Toward an efficient second‐order method for computing the surface gravitational potential on spherical‐polar meshes

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...

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Vydáno v:Astronomische Nachrichten Ročník 345; číslo 8
Hlavní autoři: Gressel, Oliver, Ziegler, Udo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Weinheim WILEY‐VCH Verlag GmbH & Co. KGaA 01.10.2024
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Témata:
accretion discs
Accretion disks
Boundary conditions
Computational grids
Gas formation
gravitational instability
Green's functions
Multipoles
Planet formation
Poisson equation
Poisson solver
self‐gravity
ISSN:0004-6337, 1521-3994
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Shrnutí: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 behavior when using thousands of computational cores. Overall, James' method is found superior owing to its favorable algorithmic complexity of ∼On3$$ \sim \mathcal{O}\left({n}^3\right) $$ compared with the ∼On4$$ \sim \mathcal{O}\left({n}^4\right) $$ scaling of the CCGF method.
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ISSN:0004-6337
1521-3994
DOI:10.1002/asna.20240056