A truly Newtonian softening length for disc simulations

Abstract

The softened point mass model is commonly used in simulations of gaseous discs including self-gravity while the value of associated length λremains, to some degree, controversial. This ``parameter'' is however fully constrained when, in a discretized disc, all fluid cells are demanded to obey Newton's law. We examine the topology of solutions in this context, focusing on cylindrical cells more or less vertically elongated. We find that not only the nominal length depends critically on the cell's shape (curvature, radial extension, height), but it is either a real or an imaginary number. Setting λas a fraction of the local disc thickness -- as usually done -- is indeed not the optimal choice. We then propose a novel prescription valid irrespective of the disc properties and grid spacings. The benefit, which amounts to 2-3 more digits typically, is illustrated in a few concrete cases. A detailed mathematical analysis is in progress.

arXiv commentAccepted for publication in MNRAS, 8 pages, 10 figures

References in corpus (11)

• Rapid inward migration of planets formed by gravitational instability
• The co-orbital corotation torque in a viscous disk: numerical simulations
• On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs
• Treating gravity in thin disk simulations
• Non-convergence of the critical cooling timescale for fragmentation of self-gravitating discs
• Numerical convergence in self-gravitating shearing sheet simulations and the stochastic nature of disc fragmentation
• Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids
• Accurate numerical potential and field in razor-thin axisymmetric discs
• A Fast Potential and Self-Gravity Solver for Non-Axisymmetric Disks
• Self-gravity in curved mesh elements
• A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

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