Open AccessThree-dimensional cylindrical Poisson solver with vacuum boundary conditions
Author(s) -
Sung Joon Moon
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1623/1/012017
Subject(s) - convergence (economics) , solver , poisson's equation , cylindrical coordinate system , boundary value problem , boundary (topology) , scaling , rotation (mathematics) , physics , mathematics , computer science , mathematical analysis , algorithm , geometry , mathematical optimization , mechanics , economics , economic growth
Self-gravity and rotation are two key ingredients in dynamics of astronomical disk systems such as galactic and protostellar disks. Despite its importance, there has not yet been so far an efficient algorithm to solve the Poisson equation in three-dimensional cylindrical coordinates under vacuum boundary conditions. By generalizing the James algorithm to cylindrical coordinates, we develop an accurate (second-order convergence) and efficient (faster than MHD) cylindrical Poisson solver that is scalable up to ∼ 10 4 cores. We develop a method to calculate the cylindrical discrete Green’s function, which is an essential element of the James algorithm to estabilish its second-order accuracy. We implement our cylindrical version of the James algorithm in Athena++ code and demonstrate its accuracy and efficiency by performing the convergence test and the weak scaling test.