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Splitting Methods in Communication, Imaging, Science, and Engineering pp 627–641Cite as

Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena

Part of the Scientific Computation book series (SCIENTCOMP)

Abstract

Operator splitting techniques were originally introduced with the main objective of saving computational costs. A multi-physics problem is thus split in subproblems of different nature with a significant reduction of the algorithmic complexity and computational requirements of the numerical solvers. Nevertheless, splitting errors are introduced in the numerical approximations due to the separate evolution of the split subproblems and can compromise a reliable simulation of the coupled dynamics. In this chapter we present a numerical technique to estimate such splitting errors on the fly and dynamically adapt the splitting time steps according to a user-defined accuracy tolerance. The method applies to the numerical solution of time-dependent stiff PDEs, illustrated here by propagating laminar flames investigated in combustion applications.

Mathematical Subject Classification (2010):

  • 65M22
  • 65G20
  • 65Z05
  • 35K55

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Fig. 19.1

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Author information

Authors and Affiliations

  1. Université Côte d’Azur, CNRS, Inria, LJAD, Paris, France

    Stéphane Descombes

  2. INRIA Sophia Antipolis-Mediterrané Research Center, Nachos Project-Team, 06902 Sophia Antipolis Cedex, Paris, France

    Stéphane Descombes

  3. CCSE, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd. MS 50A-1148, Berkeley, CA, 94720, USA

    Max Duarte

  4. CD-adapco, 200 Shepherds Bush Road, London, W6 7NL, UK

    Max Duarte

  5. CNRS UPR 288, Laboratoire EM2C, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, Paris, France

    Marc Massot

  6. CentraleSupélec, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, Paris, France

    Marc Massot

  7. Fédération de Mathématiques de l’École Centrale Paris, CNRS FR 3487, Grande Voiedes Vignes, 92295 Chatenay-Malabry Cedex, Paris, France

    Marc Massot

Authors
  1. Stéphane Descombes
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  2. Max Duarte
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  3. Marc Massot
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Editors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, Texas, USA

    Roland Glowinski

  2. Department of Mathematics, UCLA, Los Angeles, California, USA

    Stanley J. Osher

  3. Department of Mathematics, UCLA, Los Angeles, California, USA

    Wotao Yin

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Descombes, S., Duarte, M., Massot, M. (2016). Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena. In: Glowinski, R., Osher, S., Yin, W. (eds) Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-41589-5_19

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