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A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations

  • Yuanzhen Cheng
  • Alina Chertock
  • Michael Herty
  • Alexander KurganovEmail author
  • Tong Wu
Article
  • 24 Downloads

Abstract

We construct a new second-order moving-water equilibria preserving central-upwind scheme for the one-dimensional Saint-Venant system of shallow water equations. The idea is based on a reformulation of the source terms as integral in the flux function. Reconstruction of the flux variable yields then a third order equation that can be solved exactly. This procedure does not require any further modification of existing schemes. Several numerical tests are performed to verify the ability of the proposed scheme to accurately capture small perturbations of steady states.

Keywords

Shallow water equations Central-upwind scheme Well-balanced method Steady-state solutions (equilibria) Moving-water and still-water equilibria 

Mathematics Subject Classification

76M12 65M08 35L65 86-08 86A05 

Notes

Acknowledgements

The work of A. Chertock was supported in part by NSF Grants DMS-1521051 and DMS-1818684. The work of Y. Cheng was supported in part by NSF Grant DMS-1521009. The work of A. Kurganov was supported in part by NSFC Grant 11771201 and NSF Grant DMS-1521009. The work of M. Herty was supported in part by DFG HE5386/13-15, the cluster of excellence DFG EXC128 “Integrative Production Technology for High-Wage Countries” and the BMBF project KinOpt.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yuanzhen Cheng
    • 1
  • Alina Chertock
    • 2
  • Michael Herty
    • 3
  • Alexander Kurganov
    • 1
    • 4
    Email author
  • Tong Wu
    • 1
  1. 1.Mathematics DepartmentTulane UniversityNew OrleansUSA
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of MathematicsRWTH Aachen UniversityAachenGermany
  4. 4.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina

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