Conservative front tracking with improved accuracy

James Glimm; L. I. Xiaolin; Yingjie Liu; X. U. Zhiliang; Ning Zhao

doi:10.1137/S0036142901388627

Conservative front tracking with improved accuracy

James Glimm
, L. I. Xiaolin
, Yingjie Liu
, X. U. Zhiliang
, Ning Zhao

Applied Mathematics and Statistics

Stony Brook University

Stony Brook University
Nanjing University of Aeronautics and Astronautics

Research output: Contribution to journal › Article › peer-review

103 Scopus citations

Abstract

We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has script O sign(Δx) errors, improving over script O sign(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assertions are presented.

Original language	English
Pages (from-to)	1926-1947
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	41
Issue number	5
DOIs	https://doi.org/10.1137/S0036142901388627
State	Published - 2003

Keywords

Conservation
Contact discontinuity
Front tracking

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10.1137/S0036142901388627

Cite this

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title = "Conservative front tracking with improved accuracy",

abstract = "We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has script O sign(Δx) errors, improving over script O sign(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assertions are presented.",

keywords = "Conservation, Contact discontinuity, Front tracking",

author = "James Glimm and Xiaolin, \{L. I.\} and Yingjie Liu and Zhiliang, \{X. U.\} and Ning Zhao",

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language = "English",

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T1 - Conservative front tracking with improved accuracy

AU - Glimm, James

AU - Xiaolin, L. I.

AU - Liu, Yingjie

AU - Zhiliang, X. U.

AU - Zhao, Ning

PY - 2003

Y1 - 2003

N2 - We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has script O sign(Δx) errors, improving over script O sign(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assertions are presented.

AB - We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has script O sign(Δx) errors, improving over script O sign(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assertions are presented.

KW - Conservation

KW - Contact discontinuity

KW - Front tracking

UR - https://www.scopus.com/pages/publications/9244221603

U2 - 10.1137/S0036142901388627

DO - 10.1137/S0036142901388627

M3 - Article

SN - 0036-1429

VL - 41

SP - 1926

EP - 1947

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 5

ER -

Conservative front tracking with improved accuracy

Abstract

Keywords

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