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Multidimensional MHD Shock Tests of Regularized Smoothed Particle Hydrodynamics

This paper investigates to what extent the numerical scheme regularized smoothed particle hydrodynamics (RSPH) is able to accurately describe multidimensional MHD shocks. The scheme can be viewed as an extension to smoothed particle hydrodynamics (SPH), which is widely used for astrophysical applications. In the first of two previous papers, the basic idea behind the RSPH scheme was introduced and tested, primarily on one-dimensional MHD shock problems. A new formulation of the momentum equation was also proposed to secure stability in the low-β regime. A two-dimensional, linear stability analysis of this formulation was presented in the second paper. The second paper also utilized recent developments of the RSPH scheme that improve the overall description of multidimensional problems in general. Based on the results from the linear stability analysis, adjustments to the momentum equation are made in the present work, which are also applicable to the nonlinear regime. These adjustments address the problem of asymmetries in the momentum equation, which in nonlinear problems can lead to small, yet systematic errors in postshock conditions. In addition, this paper describes the first application of the improved RSPH scheme to multidimensional MHD shocks. Comparisons are made with existing methods, in particular the related SPH method. Special attention is given to the scheme's ability to maintain the 𝛁 ∙ = 0 constraint and to what extent redefining the particle distribution affects the conservation of kinetic energy and angular momentum.