Piston Problem in Common-Velocity Idealized Three-Component Models
- 1College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
- 2School of Mathematics and Systems Sciences, Liaocheng University, Liaocheng 252059, China
Abstract
This paper studies the common-velocity idealized three-component compressible model with pressure law P = ργ (0 < γ ≤ 1) and the constant-pressure model with P = 1. We systematically analyze the piston problem for these two models. When the piston velocity is lower than the initial fluid velocity, fluid blockage or severe blockage occurs, corresponding to a shock or delta shock wave solution. When the piston velocity exceeds the initial fluid velocity, the flow expands, corresponding to a rarefaction wave or vacuum solution. Furthermore, we prove that, as γ → 0+, the conservative variables (l,m,q,ρu) of the solutions to the piston problem for the compressible model converge in the sense of distributions to those for the constant-pressure model, and we present numerical simulations for finite values of γ.
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BibTeX
@article{li2026piston,
title = {{Piston Problem in Common-Velocity Idealized Three-Component Models}},
author = {Xiaoting Li and Lihui Guo and Huasheng Zhang},
journal = {Axioms},
year = {2026},
month = sep,
doi = {10.3390/axioms15100726},
url = {https://www.mdpi.com/2075-1680/15/10/726},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Piston Problem in Common-Velocity Idealized Three-Component Models
AU - Xiaoting Li
AU - Lihui Guo
AU - Huasheng Zhang
PY - 2026
DA - 2026/09/01
JO - Axioms
DO - 10.3390/axioms15100726
UR - https://www.mdpi.com/2075-1680/15/10/726
AB - This paper studies the common-velocity idealized three-component compressible model with pressure law P = ργ (0 < γ ≤ 1) and the constant-pressure model with P = 1. We systematically analyze the piston problem for these two models. When the piston velocity is lower than the initial fluid velocity, fluid blockage or severe blockage occurs, corresponding to a shock or delta shock wave solution. When the piston velocity exceeds the initial fluid velocity, the flow expands, corresponding to a rarefaction wave or vacuum solution. Furthermore, we prove that, as γ → 0+, the conservative variables (l,m,q,ρu) of the solutions to the piston problem for the compressible model converge in the sense of distributions to those for the constant-pressure model, and we present numerical simulations for finite values of γ.
SN - 2075-1680
ER -