Category: Fluids

Hagit Schechter, Robert Bridson

We propose a new ghost fluid approach for free surface and solid boundary conditions in Smoothed Particle Hydrodynamics (SPH) liquid simulations. Prior methods either suffer from a spurious numerical surface tension artifact or drift away from the mass conservation constraint, and do not capture realistic cohesion of liquid to solids. Our Ghost SPH scheme resolves this with a new particle sampling algorithm to create a narrow layer of ghost particles in the surrounding air and solid, with careful extrapolation and treatment of fluid variables to reflect the boundary conditions. We also provide a new, simpler form of artificial viscosity based on XSPH. Examples demonstrate how the new approach captures real liquid behaviour previously unattainable by SPH with very little extra cost.

Ghost SPH for Animating Water

Oleksiy Busaryev, Tamal Dey, Huamin Wang, Ren Zhong

Bubbles and foams are important features of liquid surface phenomena, but they are difficult to animate due to their thin films and complex interactions in the real world. In particular, small bubbles (having diameter <1cm) in a dense foam are highly affected by surface tension, so their shapes are much less deformable compared with larger bubbles. Under this small bubble assumption, we propose a more accurate and efficient particle-based algorithm to simulate bubble dynamics and interactions. The key component of this algorithm is an approximation of foam geometry, by treating bubble particles as the sites of a weighted Voronoi diagram. The connectivity information provided by the Voronoi diagram allows us to accurately model various interaction effects among bubbles. Using Voronoi cells and weights, we can also explicitly address the volume loss issue in foam simulation, which is a common problem in previous approaches. Under this framework, we present a set of bubble interaction forces to handle miscellaneous foam behaviors, including foam structure under Plateau’s laws, clusters formed by liquid surface bubbles, bubble-liquid and bubble-solid coupling, bursting and coalescing. Our experiment shows that this method can be straightforwardly incorporated into existing liquid simulators, and it can efficiently generate realistic foam animations, some of which have never been produced in graphics before.

Animating Bubble Interactions in a Liquid Foam

Tyler de Witt, Christian Lessig, Eugene Fiume

We present an algorithm for the simulation of incompressible fluid phenomena that is computationally efficient and leads to visually convincing simulations with far fewer degrees of freedom than existing approaches. Rather than using an Eulerian grid or Lagrangian elements, we represent vorticity and velocity using a basis of global functions defined over the entire simulation domain. We show that choosing Laplacian eigenfunctions for this basis provides benefits, including correspondence with spatial scales of vorticity and precise energy control at each scale. We perform Galerkin projection of the Navier-Stokes equations to derive a time evolution equation in the space of basis coefficients. Our method admits closed form solutions on simple domains but can also be implemented efficiently on arbitrary meshes.

Fluid Simulation Using Laplacian Eigenfunctions

Haimasree Bhattacharya, Michael Nielsen, Robert Bridson

Fluid control methods often require surface velocities interpolated throughout the interior of a shape to use the velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics — velocity extrapolation in the normal direction and potential flow — suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures the rotational components and is suitable for controlling liquid animations where tangential motion is pronounced, such as in a breaking wave.

Steady state Stokes flow interpolation for fluid control

Jihun Yu, Chris Wojtan, Greg Turk, Chee Yap

We introduce the idea of using an explicit triangle mesh to track the air/fluid interface in a smoothed particle hydrodynamics (SPH) simulator. Once an initial surface mesh is created, this mesh is carried forward in time using nearby particle velocities to advect the mesh vertices. The mesh connectivity remains mostly unchanged across time-steps; it is only modified locally for topology change events or for the improvement of triangle quality. In order to ensure that the surface mesh does not diverge from the underlying particle simulation, we periodically project the mesh surface onto an implicit surface defined by the physics simulation. The mesh surface gives us several advantages over previous SPH surface tracking techniques. We demonstrate a new method for surface tension calculations that clearly outperforms the state of the art in SPH surface tension for computer graphics. We also demonstrate a method for tracking detailed surface information (like colors) that is less susceptible to numerical diffusion than competing techniques. Finally, our temporally-coherent surface mesh allows us to simulate high-resolution surface wave dynamics without being limited by the particle resolution of the SPH simulation.

Explicit Mesh Surfaces for Particle Based Fluids

Landon Boyd, Robert Bridson

Physically-based liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both
air and liquid as incompressible, more accurately reproducing the reality observed at scales relevant to computer animation. The Fluid Implicit Particle (FLIP) method, already shown to effectively simulate incompressible fluids with low numerical dissipation, is extended to two-phase flow by associating a phase bit with each particle. The liquid surface is reproduced at each time step from the particle positions, which are adjusted to prevent mixing near the surface and to allow for accurate surface tension. The liquid surface is adjusted around small-scale features so they are represented in the grid-based pressure projection, while separate, loosely coupled velocity fields reduce unwanted influence between the phases. The resulting scheme is easy to implement, requires little parameter tuning and is shown to reproduce lively two-phase fluid phenomena.

Multi-FLIP for Energetic Two-Phase Fluid Simulation

Barbara Solenthaler, Peter Bucher, Nuttapong Chentanez, Matthias Muller, Markus Gross

We present an efficient method that uses particles to solve the 2D shallow water equations. These equations describe the dynamics of a body of water represented by a height field. Instead of storing the surface heights using uniform grid cells, we discretize the fluid with 2D SPH particles and compute the height according to the density at each particle location. The particle discretization offers the benefits that it simplifies the use of sparsely filled domains and arbitrary boundary geometry. Our solver can handle terrain slopes and supports two-way coupling of the particle-based height field with rigid objects. An improved surface definition is presented that reduces visible bumps related to the underlying particle representation. It furthermore smoothes areas with separating particles to achieve better rendering results. Both the physics and the rendering are implemented on modern GPUs resulting in interactive performances in all our presented examples.

SPH Based Shallow Water Simulation

Bo Zhu, Michiaki Iwata, Ryo Haraguchi, Takashi Ashahara, Nobukuyuki Umetani, Takeo Igarashi, Kazuo Nakazawa

This paper presents a lightweight sketching system that enables interactive illustration of complex fluid systems. Users can sketch on a 2.5-dimensional (2.5D) canvas to design the shapes and connections of a fluid circuit. These input sketches are automatically analyzed and abstracted into a hydraulic graph, and a new hybrid fluid model is used in the background to enhance the illustrations. The system provides rich simple operations for users to edit the fluid system incrementally, and the new internal flow patterns can be simulated in real time. Our system is used to illustrate various fluid systems in medicine, biology, and engineering. We asked professional medical doctors to try our system and obtained positive feedback from them.

Sketch-Based Dynamic Illustration of Fluid Systems