A Comparative Study of the Streaming Instability: Unstratified Models with Marginally Coupled Grains

TL;DR

This study systematically compares seven hydrodynamic codes modeling the streaming instability in protoplanetary disks, highlighting qualitative agreement but quantitative differences influenced by dust treatment and computational methods.

Contribution

First comprehensive comparison of diverse hydrodynamic codes for the streaming instability, assessing robustness and differences in nonlinear evolution and computational performance.

Findings

All codes reproduce key instability features like filament formation.

Particle-based models reach higher peak densities than fluid models at moderate resolution.

Differences between dust treatments diminish at higher resolutions, indicating better agreement.

Abstract

The streaming instability is a leading mechanism for concentrating solids and initiating planetesimal formation in protoplanetary disks. Although numerous studies have explored its linear growth, nonlinear evolution, and implications for planet formation, the diversity of numerical methods and dust treatments used across the literature has made it difficult to assess which features of the instability are physically robust and which arise from code-dependent choices. We present the first systematic comparison of seven hydrodynamic codes--spanning finite-volume and finite-difference schemes and modeling dust either as Lagrangian particles or as a pressureless fluid--applied to the unstratified streaming instability with a dimensionless stopping time of unity. All codes reproduce the characteristic sequence of exponential growth, filament formation, and turbulent saturation, demonstrating broad agreement in the qualitative behavior of the instability. Quantitatively, however, the dust model remains the dominant source of variation at moderate resolution: particle-based simulations reach higher peak densities and exhibit broader high-density tails than fluid-based models at $512^2$ resolution, although increasing the number of particles brings their initial maximum density evolution into close agreement with that of dust-fluid models. At $1024^2$, these differences diminish substantially, indicating better agreement of the saturated-state statistics across dust treatments. In terms of computational performance, most particle implementations suffer from imbalanced parallelized loads, while execution on a GPU is at least two to three times more energy efficient and scales better at higher resolutions than on CPUs. Given the intrinsic stochasticity of this nonlinear system, only statistical diagnostics remain meaningful across codes.