A deformable surface model for real-time water drop animation

A Novel Method for Simulating Micro-Scale Water Droplet Movements

Micro-scale fluids are tiny droplets that adhere to the surface of an object as a result of rainfall, perspiration, etc. Micro-scale fluid simulation is widely used in fields such as film and games. The existing state-of-the-art simulation methods are not suitable for simulating water droplets moving on a surface due to the fact that the water droplets cannot leave the texture space and their movements always depend on the continuous UV region. In this study, a novel method for simulating water droplets moving on a surface is proposed. We divide the droplets into two types: (1) two-dimensional droplets and (2) three-dimensional droplets and we implement the transformation between two-dimensional droplets in the texture space and three-dimensional droplets in the physical space. In the preprocessing phase, jump textures, coordinate transform textures and force field textures are generated in the non-continuous UV regions on a 3D object’s surface. In the process of simulation, water droplets are treated as rigid particles. The Velocity-Verlet-based method is adopted to solve the motion trajectory equation, and the boundary droplet transport algorithm is implemented based on jump texture. In the process of rendering, the height map is generated according to the simulation in the texture space and then the liquid bridge phenomenon between the droplets is simulated based on the Gaussian blur and the color rank algorithm. Finally, they are converted into normal texture-rendering droplets. The experimental result shows that the proposed method works well when simulating the movements of water droplets on a surface in a real-time manner, and it makes the movement simulation of dimension-reducing water droplets no longer depend on the continuous surface and continuous UV region. Moreover, the simulation efficiency of the proposed method is two times higher than that of the Smoothed Particle Hydrodynamics (SPH) method.

Particle-Based Dynamic Water Drops with High Surface Tension in Real Time

Surface tension has a great influence on the shape of the fluid interface, and is an important physical characteristic in expressing not only liquids but also liquid metals such as mercury and gallium. In the field of physics-based particle fluid simulations, it is a challenging problem to express the high surface tension generated by fluid-air or fluid-solid interaction in real time. The main reasons for this are (1) The magnitude of the force that can be stably expressed in real-time fluid simulation is limited, so when the magnitude of the surface tension increases at a large time-step, the simulation stability decreases, and (2) If we use a small time-step, a stronger force can be expressed. However, it becomes difficult to operate in real time because the computational cost increases. Techniques were proposed to solve this problem for a few specific scenes, but there has not yet been a general approach that can reliably express high surface tension in various scenarios. In this paper, we propose a real-time particle-based fluid simulation framework that can efficiently and stably express high surface tension. Unlike the previous methods, we newly model the surface tension so that the strong surface tension force generated in the droplet area with a large curvature is applied evenly in the normal and tangent directions regardless of the size of the droplet. We also propose new pressure constraints that converge quickly and accurately using this force. Our method can be effectively used in various physics-based simulation scenarios because it can easily express and control surface tension effects that appear in materials such as liquid metal as well as water.

Kinetic-Based Multiphase Flow Simulation

Multiphase flows exhibit a large realm of complex behaviors such as bubbling, glugging, wetting, and splashing which emerge from air-water and water-solid interactions. Current fluid solvers in graphics have demonstrated remarkable success in reproducing each of these visual effects, but none have offered a model general enough to capture all of them concurrently. In contrast, computational fluid dynamics have developed very general approaches to multiphase flows, typically based on kinetic models. Yet, in both communities, there is dearth of methods that can simulate density ratios and Reynolds numbers required for the type of challenging real-life simulations that movie productions strive to digitally create, such as air-water flows. In this article, we propose a kinetic model of the coupling of the Navier-Stokes equations with a conservative phase-field equation, and provide a series of numerical improvements over existing kinetic-based approaches to offer a general multiphase flow solver. The resulting algorithm is embarrassingly parallel, conservative, far more stable than current solvers even for real-life conditions, and general enough to capture the typical multiphase flow behaviors. Various simulation results are presented, including comparisons to both previous work and real footage, to highlight the advantages of our new method.

Stain Formation on Deforming Inelastic Cloth

We propose a novel approach to simulating the formation and evolution of stains on cloths in motion. We accurately capture the diffusion of a pigmented solution over a complex knitted or woven fabric through homogenization of its inhomogeneous and/or anisotropic properties into bulk anisotropic diffusion tensors. Secondary effects such as absorption, adsorption and evaporation are also accounted for through physically-based modeling. Finally, the influence of the cloth motion on the shape and evolution of the stain is captured by evaluating the inertial (e.g., centrifugal and Coriolis) forces experienced by the solution. The governing equations of motion are integrated in time directly on a deforming triangle mesh discretizing the inelastic cloth for efficiency and robustness. The deformation of the cloth can be precomputed or integrated through simplified two-way coupling, by using off-the-shell cloth simulations. Finally, numerical experiments demonstrate the plausibility of our results in practical applications by reproducing the usual shape and behavior of stains on various fabrics.

Real-Time High-Fidelity Surface Flow Simulation

Surface flow phenomena, such as rain water flowing down a tree trunk and progressive water front in a shower room, are common in real life. However, compared with the 3D spatial fluid flow, these surface flow problems have been much less studied in the graphics community. To tackle this research gap, we present an efficient, robust and high-fidelity simulation approach based on the shallow-water equations. Specifically, the standard shallow-water flow model is extended to general triangle meshes with a feature-based bottom friction model, and a series of coherent mathematical formulations are derived to represent the full range of physical effects that are important for real-world surface flow phenomena. In addition, by achieving compatibility with existing 3D fluid simulators and by supporting physically realistic interactions with multiple fluids and solid surfaces, the new model is flexible and readily extensible for coupled phenomena. A wide range of simulation examples are presented to demonstrate the performance of the new approach.

Functional Thin Films on Surfaces

The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize. Inspired by a recent variational formulation for this problem on smooth surfaces, we present a corresponding model for triangle meshes. We provide a discretization for the curvature and advection operators which leads to an efficient and stable numerical scheme, requires a single sparse linear solve per time step, and exactly preserves the total volume of the fluid. We validate our method by qualitatively comparing to known results from the literature, and demonstrate various intricate effects achievable by our method, such as droplet formation, evaporation, droplets interaction and viscous fingering. Finally, we extend our method to incorporate non-linear van der Waals forcing terms which stabilize the motion of the film and allow additional effects such as pearling.