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

Abstract

Smoothed particle hydrodynamics (SPH) has proven to be a useful numericaltool in studying a number of different astrophysical problems. Still,used on other problems, such as the modeling of low-b 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 modelstrong hydrodynamic and magnetohydrodynamic shocks, and a key issuehas therefore been to achieve a near-optimal representation of thesimulated system at all times. Using SPH, this means combining theLagrangian nature of the method with a smoothing-length profile thatvaries in both space and time. In this paper, a scheme containingtwo novel features is proposed. First, the scheme assumes a piecewiseconstant smoothing-length profile. To avoid substantial errors nearthe steps in the profile, alternative forms of the SPH equationsof motion are used. Second, a predictive attitude toward optimizingthe particle distribution is introduced by activating a mass, momentum,and energy conservation regularization process at intervals. Thescheme described has been implemented in a new code called regularizedsmoothed particle hydrodynamics (RSPH), and test results for a numberof standard hydrodynamic and magnetohydrodynamic tests in one andtwo dimensions using this code are presented.