Numerical approximations of pressureless and isothermal gas dynamics

François Bouchut, Shi Jin, Xiantao Li

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

We study several schemes of first- or second-order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations. The pressureless gas system is weakly hyperbolic, giving rise to the formation of density concentrations known as delta-shocks. For the isothermal gas system, the infinite speed of expansion into vacuum leads to zero timestep in the Godunov method based on exact Riemann solver. The schemes we consider are able to bypass these difficulties. They are proved to satisfy positiveness of density and discrete entropy inequalities, to capture the delta-shocks, and to treat data with vacuum.

Original languageEnglish (US)
Pages (from-to)135-158
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number1
DOIs
StatePublished - Feb 1 2003

Fingerprint

Gas dynamics
Gas Dynamics
Numerical Approximation
Shock
Vacuum
Godunov Method
Riemann Solver
Entropy Inequality
Second-order Accuracy
Gases
Dynamic Equation
Entropy
Kinetics
First-order
Zero
Approximation
Gas

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Numerical approximations of pressureless and isothermal gas dynamics. / Bouchut, François; Jin, Shi; Li, Xiantao.

In: SIAM Journal on Numerical Analysis, Vol. 41, No. 1, 01.02.2003, p. 135-158.

Research output: Contribution to journalArticle

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