Numerical Dissipation in RSPH Simulations of Astrophysical Flows with Application to Protoplanetary Disks

Smoothed Particle Hydrodynamics (SPH) is widely used for astrophysical applications, in particular problems of self-gravitational hydrodynamics. However, critics have argued that inherent accuracy problems with the method can be identified, in particular when it comes to describing shocks and dynamical instabilities. Regularized Smoothed Particle Hydrodynamics (RSPH) has previously been proposed as an extension to SPH. It is an attempt to increase the accuracy of the hydrodynamical description without having to abandon the Lagrangian formulation altogether. As the name implies, the method relies on a regularization technique where the solution at temporal intervals is mapped on to a new set of regularly placed particles. This technique allows us to reduce the numerical noise otherwise caused by highly irregular particle distributions and to take advantage of a more flexible approach to variable resolution. The cost of introducing the regularization scheme lies in increased methodical complexity, and in increased numerical dissipation. This paper investigates the numerical dissipation both qualitatively and quantitatively in the context of two-dimensional models relevant to the study of protoplanetary disks. Basic hydrodynamical tests highlight key properties of the RSPH approach. By comparison with an analytical solution, we are also able to quantify the dependence of the spurious viscosity on key numerical parameters. To put the theoretical discussion in perspective, we also present results from simulations of test problems involving disk-planet interactions. The results are compared to published results obtained with other codes.