Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Particle-Laden Fluid on Flow Maps

Zhiqi Li, Duowen Chen, Candong Lin, Jinyuan Liu, Bo Zhu

TL;DR

The approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops.

Abstract

We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures.

Particle-Laden Fluid on Flow Maps

TL;DR

The approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops.

Abstract

We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures.
Paper Structure (41 sections, 29 equations, 15 figures, 2 tables, 1 algorithm)

This paper contains 41 sections, 29 equations, 15 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Eulerian-Lagrangian Methods.
  4. Particle-Laden Flow.
  5. Flow Map Methods.
  6. Physical Model
  7. Naming Convention
  8. Fluid
  9. Sediment
  10. Particle Flow Map for Laden Flow
  11. Flow Map Theory
  12. Flow Map
  13. Particle Flow Map
  14. Adapting Particle Flow Map to Laden Flow
  15. Integration Form and Path Integral
  16. ...and 26 more sections

Figures (15)

  • Figure 1: Flow Maps are tracked by fluid particles $q$ and long-range mapped velocity is calculated, while sediment particles $p$ advect short-range velocity step-by-step. They interact via the background grid with interpolation and Poisson solve.
  • Figure 2: Dripping. The long tail of a descending ink will bulge and break up into many suspension drops, which forms tori afterwards
  • Figure 3: Ink Torus Breakup: Under drag force and viscous force, a ink torus disintegrate into several blobs, which deform into tori and disintegrate again, resulting in a cascade process of blob deformations and breakups.
  • Figure 4: Ink Torus Breakup Under $Re= 16.5, 18, 19.5, 21.0, 30.0$: number of blobs disintegrated from a ink torus increase with Reynolds Number, under interaction of viscous force and vorticity.
  • Figure 5: Nine Ink Drops Passing Porous Obstacle. Nine ink drops drip down from the gaps between cylinders, turning into many small falling drops.
  • ...and 10 more figures