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An ALE Formulation for Explicit Runge-Kutta Residual Distribution

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

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Abstract

We consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation of the Runge-Kutta RD schemes of Ricchiuto and Abgrall (J.Comput.Phys 229, 2010). Up to the authors knowledge, the problem of recasting RD schemes into ALE framework has been solved with first order explicit schemes and with second order implicit schemes. Our resulting scheme is explicit and second order accurate when computing discontinuous solutions.

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Author information

Authors and Affiliations

  1. Institut für Mathematik Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Remi Abgrall

  2. Politecnico di Milano, via La Masa 34, 20156, Milano, Italy

    Luca Arpaia

  3. INRIA Université Bordeaux I, 200 Rue Vieille Tour, 33405, Talence, France

    Mario Ricchiuto

Authors
  1. Remi Abgrall
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  2. Luca Arpaia
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  3. Mario Ricchiuto
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Corresponding author

Correspondence to Luca Arpaia .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Abgrall, R., Arpaia, L., Ricchiuto, M. (2014). An ALE Formulation for Explicit Runge-Kutta Residual Distribution. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_4

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