A Staggered Semi-analytic Method for Simulating Dust Grains Subject to Gas Drag

• Published in: The Astrophysical journal. Supplement series Vol. 244; no. 2; pp. 42 - 52
• Main Authors: Fung, Jeffrey, Muley, Dhruv
• Format: Journal Article
• Language: English
• Published: Saskatoon The American Astronomical Society 01.10.2019; IOP Publishing
• Subjects: Astrophysical dust processes; Astrophysical research; Circumstellar dust; Circumstellar matter; Computational astronomy; Computational methods; Computer simulation; Debris disks; Drag; Dust; Exoplanet formation; Gas dynamics; Interstellar dust; Interstellar dust processes; Mathematical analysis; Methods; Numerical simulations; Planet formation; Protoplanetary disks; Protoplanets; Robustness (mathematics); Stability; Terminal velocity; Very small grains
• ISSN: 0067-0049; 1538-4365
• DOI: 10.3847/1538-4365/ab45f3

Numerical simulations of dust-gas dynamics are one of the fundamental tools in astrophysical research, such as the study of star and planet formation. It is common to find tightly coupled dust and gas in astrophysical systems, which demands that any practical integration method be able to take time steps, , much longer than the stopping time, , due to drag. A number of methods have been developed to ensure stability in this stiff regime, but there remains large room for improvement in terms of accuracy. In this paper, we describe an easy-to-implement method, the "staggered semi-analytic method" (SSA), and conduct numerical tests to compare it to other implicit and semi-analytic methods, including the second-order implicit method and the Verlet method. SSA makes use of a staggered step to better approximate the terminal velocity in the stiff regime. In applications to protoplanetary disks, this not only leads to orders of magnitude higher accuracy than the other methods, but also provides greater stability, making it possible to take time steps 100 times larger in some situations. SSA is also second-order accurate and symplectic when . More generally, the robustness of SSA makes it applicable to linear dust-gas drag in virtually any context.