A comparison between particle and fluid approaches for streaming instability in global patch simulations

Abstract

Identifying the process relevant to planet formation is still a major task. Mechanisms have been identified that can trap dust, preventing it from migrating inwards. A particular hydrodynamic instability, known as the streaming instability, is of high interest because it may be responsible for the formation of dust clumps from which the first planetesimals form. We aim to compare the outcome of non-linear streaming instability simulations using both fundamental approaches in a more realistic global disk model. The results will not be used to identify or disentangle the effect of, e.g., numerical diffusion in fluid simulations or the possibility of having crossing particle streams. Instead, they will enable us to determine whether the Lagrangian particle approach is the most suitable for numerical studies of the streaming instability. Methods: We perform 2D, axisymmetric, global, and isothermal hydrodynamic simulations using the two codes FARGO3D (dust fluid) and PLUTO (fluid, particles) to investigate the temporal evolution of dust scale height, midplane dust-to-gas ratio, and maximum dust density as well as to study velocity distributions and vorticities. For PLUTO particle simulations, we also investigate the influence of the gas Riemann solver and spatial reconstruction orders. Our results from a resolution study up to 5120 cells per gas scale height indicate convergence between PLUTO fluid and FARGO3D. Both yield a Gaussian profile dominated by small-scale, dust-depleted voids. Particle simulations with PLUTO have not yet converged, as a transient midplane dust component persists, indicating the need for even higher resolution or more particles. Using a more accurate Riemann solver or a higher-order spatial reconstruction scheme helps to bring the dust density profile closer to the converged structure.