A high-order ENO conservative Lagrangian type scheme for the compressible Euler equations. (English) Zbl 1126.76035

Summary: We develop a class of Lagrangian type schemes for solving Euler equations of compressible gas dynamics both in Cartesian and cylindrical coordinates. The schemes are based on high-order essentially non-oscillatory (ENO) reconstruction. They are conservative for density, momentum and total energy, can maintain formal high-order accuracy both in space and time, can achieve at least uniformly second-order accuracy with moving and distorted Lagrangian meshes, are essentially non-oscillatory, and have no parameters to be tuned for individual test cases. One- and two-dimensional numerical examples in Cartesian and cylindrical coordinates are presented to demonstrate the performance of the schemes in terms of accuracy, resolution for discontinuities, and non-oscillatory properties.


76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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