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International Conference on Numerical Computations: Theory and Algorithms

NUMTA 2019: Numerical Computations: Theory and Algorithms pp 139–153Cite as

Numerical Simulation of Hyperbolic Conservation Laws Using High Resolution Schemes with the Indulgence of Fuzzy Logic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

Abstract

The aim of this paper is to solve numerically a class of problems on conservation laws, modelled by hyperbolic partial differential equations. In this paper, primary focus is over the idea of fuzzy logic-based operators for the simulation of problems related to hyperbolic conservation laws. Present approach considers a novel computational procedure which relies on using some operators from fuzzy logic to reconstruct several higher-order numerical methods known as the flux-limited methods. Further optimization of the flux limiters is discussed. The approach ensures better convergence of the approximation and preserves the basic properties of the solution of the problem under consideration. The new limiters are further applied to several real-life problems like the advection problem to demonstrate that the optimized schemes ensure better results. Simulation results are included wherever required.

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Acknowledgement

RL thanks the Delhi Technological University for the partial financial support to attend NUMTA 2019 and UGC for PhD fellowship.

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Authors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    Ruchika Lochab & Vivek Kumar

Authors
  1. Ruchika Lochab
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  2. Vivek Kumar
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Corresponding author

Correspondence to Vivek Kumar .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Lochab, R., Kumar, V. (2020). Numerical Simulation of Hyperbolic Conservation Laws Using High Resolution Schemes with the Indulgence of Fuzzy Logic. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_11

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40615-8

  • Online ISBN: 978-3-030-40616-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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