Stable fluids

By J. Stam. 1999

Building animation tools for fluid-like motions is an important and challenging problem with many applications in computer graphics. The use of physics-based models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an animator to almost effortlessly create interesting, swirling fluid-like behaviors. Also, the interaction of flows with objects and virtual forces is handled elegantly. Until recently, it was believed that physical fluid models were too expensive to allow real-time interaction. This was largely due to the fact that previous models used unstable schemes to solve the physical equations governing a fluid. In this paper, for the first time, we propose an unconditionally stable model which still produces complex fluid-like flows. As well, our method is very easy to implement. The stability of our model allows us to take larger time steps and therefore achieve faster simulations. We have used our model in conjuction with advecting solid textures to create many fluid-like animations interactively in two- and three-dimensions.

Subfields: Computer Graphics and Computer-Aided Design, Numerical Methods & Scientific Computing

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Citations in the corpus

Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow (2018, methodology): “, for tasks such as machine translation [Sutskever et al. 2014].”
DiffTaichi: Differentiable Programming for Physical Simulation (2019, methodology): “1, smoke ) with semi-Lagrangian advection (Stam, 1999) and implicit pressure projection, following the example in Autograd (Maclaurin et al., 2015).”
Mesh editing with poisson-based gradient field manipulation (2004, methodology): “CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Boundary representations Keywords: Poisson Equation, Local Transform Propagation, Mesh Deformation, Object Merging, Mesh Filtering”
Accelerating Eulerian Fluid Simulation With Convolutional Networks (2016, methodology): “We then calculate the per-vertex force, fvc, update of [Stam 1999]:”
Implementation of a fast fluid dynamics model in OpenFOAM for simulating indoor airflow (2016, methodology): “Since the major development by Stam [10] in the area of computer games, FFD has been used for flow simulations.”
Two-way coupling of fluids to rigid and deformable solids and shells (2008, methodology): “Note that the advection velocity u ADV is used to formulate the rays in the typical semi-Lagrangian scheme [Stam 1999], but the advected quantity is the actual ﬂuid velocity u nF . u ADV is also used to advect all other ﬂuid scalar quantities to time t n +1 .”
A parallel multigrid Poisson solver for fluids simulation on large grids (2010, methodology): “We use simple semi-Lagrangian advection [Sta99] for the density and level sets.”
Development of a fast fluid dynamics-based adjoint method for the inverse design of indoor environments (2017, methodology): “After a major development by Stam (1999) in the area of computer games, FFD has been further developed for © 2016 International Building Performance Simulation Association (IBPSA) simulating indoor airflow (Zuo and Chen 2009; Jin, Zuo, and Chen 2012; Xue, Liu, and Zhai 2016; Liu et al. 2016a).”
Interactive localized liquid motion editing (2013, methodology): “Navier-Stokes fluid model has been popular in computer graphics since the early work [Foster and Metaxas 1996; Foster and Metaxas 1997b; Stam 1999; Enright et al. 2002].”
Practical animation of liquids (2001, methodology): “We start with the Navier-Stokes equations for incompressible flow and solve for liquid motion using an adaptation of a semiLagrangian method introduced recently to graphics for solving fluid flows [25].”
Rigid fluid: animating the interplay between rigid bodies and fluid (2004, methodology): “In [Foster and Metaxas 1996; Foster and Metaxas 1997; Stam 1999; Fedkiw et al. 2001], the rigid bodies were treated as boundary conditions with set velocities.”
Sparse matrix solvers on the GPU: conjugate gradients and multigrid (2003, methodology): “As a challenge problem we implemented Stam’s solver for the incompressible viscous Navier-Stokes equations [1999].”
Visual simulation of smoke (2001, methodology): “Consequently our simulations are almost as fast as the one’s obtained from the basic Stable Fluids algorithm [17].”
An Unconditionally Stable MacCormack Method (2008, methodology): “For example, after [22] popularized the semi-Lagrangian method in the field of computer graphics, [9] showed that vorticity confinement [24] could be used to alleviate the high amount of dissipation allowing for visually intricate, albeit non-physical flows (see also [20] which used vortex particles”
Linear algebra operators for GPU implementation of numerical algorithms (2003, methodology): “The diffusion operator is discretized by means of central differences, and, as proposed in [Stam 1999], we solve for the advection part by tracing the velocity field backward in time.”