Global Transonic Solutions of Planetary Atmospheres in Hydrodynamic Region $\mbox{--}$ Hydrodynamic Escape Problem due to Gravity and Heat

TL;DR

This paper proves the global existence of transonic solutions to the hydrodynamic escape problem in planetary atmospheres, using a novel generalized Glimm method with new Riemann solvers, ensuring physically consistent solutions.

Contribution

It introduces a new generalized Glimm method with innovative Riemann solvers for the hydrodynamic escape problem, establishing global transonic solutions with physical relevance.

Findings

Existence of global transonic solutions is proven.

A stable numerical scheme matching physical observations is developed.

The hydrodynamical region range is characterized.

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. The new version of Riemann and boundary-Riemann solvers, are provided as building blocks of the generalized Glimm method by inventing the contraction matrices for 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 hydrodynamical region is also obtained.