On the momentum diffusion over multiphase surfaces with meshless methods

TL;DR

This paper examines how different momentum diffusion operators affect multiphase fluid simulations using meshless methods, highlighting under-predictions at interfaces and proposing an improved scheme that accounts for viscosity jumps.

Contribution

It introduces a new multiphase GFD diffusion scheme that efficiently models viscosity discontinuities in meshless Lagrangian methods.

Findings

Traditional operators under-predict shear divergence at interfaces.

Larger viscosity ratios amplify the under-prediction effects.

The proposed scheme reduces discrepancies in bubble ascent velocity by over 57%.

Abstract

This work investigates the effects of the choice of momentum diffusion operator on the evolution of multiphase fluid systems resolved with Meshless Lagrangian Methods (MLM). Specifically, the effects of a non-zero viscosity gradient at multiphase interfaces are explored. This work shows that both the typical Smoothed Particle Hydrodynamics (SPH) and Generalized Finite Difference (GFD) diffusion operators under-predict the shear divergence at multiphase interfaces. Furthermore, it was shown that larger viscosity ratios increase the significance of this behavior. A multiphase GFD scheme is proposed that makes use of a computationally efficient diffusion operator that accounts for the effects arising from the jump discontinuity in viscosity. This scheme is used to simulate a 3D bubble submerged in a heavier fluid with a density ratio of 2:1 and a dynamic viscosity ratio of 100:1. When comparing the effects of momentum diffusion operators, a discrepancy of 57.2% was observed in the bubble's ascent velocity.