Statistical riemann problems and a composition law for errors in numerical solutions of shock physics problems

James Glimm, John W. Grove, Yonghee Kang, Taewon Lee, Xiaolin Li, David H. Sharp, Yan Yu, Kenny Ye, Ming Zhao

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We seek error models for shock physics simulations that are robust and understandable. The purpose of this paper is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. We illustrate this idea in a simple context. This paper employs several simplifying assumptions (restriction to one spatial dimension, use of a simplified (gamma law) equation of state, and consideration of a single numerical method). In separate papers we will address the effect of these assumptions.

Original languageEnglish (US)
Pages (from-to)666-697
Number of pages32
JournalSIAM Journal on Scientific Computing
Volume26
Issue number2
DOIs
StatePublished - Apr 15 2005
Externally publishedYes

    Fingerprint

Keywords

  • Composition law
  • Error model
  • Riemann problem
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this