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CAT-MOOD Methods for Conservation Laws in One Space Dimension

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Hyperbolic Problems: Theory, Numerics, Applications. Volume II (HYP 2022)

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 35))

Abstract

In this paper we blend high-order Compact Approximate Taylor (CAT) numerical methods with the a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of conservation laws. The resulting methods are highly accurate for smooth solutions, essentially non-oscillatory for discontinuous ones, and almost fail-safe positivity preserving. Some numerical results for scalar conservation laws and systems are presented to show the appropriate behavior of CAT-MOOD methods.

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Acknowledgements

This research has received funding from the European Union’s NextGenerationUE—Project: Centro Nazionale HPC, Big Data e Quantum Computing, ‘Spoke 1’ (No. CUP E63C22001000006). E. Macca was partially supported by GNCS No. CUP E53C22001930001 Research Project ‘Metodi numerici per problemi differenziali multiscala: schemi di alto ordine, ottimizzazione, controllo’. E. Macca and G. Russo are members of the INdAM Research group GNCS. The research of C. Parés has been partially supported by the grant PDC2022-133663-C21 funded by MCIN/AEI/10.13039/501100011033 and ‘European Union NextGenerationEU/PRTR” and the grant PID2022-137637NB-C21 funded by MCIN/AEI/10.13039/50110001103 and ‘ERDF A way of making Europe’.

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Authors and Affiliations

  1. University of Catania, Catania, Italy

    Emanuele Macca

  2. University of Bordeaux, CNRS, Bordeaux, France

    Raphaël Loubère

  3. University of Málaga, Malaga, Spain

    Carlos Parés

  4. University di Catania, Catania, Italy

    Giovanni Russo

Authors
  1. Raphaël Loubère
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  2. Emanuele Macca
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  3. Carlos Parés
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  4. Giovanni Russo
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Corresponding author

Correspondence to Emanuele Macca .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Estadística e I.O., Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

    Carlos Parés

  2. Departamento de Análisis Matemático, Estadística e I.O., Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

    Manuel J. Castro

  3. Departamento de Análisis Matemático, Estadística e I.O., Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

    Tomás Morales de Luna

  4. Departamento de Análisis Matemático, Estadística e I.O., Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

    María Luz Muñoz-Ruiz

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Loubère, R., Macca, E., Parés, C., Russo, G. (2024). CAT-MOOD Methods for Conservation Laws in One Space Dimension. In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-031-55264-9_15

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