 The adiabatic exponential limits of Riemann solutions in the isentropic three-component modelYiheng Jiang and Chun Shen Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PB, 48-70 Abstract: The explicit construction of Riemann solutions is achieved for an ideally isentropic three-component model owning a unitary velocity and a collective pressure in one space dimension under the hypotheses without mass and heat transfer and also without viscosity. In addition, the asymptotic results of Riemann solutions are explored at length by sending the adiabatic exponent drop to one. On the one side, it reveals the concentration phenomenon, where the Riemann solution with a 1-shock, 2,3-contact and 4-shock waves converges to a delta shock solution. On the other side, it also exhibits the cavitation phenomenon, where all internal states in the 1-rarefaction and 4-rarefaction waves become vacuum ones by sending this limit. Finally, some representative numerical simulations are offered to observe the formation of delta shock wave and vacuum state in a more intuitive way as the adiabatic exponent tends to one, which is consistent with the theoretical analysis. Keywords: Riemann solution; Delta shock wave; Vacuum state; Three-phase flow; Hyperbolic conservation law (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pb:p:48-70 DOI: 10.1016/j.matcom.2025.10.002 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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