Tests of Spurious Transport in Smoothed Particle Hydrodynamics

We have performed a series of systematic tests to evaluate quantitatively the effects of spurious transport in three-dimensional smoothed particle hydrodynamics (SPH) calculations. Our tests investigate (i) particle diffusion, (ii) shock heating, (iii) numerical viscosity, and (iv) angular momentum transport. The effects of various program parameters on spurious mixing and on viscosity are investigated. The results are useful for quantifying the accuracy of the SPH scheme, especially for problems where shear flows or shocks are present, as well as for problems where true hydrodynamic mixing is relevant. In particular, the particle diffusion coefficients we measure can be used to help estimate the spurious fluid mixing in SPH applications. We examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by Hernquist and Katz, and by Balsara. Our tests suggest a single set of values for the AV parameters which are appropriate in a large number of situations: α ≈ 0.5, β ≈ 1 for the classical AV of Monaghan, α ≈ β ≈ 0.5 for the Hernquist and Katz AV, and α ≈ β ≈ γ/2 for the Balsara AV (where y is the adiabatic index). We also discuss how these choices should be modified depending on the goals of the particular application. For instance, if spurious particle mixing is not a concern and only weak shocks (Mach number M ≲ 2) are expected during a calculation, then a smaller value of α is appropriate. Somewhat larger values for α and β may be preferable if an accurate treatment of high Mach number shocks (M ≳ 10) is required. We find that both the Hernquist and Katz and Balsara forms introduce only small amounts of numerical viscosity. Furthermore, both Monaghan's and Balsara's AV do well at treating shocks and at limiting the amount of spurious mixing. For these reasons, we endorse the Balsara AV for use in a broad range of applications.