Codimensional non-Newtonian fluids

Abstract

We present a novel method to simulate codimensional nonNewtonian fluids on simplicial complexes. Our method extends previous work for codimensional incompressible flow to various types of non-Newtonian fluids including both shear thinning and thickening, Bingham plastics, and elastoplastics. We propose a novel time integration scheme for semi-implicitly treating elasticity, which when combined with a semi-implicit method for variable viscosity alleviates the need for small time steps. Furthermore, we propose an improved treatment of viscosity on the rims of thin fluid sheets that allows us to capture their elusive, visually appealing twisting motion. In order to simulate complex phenomena such as the mixing of colored paint, we adopt a multiple level set framework and propose a discretization on simplicial complexes that facilitates the tracking of material interfaces across codimensions. We demonstrate the efficacy of our approach by simulating a wide variety of non-Newtonian fluid phenomena exhibiting various codimensional features.

Conformation constraints for efficient viscoelastic fluid simulation

“…Some viscosity models advocate de ning viscous stress as a function of shear rate [Peer et al 2015;Zhu et al 2015]. In the purely viscous case, our model converges instead to a null-strain-rate constraint, as discussed in Section 3.2. e di erence w.r.t.…”

“…Remeshing strategies helped them preserve thin surfaces and reduce the simulation cost. Zhu et al [2015] simulated viscous e ects on features of di erent dimensions, all handled in a uniform manner. ey achieved high-quality simulation of very thin features for non-Newtonian uids.…”

“…Additionally, while some of our examples demonstrate the simulation of ne features, the ability to resolve such ne features is eventually limited by the particle resolution of the simulation. Fusing codimensional representations [Zhu et al 2015] with constraint-based viscoelasticity would enable even richer e ects under manageable computational cost.…”

An SPH model to simulate the dynamic behavior of shear thickening fluids

“…The modified Herschel-Bulkley model is an abstract general form for a bulk rheology that can include shear thinning and shear thickening in a mathematical sense, but this model misses almost all of the important features of real-world STFs, including the critical stresses that set the range of shear thickening in a viscosity function, so that shear thickening appears as a transition from a low-viscosity state to a high-viscosity state at a critical shear rate, 6 as well as the hysteresis and velocity-dependent stiffness mentioned in Section 1.1. More recently, non-Newtonian fluids linking stiffness to the shear rate 22 have been proposed achieving shear-thickening and shear-thinning behavior, but again without considering hysteresis and not addressing the specific phenomenon that is the target of this paper. 7 The key physics that has to be taken into account to describe the phenomena shown in Figures 1 and 2 is hysteresis in the constitutive relation 7,21 and the velocity-dependent stiffness, 11 and this is the focus of our proposed model, which is able to produce visually successful simulations of the most interesting (and peculiar) phenomena observed in STFs.…”

Variational stokes

“…Specialized Lagrangian approaches for slender viscous threads and sheets have been proposed [Batty et al 2012;Bergou et al 2010;Zhu et al 2015Zhu et al , 2014 that extend ideas from rod and shell simulation. In particular, the viscous threads of Bergou et al accurately reproduce both stationary coiling and the intricate patterns arising in a "fluid mechanical sewing machine" .…”