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We describe a high-order numerical magnetohydrodynamics (MHD) solver builtupon a novel non-linear entropy stable numerical flux function that supportseight travelling wave solutions. By construction the solver conserves mass,momentum, and energy and is entropy stable. The method is designed to treat thedivergence-free constraint on the magnetic field in a similar fashion to ahyperbolic divergence cleaning technique. The solver described herein isespecially well-suited for flows involving strong discontinuities. Furthermore,we present a new formulation to guarantee positivity of the pressure. Wepresent the underlying theory and implementation of the new solver into themulti-physics, multi-scale adaptive mesh refinement (AMR) simulation code$\texttt{FLASH}$ (http://flash.uchicago.edu). The accuracy, robustness andcomputational efficiency is demonstrated with a number of tests, includingcomparisons to available MHD implementations in $\texttt{FLASH}$.

A Novel High-Order, Entropy Stable, 3D AMR MHD Solver with Guaranteed Positive Pressure