Abstract: We present a novel, incompressible fluid simulation method based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. For this, the information about density fluctuations is actively propagated through the fluid and pressure values are updated until the targeted density is satisfied. With this approach, we avoid the computational expenses of solving a pressure Poisson equation, while still being able to use large time steps in the simulation. The achieved results show that our predictive-corrective incompressible SPH (PCISPH) method clearly outperforms the commonly used weakly compressible SPH (WCSPH) model by more than an order of magnitude while the computations are in good agreement with the WCSPH results.

Abstract: To simulate multiple fluids realistically many important interaction effects have to be captured accurately. Smoothed Particle Hydrodynamics (SPH) has shown to be a simple, yet flexible method to cope with many fluid simulation problems in a robust way. Unfortunately, the results obtained when using SPH to simulate miscible fluids are severely affected, especially if density ratios become large. The undesirable effects reach from unphysical density and pressure variations to spurious and unnatural interface tensions, as well as severe numerical instabilities. In this work, we present a formulation based on SPH which can handle density discontinuities at interfaces between multiple fluids correctly without increasing the computational costs compared to standard SPH. The basic idea is to replace the density computation in SPH by a measure of particle densities and consequently derive new formulations for pressure and viscous forces. The new method enables the user to select the desired amount of interface tension according to the simulation problem at hand. We succeed to stably simulate multiple fluids with high density contrasts without the above described artifacts apparent in standard SPH simulations.

Abstract: In this paper, we propose a novel GPU-friendly algorithm for the Smoothed Particle Hydrodynamics (SPH) simulation for weakly compressible fluids. The major goal of our algorithm is to implement a GPU-based SPH simulation that can simulate and render a large number of particles at interactive speed. Additionally, our algorithm exhibits the following three features. Firstly, our algorithm supports adaptive sampling of the fluids. Particles can be split into several sub-particles in geometrically complex regions to provide a more accurate simulation. At the same time, nearby particles deep inside the fluids are merged to a single particle to reduce the number of particles. Secondly, the fluids are visualized by directly computing the intersection between ray and an isosurface defined by the surface particles. A dynamic particle grouping algorithm and equation solver are employed to quickly find the ray-isosurface intersection. Thirdly, based on the observation that the SPH simulation is a naturally parallel algorithm, the whole SPH simulation, including the adaptive sampling of the fluids as well as surface particle rendering, is executed on the GPU to fully utilize the computational power and parallelism of modern graphics hardware. Our experimental data shows that we can simulate about 50K adaptively sampled particles, or up to 120K particles in the fixed sampling case at a rate of approximately 20 time steps per second.

Abstract: Particle simulations as well as geometric modeling techniques have demonstrated their ability to process and render points interactively. However, real-time particle-based fluid simulations suffer from poor rendering quality due to low surface particle resolutions. Surfaces appear blobby, surface details are lost, and features like edges are degraded due to smoothing effects. This paper presents a novel point refinement method for irregularly sampled, dynamic points coming from a particle-based fluid simulation. Our interpolation algorithm can handle complex geometries including splashes, and at the same time preserves features like edges. Point collisions are avoided resulting in a nearly uniform sampling facilitating surface reconstruction techniques. No point preprocessing is necessary, and point neighborhoods are dynamically updated reducing computation and memory costs. We show that our algorithm can efficiently detect and refine the surface points of a fluid and we demonstrate the improvement of rendering quality and applicability to real-time simulations.

Abstract: We present a new method for the simulation of melting and solidification in a unified particle model. Our technique uses the Smoothed Particle Hydrodynamics (SPH) method for the simulation of liquids, deformable as well as rigid objects, which eliminates the need to define an interface for coupling different models. Using this approach, it is possible to simulate fluids and solids by only changing the attribute values of the underlying particles. We significantly changed a prior elastic particle model to achieve a flexible model for melting and solidification. By using an SPH approach and considering a new definition of a local reference shape, the simulation of merging and splitting of different objects, as may be caused by phase change processes, is made possible. In order to keep the system stable even in regions represented by a sparse set of particles we use a special kernel function for solidification processes. Additionally, we propose a surface reconstruction technique based on considering the movement of the center of mass to reduce rendering errors in concave regions. The results demonstrate new interaction effects concerning the melting and solidification of material, even while being surrounded by liquids.

Abstract: The interesting and complex behavior of fluids emerges mainly from interaction processes. While interactions of fluids with static or dynamic solids has caught some attention in computer graphics lately, the mutual interaction of different types of fluids such as air and water or water and wax has received much less attention although these types of interaction are the basis for a variety of important phenomena. In this paper we propose a new technique to model fluid-fluid interaction based on the Smoothed Particle Hydrodynamics (SPH) method. For the simulation of air-water interaction, air particles are generated on the fly only where needed. We also model dynamic phase changes and interface forces. Our technique makes possible the simulation of phenomena such as boiling water, trapped air and the dynamics of a lava lamp.

Abstract: Mass-spring systems are of special interest for soft tissue modeling in surgical simulation due to their ease of implementation and real-time behavior. However, the parameter identification (masses, spring constants, mesh topology) still remains a challenge. In previous work, we proposed an approach based on the training of mass-spring systems according to known reference models. Our initial focus was the determination of mesh topology in 2D. In this paper, we extend the method to 3D. Furthermore, we introduce a new approach to simultaneously identify mesh topology and spring stiffness values. Linear elastic FEM deformation computations are used as reference. Additionally, our results show that uniform distributions of spring stiffness constants fails to simulate linear elastic deformations.