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Notes on RKDG Methods for Shallow-Water Equations in Canal Networks

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Abstract

PDE models for network flows are used in a number of different applications, including modeling of water channel networks. While the theory and first-order numerics are well developed, high-order schemes are not well developed. We propose a Runge–Kutta discontinuous Galerkin method as an efficient, effective and compact numerical approach for numerical simulations of 1-D models for water flow in open canals. Our numerical tests show the advantages of RKDG over first-order schemes.

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Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    Maya Briani

  2. Rutgers University–Camden, 311 N. 5th Street, Camden, NJ, 08102, USA

    Benedetto Piccoli

  3. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    Jing-Mei Qiu

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  1. Maya Briani
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  2. Benedetto Piccoli
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  3. Jing-Mei Qiu
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Correspondence to Jing-Mei Qiu.

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Briani, M., Piccoli, B. & Qiu, JM. Notes on RKDG Methods for Shallow-Water Equations in Canal Networks. J Sci Comput 68, 1101–1123 (2016). https://doi.org/10.1007/s10915-016-0172-2

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  • DOI: https://doi.org/10.1007/s10915-016-0172-2

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