Numerical Stability Analysis for a Stationary and Translating Droplet at Extremely Low Viscosity Values Using the Lattice Boltzmann Method Color-Gradient Multi-Component Model with Central Moments Formulation

Multicomponent models based on the Lattice Boltzmann Method (LBM) have clear advantages with respect to other approaches, such as good parallel per-formances and scalability and the automatic resolution of breakup and coalescence events. Multicomponent flow simulations are useful for a wide range of applications, yet many multicomponent models for LBM are limited in their numerical stability and therefore do not allow exploration of physically relevant low viscosity regimes. Here we perform a quantitative study and validations, varying parameters such as viscosity, droplet radius, domain size and acceleration for stationary and translating droplet sim-ulations for the color-gradient method with central moments (CG-CM) formulation, as this method promises increased numerical stability with respect to the non-CM formu-lation. We focus on numerical stability and on the effect of decreasing grid-spacing, i.e. increasing resolution, in the extremely low viscosity regime for stationary droplet simulations. The effects of small-and large-scale anisotropy, due to grid-spacing and domain-size, respectively, are investigated for a stationary droplet. The effects on nu-merical stability of applying a uniform acceleration in one direction on the domain, i.e. on both the droplet and the ambient, is explored into the low viscosity regime, to probe the numerical stability of the method under dynamical conditions.

Automated summary

Multicomponent models based on LBM have advantages in parallel performances, scalability, and automatic resolution of events. However, current models have limitations in numerical stability, preventing exploration of low viscosity regimes.