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The asymptotic limits of Riemann solutions for the isentropic drift‐flux model of compressible two‐phase flows
Author(s) -
Shen Chun
Publication year - 2020
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.6146
Subject(s) - riemann problem , rarefaction (ecology) , discontinuity (linguistics) , shock wave , mathematics , compressibility , isentropic process , riemann hypothesis , mathematical analysis , classification of discontinuities , compressible flow , riemann solver , shock (circulatory) , momentum (technical analysis) , kinematic wave , equation of state , physics , mechanics , thermodynamics , ecology , finite volume method , biology , surface runoff , species diversity , medicine , finance , economics
The formation of vacuum state and delta shock wave are observed and studied in the limits of Riemann solutions for the one‐dimensional isentropic drift‐flux model of compressible two‐phase flows by letting the pressure in the mixture momentum equation tend to zero. It is shown that the Riemann solution containing two rarefaction waves and one contact discontinuity turns out to be the solution containing two contact discontinuities with the vacuum state between them in the limiting situation. By comparison, it is also proved rigorously in the sense of distributions that the Riemann solution containing two shock waves and one contact discontinuity converges to a delta shock wave solution under this vanishing pressure limit.