, and adaptive sampling to efficiently perform simulations of larger volumes. Due to the Lagrangian nature of our method, it can be easily implemented and efficiently parallelized. The results show that our method can produce visually complex liquid animations with thin structures and vivid motions.

Constraint fluids

We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic multiphysics integration in which interactions are modeled via similar constraints between the fluid pseudoparticles and impenetrable surfaces of other bodies. These conditions embody Archimede's principle for solids and thus buoyancy results as a direct consequence. We use a variational time stepping scheme suitable for general constrained multibody systems we call SPOOK. Each step requires the solution of only one Mixed Linear Complementarity Problem (MLCP) with very few inequalities, corresponding to solid boundary conditions. We solve this MLCP with a fast iterative method. Overall stability is vastly improved in comparison to the unconstrained version of SPH, and this allows much larger time steps, and an increase in overall performance by two orders of magnitude. Proof of concept is given for computer graphics applications and interactive simulations.

FoamVis: visualization of 2D foam simulation data

Research in the field of complex fluids such as polymer solutions, particulate suspensions and foams studies how the flow of fluids with different material parameters changes as a result of various constraints. Surface Evolver, the standard solver software used to generate foam simulations, provides large, complex, time-dependent data sets with hundreds or thousands of individual bubbles and thousands of time steps. However this software has limited visualization capabilities, and no foam specific visualization software exists. We describe the foam research application area where, we believe, visualization has an important role to play. We present a novel application that provides various techniques for visualization, exploration and analysis of time-dependent 2D foam simulation data. We show new features in foam simulation data and new insights into foam behavior discovered using our application.

Direct forcing for Lagrangian rigid-fluid coupling

We propose a novel boundary handling algorithm for particle-based fluids. Based on a predictor-corrector scheme for both velocity and position, one- and two-way coupling with rigid bodies can be realized. The proposed algorithm offers significant improvements over existing penalty-based approaches. Different slip conditions can be realized and non-penetration is enforced. Direct forcing is employed to meet the desired boundary conditions and to ensure valid states after each simulation step. We have performed various experiments in 2D and 3D. They illustrate one- and two-way coupling of rigid bodies and fluids, the effects of hydrostatic and dynamic forces on a rigid body as well as different slip conditions. Numerical experiments and performance measurements are provided.