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The limiting behavior of the Riemann solution to the isentropic Euler system for logarithmic equation of state with a source term
Author(s) -
Sen Anupam,
Raja Sekhar T.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7254
Subject(s) - riemann problem , isentropic process , mathematics , riemann hypothesis , euler equations , euler system , logarithm , mathematical analysis , equation of state , semi implicit euler method , euler's formula , roe solver , riemann's differential equation , backward euler method , physics , riemann xi function , thermodynamics
We investigate the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equation of state with the Coulomb‐like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. Unlike the homogeneous case, the Riemann solution is no longer self‐similar. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero‐pressure gas dynamics system with a body force when the pressure vanishes.