Measuring the effects of artificial viscosity in SPH simulations of rotating fluid flows

A commonly cited drawback of smoothed particle hydrodynamics (SPH) is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for quantifying its effect include approximate analytic formulae and disc-averaged behaviour in specific ring-spreading simulations, based on the kinematic effects produced by the artificial viscosity. These methods have disadvantages, in that they typically are applicable to a very small range of physical scenarios, have a large number of simplifying assumptions and often are tied to specific SPH formulations which do not include corrective (e.g. Balsara) or time-dependent artificial viscosity terms. In this study we have developed a simple, generally applicable and practical technique for evaluating the local effect of artificial viscosity directly from the creation of specific entropy for each SPH particle. This local approach is simple and quick to implement, and it allows a detailed characterization of viscous effects as a function of position. Several advantages of this method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability. In order to compare this new method with existing ones, simple disc flow examples are used. Even in these basic cases, the very roughly approximate nature of the previous methods is shown. Our local method provides a detailed description of the effects of the artificial viscosity throughout the disc, even for extended examples which implement Balsara corrections. As a further use of this approach, explicit dependencies of the effective viscosity in terms of SPH and flow parameters are estimated from the example cases. In an appendix, a method for the initial placement of SPH particles is discussed which is very effective in reducing numerical fluctuations.