Global transonic solutions of planetary atmospheres in a hydrodynamic region-hydrodynamic escape problem due to gravity and heat

Bo Chih Huang, Shih Wei Chou, John M. Hong, Chien Chang Yen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The hydrodynamic escape problem (HEP), which is characterized by a free boundary value problem of Euler equation with gravity and heat, is crucial for investigating the evolution of planetary atmospheres. In this paper, the global existence of transonic solutions to the HEP is established using the generalized Glimm method. New versions of Riemann and boundary-Riemann solvers are provided as building blocks of the generalized Glimm method by applying the contraction matrices to the homogeneous Riemann (or boundary-Riemann) solutions. The extended Glimm{ Goodman wave interaction estimates are investigated for obtaining a stable scheme and positive gas velocity, which matches the physical observation. The limit of approximation solutions serves as an entropy solution of bounded variations. Moreover, the range of the feasible hydrodynamical region is also obtained.

Original languageEnglish
Pages (from-to)4268-4310
Number of pages43
JournalSIAM Journal on Mathematical Analysis
Volume48
Issue number6
DOIs
StatePublished - 2016

Keywords

  • Generalized Glimm scheme
  • Generalized Riemann and boundary-Riemann problems
  • Hydrodynamic escape problem
  • Hydrodynamic region
  • Nonlinear hyperbolic systems of balance laws

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