Regular and non-regular solutions of the Riemann problem in ideal magnetohydrodynamics

Abstract

We have built a code to numerically solve the Riemann problem in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition to investigate a variety of solutions more thoroughly. The code can handle not only regular solutions, in which no intermediate shocks are involved, but also all types of non-regular solutions if any. As a first application, we explored the neighborhood of the initial condition that was first picked up by Brio & Wu (1988) and has been frequently employed in the literature as a standard problem to validate numerical codes. Contrary to the conventional wisdom that there will always be a regular solution, we found an initial condition, for which there is no regular solution but a non-regular one. The latter solution has only regular solutions in its neighborhood and actually sits on the boundary of regular solutions. This implies that the regular solutions are not sufficient to solve the ideal MHD Riemann problem and suggests that at least some types of non-regular solutions are physical. We also demonstrate that the non-regular solutions are not unique. In fact, we found for the Brio & Wu initial condition that there are uncountably many non-regular solutions. This poses an intriguing question: why a particular non-regular solution is always obtained in numerical simulations? This has important ramifications to the discussion of which intermediate shocks are really admissible.

Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics

“…It has provoked debate over the years (e.g. Wu 1988;Dai & Woodward 1994a;Falle & Komissarov 2001;Takahashi, Yamada, & Yamada 2013) because of the presence of a compound slow shock and rarefaction in the solution, which is stable only when the magnetic field is coplanar and there is no perturbation to the tangential (B z ) magnetic field (Barmin, Kulikovskiy, & Pogorelov 1996). Whether or not such solutions can exist in nature remains controversial (e.g.…”

Observations of an Interplanetary Intermediate Shock Associated With a Magnetic Reconnection Exhaust

“…Over the past more than four decades, there have been a large number of numerical investigations for ISs. In spite of evolutionary conditions, ISs are commonly observed to be stable shocks in numerical simulations (e.g., Wu 1987;Wu & Hada 1991;Takahashi et al 2013Takahashi et al , 2014, and two interplanetary ISs have been observed and reported (Chao et al 1993;Feng & Wang 2008). However, both ISs were identified through fitting the R-H relations based on one spacecraft observation.…”

Magnus: A New Resistive MHD Code with Heat Flow Terms

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