Homogenized equations for isentropic gas in a pipe with periodically-varying cross-section
Abstract
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effective equations, which take the form of a constant-coefficient system of evolution equations, including dispersive higher-order derivative terms. We provide an approximate Riemann solver for the variable-cross-section isentropic gas equations, and compare numerical solutions of the original system with those of the homogenized system. We observe that the resulting solutions take the form of solitary waves, rather than shock waves, under fairly general conditions.
Fields of Study & Subjects
Integrated Energy Systems Optimization
Advanced Mathematical Modeling in Engineering
Advanced Thermodynamic Systems and Engines
Publication details
- Journal / source
- Communications in Mathematical Sciences
- Volume
- 24
- Issue
- 4
- Pages
- 1053–1071
- Publication date
- 1 January 2026
- Language
- EN