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In this paper we describe an adaptive moving mesh technique and its application to the 2D Euler equations. The adaptive mesh is derived from the minimization of a mesh-energy integral. A robust and efficient monitor function with a time-dependent, automatically chosen, adaptivity parameter is used to track individual features of the physical solutions, such as shocks and emerging instabilities. The results of a series of numerical experiments are presented, including shock waves and a Rayleigh-Taylor instability.

Robust and efficient adaptive moving mesh solution of the 2-D Euler equations