## Measuring the Effects of Artificial Viscosity in SPH Simulations of Rotating Fluid Flows

by **Taylor, Paul A.** and **Miller, John C.**

14 pages, 9 figures, submitted to MNRAS

A commonly cited drawback of SPH is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for understanding its effect include approximative analytic formulae and disc-averaged behaviour in specific ring-spreading simulations, based on the kinematic contribution of the artificial viscosity. In this work, we have developed a simple, general technique for evaluating the local effect of artificial viscosity directly from the entropic function of each SPH particle. This is simple and quick to implement, and it allows a detailed characterization of its effects as a function of position. Several advantages of this local method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability to arbitary flow geometries and equations of state. Here, we apply this approach to various disc flows, including simulations which implement the commonly-used Balsara switch. Comparisons with existing analytic estimates are made, and examples of quantifying explicit dependencies of the effective viscosity in terms of SPH and flow parameters are given. Additionally, a method for the initial placement of SPH particles which reduces numerical fluctuations is discussed and utilised.