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Journal of Scientific Computing

, Volume 69, Issue 1, pp 274–291 | Cite as

Application of a Multi-dimensional Limiting Process to Central-Upwind Schemes for Solving Hyperbolic Systems of Conservation Laws

  • Seongju Do
  • Youngsoo Ha
  • M. Kang
  • Chang Ho Kim
Article

Abstract

In this paper, we study semi-discrete central-upwind difference schemes with a modified multi-dimensional limiting process (MLP) to solve two-dimensional hyperbolic systems of conservation laws. In general, high-order central difference schemes for conservation laws involve no Riemann solvers or characteristic decompositions but have a tendency to smear linear discontinuities. To overcome this drawback of central-upwind schemes, we use a MLP that uses multi-dimensional information for slope limitation to control the oscillations across discontinuities for multi-dimensional applications. Some numerical results are provided to demonstrate the performance of the proposed scheme.

Keywords

Central-upwind scheme MLP limiter Hyperbolic conservation laws Euler equations Finite difference method 

Mathematics Subject Classification

65M12 65M70 41A10 42C05 

Notes

Acknowledgments

Youngsoo Ha and Chang Ho Kim were supported by National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2014M1A7A1A03029872), also Youngsoo Ha was supported by the National Research Foundation of Korea (NRF) (NRF-2013R1A1A2013793). Myungjoo Kang was supported by NRF (2014R1A2A1A10050531, 2015R1A5A1009350) and MOTIE (10048720).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Seongju Do
    • 1
  • Youngsoo Ha
    • 1
  • M. Kang
    • 1
  • Chang Ho Kim
    • 2
  1. 1.Department of Mathematical SciencesSeoul National UniversitySeoulRepublic of Korea
  2. 2.Department of Computer Engineering, Glocal CampusKonkuk UniversityChungjuRepublic of Korea

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