Modeling dust dynamics in OpenGadget3 -- I. SPH implementation of the One-Fluid model

TL;DR

This work implements the full One-Fluid dust–gas model in OpenGadget3, introducing time-dependent artificial viscosity and conductivity and a diffusion-like dust pressure term to extend applicability beyond the terminal velocity approximation. The SPH discretization conserves mass, momentum, and energy, and includes implicit drag integration via operator splitting, a unified viscosity framework, and adaptive dust diffusion using a pressure-like mechanism. Validation across DUSTYBOX, DUSTYWAVE, DUSTYSHOCK (1D/2D), and dusty Sedov–Taylor benchmarks, plus complex flows like Cold Keplerian disks, dusty protoplanetary disks, and Kelvin–Helmholtz instabilities, demonstrates stability and accuracy across drag regimes and dust fractions, with diffusion mitigating excessive dust clumping in weakly coupled regimes. The results indicate the approach is robust for a wide range of astrophysical environments, though extreme low-drag, high-dust situations still pose challenges and may require additional techniques or grain-size extensions. Overall, the enhanced One-Fluid model broadens the capability of SPH simulations to study gas–dust dynamics in OpenGadget3 with reliable numerical behavior.

Abstract

Dust dynamics plays a critical role in astrophysical processes and has been modeled in hydrodynamical simulations using various approaches. Among particle-based methods like Smoothed Particle Hydrodynamics (SPH), the One-Fluid model has proven to be highly effective for simulating gas-dust mixtures. This study presents the implementation of the One-Fluid model in OpenGadget3, introducing improvements to the original formulation. These enhancements include time-dependent artificial viscosity and conductivity, as well as a novel treatment of dust diffusion using a pressure-like term. The improved model is tested using a suite of dust dynamics benchmark problems: DUSTYBOX, DUSTYWAVE, and DUSTYSHOCK, with the latter extended to multidimensional scenarios, as well as a dusty Sedov-Taylor blast wave. Additional tests include simulations of Cold Keplerian Disks, dusty protoplanetary disks, and Kelvin-Helmholtz instabilities to evaluate the model's robustness in more complex flows. The implementation successfully passes all standard benchmark tests. It demonstrates stability and accuracy in both simple and complex simulations. The new diffusion term improves the handling of flows with large dust-to-gas ratios and low drag coefficients, although limitations of the One-Fluid model in these regimes remain. The enhanced One-Fluid model is a reliable and robust tool for simulating dust dynamics in OpenGadget3. While it retains some limitations inherent to the original formulation, the introduced improvements expand its applicability and address some challenges in gas-dust dynamics.

Figures (14)

• Figure 1: Distribution of the shock indicator defined in Eq. \ref{['eq:shock_indicator']} for the Cold Keplerian Disk (top panel) and the Kelvin-Helmholtz instability (bottom panel) simulations.
• Figure 2: Result of the DUSTYBOX benchmark test. The continuous lines represent the analytical solution, while the dots are the simulation outputs. The results are shown for four different values of the drag coefficient $K$.
• Figure 3: Results from the DUSTYWAVE benchmark test, for three different values of drag coefficient $K$. The continuous lines represent the analytical solution and the dots the output of the simulations. Gas and dust velocities are plotted separately.
• Figure 4: DUSTYSHOCK benchmark test for zero drag. The blue and red dots represent the output of the simulation for gas and dust, respectively, while the continuous line shows the solution for the gas evolution. As expected, while the gas undergoes the typical Sod shock tube evolution, the dust remains unperturbed.
• Figure 5: DUSTYSHOCK benchmark test for strong drag ($K = 10^6$). The blue and red dots represent the output of the simulation for gas and dust, respectively, while the continuous line shows the solution for the gas evolution. The evolution of the dust now closely follows the gas, and both evolve at a lower speed compared to a gas-only simulation, with the modified sound speed shown in Eq. \ref{['eq:modified_sound_speed']}.