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Finding an Approximate Riemann Solver via Relaxation: Concept and Advantages

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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

We first explain the general concept of relaxation models using the **-**n model for scalar conservation laws. Then we consider the Suliciu model specifically for the homogeneous Euler equations. In a third step, using a two-speed relaxation model for the Euler equations with gravity as an example, we show how the construction of the relaxation system can endow the resulting method with useful properties. Finally, these properties are verified in numerical tests.

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Acknowledgements

We acknowledge the use of the Seven-League Hydro Code (https://slh-code.org) for our numerical experiments. The work of Claudius Birke and Christian Klingenberg is supported by the German Research Foundation (DFG) through the grant KL 566/22-1.

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Authors and Affiliations

  1. Julius -Maximilians -Universität Würzburg, Emil -Fischer -Straße 40, 97074, Würzburg, Germany

    Claudius Birke & Christian Klingenberg

Authors
  1. Claudius Birke
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  2. Christian Klingenberg
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Corresponding author

Correspondence to Christian Klingenberg .

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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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Birke, C., Klingenberg, C. (2024). Finding an Approximate Riemann Solver via Relaxation: Concept and Advantages. 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_2

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