Fast sweeping methods for hyperbolic systems of conservation laws at steady state II

Björn Engquist; Brittany D. Froese; Yen Hsi Richard Tsai

doi:10.1016/j.jcp.2015.01.028

Fast sweeping methods for hyperbolic systems of conservation laws at steady state II

Björn Engquist, Brittany D. Froese, Yen Hsi Richard Tsai

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

13 Scopus citations

Abstract

The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.

Original language	English (US)
Pages (from-to)	70-86
Number of pages	17
Journal	Journal of Computational Physics
Volume	286
DOIs	https://doi.org/10.1016/j.jcp.2015.01.028
State	Published - Apr 1 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Keywords

Conservation laws
Fast sweeping methods
Hyperbolic equations
Numerical analysis

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10.1016/j.jcp.2015.01.028

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title = "Fast sweeping methods for hyperbolic systems of conservation laws at steady state II",

abstract = "The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.",

keywords = "Conservation laws, Fast sweeping methods, Hyperbolic equations, Numerical analysis",

author = "Bj{\"o}rn Engquist and Froese, {Brittany D.} and Tsai, {Yen Hsi Richard}",

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doi = "10.1016/j.jcp.2015.01.028",

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AU - Engquist, Björn

AU - Froese, Brittany D.

AU - Tsai, Yen Hsi Richard

PY - 2015/4/1

Y1 - 2015/4/1

N2 - The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.

AB - The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.

KW - Conservation laws

KW - Fast sweeping methods

KW - Hyperbolic equations

KW - Numerical analysis

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VL - 286

SP - 70

EP - 86

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Fast sweeping methods for hyperbolic systems of conservation laws at steady state II

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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