The softened point mass model is commonly used in simulations of gaseous discs including self-gravity while the value of associated length lambda remains, to some degree, controversial. This ``parameter is however fully constrained when, in a discretized disc, all fluid cells are demanded to obey Newtons 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 cells shape (curvature, radial extension, height), but it is either a real or an imaginary number. Setting lambda 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.
Download