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Paper: On the Existence and Non-uniqueness of Solutions of Riemann Problems in Ideal Magnetohydrodynamics
Volume: 488, 8th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2013)
Page: 261
Authors: Takahashi, K.; Yamada, S.
Abstract: We have built a new exact Riemann solver for ideal magnetohydrodynamics (MHD) that can handle all types of the non-regular waves, such as intermediate shocks and switch-on/off waves. This code can find all the exact solutions for a given MHD Riemann problem. Using the solver, we found that there are uncountably many non-regular solutions for the Brio & Wu problem, which is one of the best-known MHD Riemann problems as it is used as a test problem for numerical codes. This result has cast a question on the numerical MHD simulations: Why do most of the numerical MHD codes always produce a typical non-regular solution which consists of a compound wave?
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