Discontinuous fluids

Abstract

Figure 1: Capillary instability of a liquid jet; liquid pouring on to a sphere; and bubbly water. ×ØÖ ØAt interfaces between different fluids, properties such as density, viscosity, and molecular cohesion are discontinuous. To animate small-scale details of incompressible viscous multi-phase fluids realistically, we focus on the discontinuities in the state variables that express these properties. Surface tension of both free and bubble surfaces is modeled using the jump condition in the pressure field; and discontinuities in the velocity gradient field, driven by viscosity differences, are also considered. To obtain derivatives of the pressure and velocity fields with sub-grid accuracy, they are extrapolated across interfaces using continuous variables based on physical properties. The numerical methods that we present are easy to implement and do not impact the performance of existing solvers. Small-scale fluid motions, such as capillary instability, breakup of liquid sheets, and bubbly water can all be successfully animated. ½ ÁÒØÖÓ Ù Ø ÓÒClose-up scenes of splashing water have mysterious attractions. To emphasize the luxurious image of their products in an advertisement, to depict the tense atmosphere before the sword-fight in a movie, or just to show off the performance of their brand-new digital camera, many people are trying to catch a moment of this beauty. £

Divergence‐constrained moving least squares for fluid simulation

“…A fast GPU implementation 1 would also be required to make this method popular. Finally, we are considering the use of discontinuous divergence-free interpolation of multi-phase fluids for modeling bubbles [21] and flames [22]. …”

The Use of Security Professionals in Counterinsurgency Operations

“…This poses a severe limitation for high viscosities, and limits the spatial size and time scale of the problems that can be considered. A first step towards an implicit treatment of viscosity for sharp interface methods was proposed in [15]. Assuming µ and ρ are spatially constant within each phase and applying ∇ · V = 0 allows one to write the viscous term in 33 as ∇ · (ν∇ V ) where ν = µ/ρ.…”

“…Unfortunately, equation 59 couples the u, v and w terms together meaning that one would require an implicit method that applies to the entire coupled system of equations, as opposed to the usual component by component approaches. Since [15] was mainly focused on computer graphics applications, they made the simplifying assumption that all the viscous fluxes were balanced setting the right hand side of equation 59 to a three by three zero matrix. This allowed them to fully decouple the viscous terms into three separate scalar equations.…”

“…For example, [15] independently used these techniques for the visual simulation of incompressible viscous two-phase fluids with realistic small-scale details. Although they used a slightly simplified approach, decoupling the pressure discontinuity from the viscosity discontinuity, they still obtained sharp interface profiles of solution variables and showed that the method is highly preferable to a smeared out delta function approach.…”

Simulação Eficiente De Fluidos No Espaço Paramétrico De Malhas Estruturadas Tridimensionais

“…Alguns trabalhos procuraram modelar superfícies livres [6], mudanças de fase [7] e interações entre tipos diferentes de fluidos [8,9] ou entre um fluido e um sólido rígido ou deformável [10][11][12]. Outros utilizaram a formulação de fluidos para simular fenômenos especiais, como o fogo [13].…”