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

Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton–Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information alon...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2013-12, Vol.255, p.316-338
Main Authors: Engquist, Björn, Froese, Brittany D., Tsai, Yen-Hsi Richard
Format: Article
Language:English
Subjects:
Computation
Conservation laws
Convergence
Fast sweeping methods
Hyperbolic equations
Mathematical analysis
Mathematical models
Numerical analysis
Steady state
Sweeping
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton–Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine–Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.08.036