2024/07/16 by Oliver Gressel, Gressel, Oliver, U. Ziegler +1 · 1 citation
Earth and Planetary Sciences · Engineering · #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Geophysical and Geoelectrical Methods #Geophysics and Gravity Measurements #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Solar and Stellar Astrophysics (astro-ph.SR) #Spacecraft and Cryogenic Technologies
paper · pdf · doi:10.48550/arxiv.2407.11648
openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Astrophysical accretion discs that carry a significant mass compared with their central object are subject to the effect of self-gravity. In the context of circumstellar discs, this can, for instance, cause fragmentation of the disc gas, and -- under suitable conditions -- lead to the direct formation of gas-giant planets. If one wants to study these phenomena, the disc's gravitational potential needs to be obtained by solving the Poisson equation. This requires to specify suitable boundary conditions. In the case of a spherical-polar computational mesh, a standard multipole expansion for obtaining boundary values is not practicable. We hence compare two alternative methods for overcoming this limitation. The first method is based on a known Green's function expansion (termed "CCGF") of the potential, while the second (termed "James' method") uses a surface screening mass approach with a suitable discrete Green's function. We demonstrate second-order convergence for both methods and test the weak scaling behaviour when using thousands of computational cores. Overall, James' method is found superior owing to its favourable algorithmic complexity of ∼ O(n3) compared with the \simO(n4) scaling of the CCGF method.