Realistic Animation of Liquids

By Nick Foster, Dimitris N. Metaxas. 1996

Abstract We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the Navier–Stokes equations which couple momentum and mass conservation to completely describe fluid motion. Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semisubmerged obstacles. Velocity and pressure are defined everywhere within this environment and updated using a set of finite difference expressions. The resulting vector and scalar fields are used to drive a height field equation representing the liquid surface. The nature of the coupling between obstacles in the environment and free variables allows for the simulation of a wide range of effects that were not possible with previous computer graphics fluid models. Wave effects such as reflection, refraction, and diffraction, as well as rotational effects such as eddies, vorticity, and splashing are a natural consequence of solving the system. In addition, the Lagrange equations of motion are used to place buoyant dynamic objects into a scene and track the position of spray and foam during the animation process. Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending terms to the Navier–Stokes equations to include forcing functions. Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years.

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Citations in the corpus

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].”
Linear algebra operators for GPU implementation of numerical algorithms (2003, methodology): “…in physics based simulation and modelling, and they have been frequently employed in computer graphics to provide realistic simulation of real-world phenomena [Kaas and Miller 1990; Chen and da Vito-ria Lobo 1995; Foster and Metaxas 1996; Stam 1999; Foster and Fedkiw 2001; Fedkiw et al. 2001].”
To appear in the ACM SIGGRAPH conference proceedings Modular Bases for Fluid Dynamics (unknown): “Our implementation uses a MAC grid [Foster and Metaxas 1996], although other velocity discretizations are possible.”
Coupling water and smoke to thin deformable and rigid shells (2005, methodology): “The full three dimensional Navier-Stokes equations were solved in [Foster and Metaxas 1996; Foster and Metaxas 1997a] using a particle in cell approach.”
Graphical modeling and animation of ductile fracture (2002, unknown): “With the introduction in 1998 of simulated water in Antz [5, 14] and clothing in Geri’s Game [4, 15], passive simulation was clearly demonstrated to be a viable technique for commercial animation.”
Lagrangian Fluid Simulation with Continuous Convolutions (2020, methodology): “Following the earlier development of physics-based ﬂuid simulation for special effects by Foster & Metaxas (1996), the introduction of SPH (M¨uller et al., 2003) has led to a large class of powerful algorithms (Solenthaler & Pajarola, 2009; Bender & Koschier, 2015).”
Stable fluids (1999, background): “Also we have not addressed the problem of simulating fluids with free boundaries, such as water [6].”
Animation and rendering of complex water surfaces (2002, methodology): “[Foster and Metaxas 1996] utilized the work of [Harlow and Welch 1965] in developing a 3D Navier-Stokes methodology for the realistic animation of liquids.”