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 λ remains, 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 λ as 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.

Electrically Charged Matter in Permanent Rotation Around Magnetized Black Holes: A Toy Model for Self-Gravitating Fluid Tori

“…The free-parameter, λ, called "the smoothing length", takes into account the vertical and the radial extension of the torus. Various prescriptions have been chosen for this parameter: (i) a function of the disk parameter,(ii) a function of space or (ii) a constant value (Masset 2002;Huré & Pierens 2005;Müller et al 2012;Huré & Trova 2015), however no universal value has been adopted; see Huré & Pierens (2009) for an non exhaustive list. In our work, the softening length is a function of the loop radius (i.e location of the maximum pressure), λ = 0.4r c .…”