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

doi:10.1137/S1064827503427534

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 journal › Article › peer-review

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 language	English (US)
Pages (from-to)	666-697
Number of pages	32
Journal	SIAM Journal on Scientific Computing
Volume	26
Issue number	2
DOIs	https://doi.org/10.1137/S1064827503427534
State	Published - 2005
Externally published	Yes

Keywords

Composition law
Error model
Riemann problem
Uncertainty quantification

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1137/S1064827503427534

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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.",

keywords = "Composition law, Error model, Riemann problem, Uncertainty quantification",

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AU - Glimm, James

AU - Grove, John W.

AU - Kang, Yonghee

AU - Lee, Taewon

AU - Li, Xiaolin

AU - Sharp, David H.

AU - Yu, Yan

AU - Ye, Kenny

AU - Zhao, Ming

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Composition law

KW - Error model

KW - Riemann problem

KW - Uncertainty quantification

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

Abstract

Keywords

ASJC Scopus subject areas

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