Toward Interactive-Rate Simulation of Fluids with Moving Obstacles Using Navier-Stokes Equations

Chen, Jim X.; Lobo, Niels da Vitoria

doi:10.1006/gmip.1995.1012

Cited by 103 publications

(40 citation statements)

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“…Kass and Miller [17] approximated the 2D shallow water equations to get a dynamic height field surface that interacted with a static ground "object". Chen and Lobo [4] extended the height field approach by using the pressure arising from a 2D solution of the NavierStokes equations to modulate surface elevation. O'Brien and Hodgins [20] simulated splashing liquids by combining a particle system and height field, while Miller and Pearce [19] used viscous springs between particles to achieve dynamic flow in 3D.…”

Section: Previous Workmentioning

confidence: 99%

Practical Animation of Liquids

Foster¹,

Fedkiw²

2001

227

216

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We present a general method for modeling and animating liquids. The system is specifically designed for computer animation and handles viscous liquids as they move in a 3D environment and interact with graphics primitives such as parametric curves and moving polygons. We combine an appropriately modified semiLagrangian method with a new approach to calculating fluid flow around objects. This allows us to efficiently solve the equations of motion for a liquid while retaining enough detail to obtain realistic looking behavior. The object interaction mechanism is extended to provide control over the liquid's 3D motion. A high quality surface is obtained from the resulting velocity field using a novel adaptive technique for evolving an implicit surface.

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Section: Previous Workmentioning

confidence: 99%

Practical Animation of Liquids

Foster¹,

Fedkiw²

2001

227

216

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show abstract

“…[O'Brien and Hodgins 1995] combined a particle system with shallow-water equations to simulate splashing of low viscosity fluid. [Chen and Lobo 1995] used 2D Navier-Stokes equations, taking the pressure to be proportional to height to get the third dimension. The method is interactive though the physical justification for interpreting pressure as height is questionable.…”

Section: Previous Workmentioning

confidence: 99%

A viscous paint model for interactive applications

Baxter

Liu²

2004

Computer Animation & Virtual

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“…This coefficient sequence can be represented by the generating function u 0 x = 4 + 12x + 10x 2 + 5x 3 + 8x 4 . The upper right curve shows the coefficients of u 1 x = s x u 0 x 2 , (Remember, the coefficients of…”

Section: The Associated Subdivision Schemementioning

confidence: 99%

Subdivision schemes for fluid flow

Weimer

Warren

1999

Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques - SIGGRAPH '99

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Figure 1: Modeling a helical flow using subdivision. AbstractThe motion of fluids has been a topic of study for hundreds of years. In its most general setting, fluid flow is governed by a system of non-linear partial differential equations known as the Navier-Stokes equations. However, in several important settings, these equations degenerate into simpler systems of linear partial differential equations. This paper will show that flows corresponding to these linear equations can be modeled using subdivision schemes for vector fields. Given an initial, coarse vector field, these schemes generate an increasingly dense sequence of vector fields. The limit of this sequence is a continuous vector field defining a flow that follows the initial vector field. The beauty of this approach is that realistic flows can now be modeled and manipulated in real time using their associated subdivision schemes.

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Toward Interactive-Rate Simulation of Fluids with Moving Obstacles Using Navier-Stokes Equations

Cited by 103 publications

References 0 publications

Practical Animation of Liquids

Practical Animation of Liquids

A viscous paint model for interactive applications

Subdivision schemes for fluid flow

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