Time-periodic transonic shock solution in divergent nozzles

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Zhang, Xiaomin, Qu, Peng, Yu, Huimin
Formato: Preprint
Publicado: 2025
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866912205189939200
author Zhang, Xiaomin
Qu, Peng
Yu, Huimin
author_facet Zhang, Xiaomin
Qu, Peng
Yu, Huimin
contents We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this paper, we describe the gas by a quasi-one-dimensional compressible Euler equations with temporal periodic boundary conditions and prove the global existence and dynamical stability of the time-periodic transonic shock solution with an iteration method. The major difficulty is to determine the position of the moving shock front, which can be obtained by a free boundary problem in the subsonic domain. We decouple this free boundary problem by the $Rankine-Hugoniot$ conditions and a two-step iteration process.
format Preprint
id arxiv_https___arxiv_org_abs_2501_15212
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Time-periodic transonic shock solution in divergent nozzles
Zhang, Xiaomin
Qu, Peng
Yu, Huimin
Analysis of PDEs
We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this paper, we describe the gas by a quasi-one-dimensional compressible Euler equations with temporal periodic boundary conditions and prove the global existence and dynamical stability of the time-periodic transonic shock solution with an iteration method. The major difficulty is to determine the position of the moving shock front, which can be obtained by a free boundary problem in the subsonic domain. We decouple this free boundary problem by the $Rankine-Hugoniot$ conditions and a two-step iteration process.
title Time-periodic transonic shock solution in divergent nozzles
topic Analysis of PDEs
url https://arxiv.org/abs/2501.15212