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

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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.

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, 151-747, Seoul, Republic of Korea

    Seongju Do, Youngsoo Ha & M. Kang

  2. Department of Computer Engineering, Glocal Campus, Konkuk University, 380-701, Chungju, Republic of Korea

    Chang Ho Kim

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  1. Seongju Do
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  2. Youngsoo Ha
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  3. M. Kang
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  4. Chang Ho Kim
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Correspondence to Youngsoo Ha.

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Do, S., Ha, Y., Kang, M. et al. Application of a Multi-dimensional Limiting Process to Central-Upwind Schemes for Solving Hyperbolic Systems of Conservation Laws. J Sci Comput 69, 274–291 (2016). https://doi.org/10.1007/s10915-016-0193-x

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  • DOI: https://doi.org/10.1007/s10915-016-0193-x

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