We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on the role of time-parallel transport in eliminating---without approximation---all but an O(n) band of entries of the physical system's energy Hessian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.

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Discrete viscous threads

An SPH projection method for simulating fluid-hypoelastic structure interaction

Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications

Improved Incompressible Smoothed Particle Hydrodynamics method for simulating flow around bluff bodies

We present a fully implicit Eulerian technique for simulating free surface viscous liquids which eliminates artifacts in previous approaches, efficiently supports variable viscosity, and allows the simulation of more compelling viscous behaviour than previously achieved in graphics. Our method exploits a variational principle which automatically enforces the complex boundary condition on the shear stress at the free surface, while giving rise to a simple discretization with a symmetric positive definite linear system. We demonstrate examples of our technique capturing realistic buckling, folding and coiling behavior. In addition, we explain how to handle domains whose boundary comprises both ghost fluid Dirichlet and variational Neumann parts, allowing correct behaviour at free surfaces and solid walls for both our viscous solve and the variational pressure projection of Batty et al. [BBB07].

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Accurate viscous free surfaces for buckling, coiling, and rotating liquids

In this paper, an incompressible smoothed particle hydrodynamics (SPH) method is presented to solve unsteady free-surface flows. Both Newtonian and viscoelastic fluids are considered. In the case of viscoelastic fluids, both the Maxwell and Oldroyd-B models are investigated. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme and employs an adaptive smoothing length based on density variations. To alleviate the numerical difficulties encountered when fluid is highly stretched, an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material. Two challenging test cases, the impacting drop and the jet buckling problems, are solved to demonstrate the capability of the proposed scheme in handling viscoelastic flows with complex free surfaces. The jet buckling test case was solved for a wide range of Weissenberg numbers. It was shown that in all cases the method is stable and fairly accurate and agrees well with the available data.

A. Rafiee

Papers

An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows