Variational stokes

Abstract

Fig. 1. By carefully treating coupling between viscosity and pressure forces, our unified Stokes-based fluid solver can reproduce the classic liquid rope coiling instability of viscous liquids like honey, while prior grid-based methods cannot.We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.

Functional optimization of fluidic devices with differentiable stokes flow

“…Notably most such works that target evolving fluid domains are focused towards dynamic simulation rather than stationary flows. Steady-state flows, and especially Stokes fluids, have received occasional attention within the graphics literature, in applications related to fluid control [Bhattacharya et al 2012], simulation of highly viscous media such as paint [Baxter et al 2004], or as a complement to an unsteady-flow solver for viscous liquids [Larionov et al 2017].…”

Distributing and Load Balancing Sparse Fluid Simulations

“…Our simulation uses 8 particles per cell, and a block diagonal preconditioner using incomplete Cholesky factorization. Our solver does not account for advanced effects such as surface tension and viscosity [BB12,LBB17]. We expect that our methodology would provide similar benefits under variations of the basic FLIP algorithm.…”