Characterization of the transonic stationary solutions of the hydrodynamic escape problem

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109174

Title:	Characterization of the transonic stationary solutions of the hydrodynamic escape problem
Authors:	洪盟凱;HONG, JOHN M.;YEN, CHIEN-CHANG;HUANG, BO-CHIH
Contributors:	理學院數學系
Keywords:	Adiabatic flow;Computational fluid dynamics;Conduction;Conduction heating;Conservation laws;Critical point;Fluid flow;Hydrodynamics;Level curves;Mathematical models;Nozzles;Sonics;Temperature effects;Transonic flow;Velocity;Velocity distribution;Viscosity
Date:	2014-01-01
Issue Date:	2026-04-23 16:12:06 (UTC+8)
Publisher:	Society for Industrial and Applied Mathematics Publications;Society for Industrial and Applied Mathematics
Abstract:	摘要： This paper presents the characterization of the transonic stationary solutions for the hydrodynamic escape problem (HEP), which is an important issue in the study of the evolution of planetary atmospheres. The transonic stationary solutions of the HEP involve effects of gravity, heat, and conduction, which are based in reality in this study and the sonic points are singular points in the time independent model. The characterization is established by the geometric singular perturbation method on the adiabatic wind solution of the HEP. The existence and nonexistence of the adiabatic wind solution with or without heat effect has been explored. The smooth transonic stationary solution under the effect of conduction is verified by analyzing the adiabatic wind solution. The singularity at the sonic points can be moved to the thermal critical points under the effect of conduction. By introducing the artificial viscosity, the dynamics at the thermal critical points and sonic points is studied in detail. Such a smooth transonic solution is proved to be a regular perturbation of the adiabatic wind solution. Discontinuous standing shock solutions are constructed and their stationary layer profiles have also been studied. Simulations of the adiabatic wind solution with or without heat and conduction effects are presented to illustrate the relevant theoretical results. 出版者： Society for Industrial and Applied Mathematics 出版日期： 2014-01-01 出處： SIAM journal on applied mathematics, 2014-01, Vol.74 (6), p.1709-1741 資源來源： JSTOR Arts and Sciences I 版權： Copyright ©2015 Society for Industrial and Applied Mathematics 識別號： ISSN: 0036-1399 識別號： EISSN: 1095-712X 識別號： DOI: 10.1137/130919957
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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