Tests of spurious transport in smoothed particle hydrodynamics

We have performed a series of systematic tests to evaluate quantitatively t he effects of spurious transport in three-dimensional smoothed particle hyd rodynamics (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 sh ocks are present, as well as for problems where true hydrodynamic mixing is relevant. In particular, the particle diffusion coefficients we measure ca n be used to help estimate the spurious fluid mixing in SPH applications. W e examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by Hernquist and Katz, and by Balsara. Our tests sugg est a single set of values for the AV parameters which are appropriate in a large number of situations: alpha approximate to 0.5, beta approximate to 1 for the classical AV of Monaghan, alpha x beta x 0.5 for the Hernquist an d Katz AV, and alpha approximate to beta approximate to gamma/2 for the Bal sara AV (where gamma is the adiabatic index). We also discuss how these cho ices should be modified depending on the goals of the particular applicatio n. For instance, if spurious particle mixing is not a concern and only weak shocks (Mach number M less than or similar to 2) are expected during a cal culation, then a smaller value of a is appropriate. Somewhat larger values for alpha and beta may be preferable if an accurate treatment of high Mach number shocks (M greater than or similar to 10) is required. We find that b oth the Hernquist and Katz and Balsara forms introduce only small amounts o f numerical viscosity. Furthermore, both Monaghan's and Balsara's AV do wel l at treating shocks and at limiting the amount of spurious mixing. For the se reasons, we endorse the Balsara AV for use in a broad range of applicati ons. (C) 1999 Academic Press.