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.

Accepted for publication in MNRAS, 8 pages, 10 figures

References in corpus (2)

• Treating gravity in thin disk simulations
• A Fast Potential and Self-Gravity Solver for Non-Axisymmetric Disks

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