Resolving fluid boundary layers with particle strength exchange and weak adaptivity

Abstract

Most fluid scenarios in graphics have a high Reynolds number, where viscosity is dominated by inertial effects, thus most solvers drop viscosity altogether: numerical damping from coarse grids is generally stronger than physical viscosity while resembling it in character. However, viscosity remains crucial near solid boundaries, in the boundary layer , to a large extent determining the look of the flow as a function of Reynolds number. Typical graphics simulations do not resolve boundary layer dynamics, so their look is determined mostly by numerical errors with the given grid size and time step, rather than physical parameters. We introduce two complementary techniques to capture boundary layer dynamics, bringing more physical control and predictability. We extend the FLIP particle-grid method with viscous particle strength exchange[Rivoalen and Huberson 2001] to better transfer momentum at solid boundaries, dubbed VFLIP. We also introduce Weakly Higher Resolution Regional Projection (WHIRP), a cheap and simple way to increase grid resolution where important by overlaying high resolution grids on the global coarse grid.

Dynamic Upsampling of Smoke through Dictionary-based Learning

“…However, a large number of particles are necessary to obtain realistic smoke animations to avoid poor numerical accuracy for turbulent flows. Hybrid methods [Jiang et al 2015;Raveendran et al 2011;Zhang and Bridson 2014;Zhang et al 2016;Zhu and Bridson 2005], which combine both particles and grids, can be substantially faster, but particle-grid interpolations usually produce strong dissipation unless polynomial basis functions are used for improved numerics [Fu et al 2017]. These methods remain very costly in the context of turbulent smoke simulation.…”

“…behavior of smoke realistically requires not only sophisticated non-dissipative numerical solvers [Li et al 2020;Mullen et al 2009;Qu et al 2019;Zhang et al 2015], but also a spatial discretization with sufficiently high resolution to capture fine-scale structures, either uniformly [Kim et al 2008b;Zehnder et al 2018] or adaptively [Losasso et al 2004;Weißmann and Pinkall 2010a;Zhang et al 2016]. This inevitably makes such direct numerical simulations computationally intensive.…”

Stormscapes

“…Since the seminal work of Stam [1999] many methods have been introduced to improve solvers for two way coupling [Lu et al 2016;Teng et al 2016;Zhu and Bridson 2005], based on reduced order methods [Gupta and Narasimhan 2007;Jones et al 2016;Treuille et al 2006], Smoothed Particle Hydrodynamics [Ihmsen et al 2014;Koschier et al 2019], or with an emphasis on compute and memory efficiency [Ferstl et al 2014;Losasso et al 2004;McAdams et al 2010;Setaluri et al 2014;Zehnder et al 2018]. Numerous methods focus on even more intricate features of fluid flows, for example based on eigenfunctions [Cui et al 2018], momentum transfer and regional projections [Zhang et al 2016], style-transfer [Sato et al 2018b], optimization [Inglis et al 2017], or based on narrow band representations [Ferstl et al 2016]. More recently, it has also been recognized that neural networks provide a powerful means to represent details of fluids, for example with an emphasis on temporal coherency [Xie et al 2018], liquid splash modeling [Um et al 2018], Lagrangian simulations [Ummenhofer et al 2020], or even style-transfer [Kim et al 2020].…”

A polynomial particle-in-cell method

“…Foster and Metaxas used particles for tracking liquids in [Foster and Metaxas 1996]. Most applications in computer graphics are for incompressible flows using a MAC-grid [Harlow and Welch 1965] pressure projection to enforce incompressibility in the grid momentum update [Batty et al 2007;Batty and Bridson 2008;Boyd and Bridson 2012;Larionov et al 2017;McAdams et al 2009;Zhang et al 2016]. Unilateral incompressibility, where a divergence-inequality constraint replaces the divergence-free constraint, has been used with FLIP for a wide range of applications.…”