A comparison of particle and fluid approaches for modeling the streaming instability in global patch simulations

Identifying the process relevant to planet formation is still a major task. Mechanisms have been identified that can trap dust and prevent it from migrating inward. A particular hydrodynamic instability, known as the streaming instability, is of high interest because it might cause the formation of dust clumps from which the first planetesimals form. We compared the outcome of nonlinear streaming instability simulations using two fundamental approaches in a more realistic global disk model. The results were not used to identify or disentangle the effect of numerical diffusion in fluid simulations, for instance, or the possibility of crossing particle streams. Instead, they enabled us to determine whether the Lagrangian particle approach is most suitable for numerical studies of the streaming instability. We performed 2D axisymmetric global and isothermal hydrodynamic simulations using the two codes FARGO3D (dust fluid) and PLUTO (fluid and particles) to investigate the temporal evolution of dust scale height, the midplane dust-to-gas ratio, and the maximum dust density, as well as to study velocity distributions and vorticities. For PLUTO particle simulations, we also investigated the influence of the gas Riemann solver and spatial reconstruction orders. Our results from a resolution study of up to 5120 cells per gas scale height indicate convergence between PLUTO fluid and FARGO3D. The two codes yield a Gaussian profile that is dominated by small-scale dust-depleted voids. The particle simulations with PLUTO have not yet converged because a transient midplane dust component persists, indicating the need for an even higher resolution or more particles. A more accurate Riemann solver or a higher-order spatial reconstruction scheme helps to cause the dust density profile to approach the converged structure. At the highest resolution, the maximum dust density in fluid simulations is only 36$%$ of that in particle simulations, which is similar to other code-comparison works. When the streaming instability is studied in a global sense, the choice of the Riemann solver and spatial reconstruction order becomes more important than the approach itself (fluid or particles). When the computational performance of the two dust treatments is included, the fluid approach provides an efficient and suitable tool for streaming instability simulations.