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The Shifted Box Scheme for Scalar Transport Problems

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When solving certain scalar transport problems, it is important to use fast methods that do not produce any parasitic oscillating solutions, but still have good energy conservation properties. The well known box scheme has these properties, but the use is restricted by severe conditions on the sign of the coefficients. In order to avoid this restriction, we introduce a modified method, that we call the shifted box scheme. It is very efficient for initial-boundary value problems, since it does not require more work per time step than an explicit scheme, while still being unconditionally stable.

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Authors and Affiliations

  1. Division of Scientific Computing, Uppsala University, Box 337, SE-75105, Uppsala, Sweden

    Bertil Gustafsson

  2. Institute of Computational Mathematics in Engineering (ICME), Stanford University, California, USA

    Bertil Gustafsson

  3. Department of Mechanical Engineering, Stanford University, California, USA

    Yaser Khalighi

Authors
  1. Bertil Gustafsson
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  2. Yaser Khalighi
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Correspondence to Bertil Gustafsson.

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Dedicated to David Gottlieb on the occasion of his 60th anniversary.

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Gustafsson, B., Khalighi, Y. The Shifted Box Scheme for Scalar Transport Problems. J Sci Comput 28, 319–335 (2006). https://doi.org/10.1007/s10915-006-9079-7

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  • DOI: https://doi.org/10.1007/s10915-006-9079-7

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