Regularized Smoothed Particle Hydrodynamics: A New Approach to Simulating Magnetohydrodynamic Shocks

Smoothed particle hydrodynamics (SPH) has proven to be a useful numerical tool in studying a number of different astrophysical problems. Still, used on other problems, such as the modeling of low-β MHD systems, the method has so far not performed as well as one might have hoped. The present work has been motivated by the desire to accurately model strong hydrodynamic and magnetohydrodynamic shocks, and a key issue has therefore been to achieve a near-optimal representation of the simulated system at all times. Using SPH, this means combining the Lagrangian nature of the method with a smoothing-length profile that varies in both space and time. In this paper, a scheme containing two novel features is proposed. First, the scheme assumes a piecewise constant smoothing-length profile. To avoid substantial errors near the steps in the profile, alternative forms of the SPH equations of motion are used. Second, a predictive attitude toward optimizing the particle distribution is introduced by activating a mass, momentum, and energy conservation regularization process at intervals. The scheme described has been implemented in a new code called regularized smoothed particle hydrodynamics (RSPH), and test results for a number of standard hydrodynamic and magnetohydrodynamic tests in one and two dimensions using this code are presented.