Abstract
The Riemann problem for the two-dimensional steady pressureless isentropic flow in gas dynamics is solved completely. The Riemann solutions contain two kinds: delta-shock solutions and vacuum solutions. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta-shock solutions is established. Moreover, the stability of delta-shock solution to a reasonable viscous perturbation is proven. The numerical results coinciding with the theoretical solutions are also presented.
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Supported by NNSF of China under Grant 10961025 and NSF of Yunnan province under Grant 2007A020M.
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Cheng, H., Yang, H. Delta Shock Waves as Limits of Vanishing Viscosity for 2-D Steady Pressureless Isentropic Flow. Acta Appl Math 113, 323–348 (2011). https://doi.org/10.1007/s10440-010-9602-6
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DOI: https://doi.org/10.1007/s10440-010-9602-6
Keywords
- Steady pressureless isentropic flow
- Delta shock wave
- Generalized Rankine-Hugoniot relation
- Entropy condition
- Numerical simulations