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Adaptive Geometrical Multiscale Modeling for Hydrodynamic Problems

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • L. Mauri

    (Arianet s.r.l.)

  • S. Perotto

    (Politecnico di Milano, MOX, Dipartimento di Matematica “F. Brioschi”)

  • A. Veneziani

    (Emory University, Department of Mathematics and Computer Science)

Abstract

Hydrodynamic problems often feature geometrical configurations that allow a suitable dimensional model reduction. One-dimensional models may be sometimes accurate enough for describing a dynamic of interest. In other cases, localized relevant phenomena require more precise models. To improve the computational efficiency, geometrical multiscale models have been proposed, where reduced (1D) and complete (2D–3D) models are coupled in a unique numerical solver. In this paper we consider an adaptive geometrical multiscale modeling: the regions of the computational domain requiring more or less accurate models are automatically and dynamically selected via a heuristic criterion. To the best of our knowledge, this is a first example of automatic geometrical multiscale model reduction.

Suggested Citation

  • L. Mauri & S. Perotto & A. Veneziani, 2013. "Adaptive Geometrical Multiscale Modeling for Hydrodynamic Problems," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 723-730, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_76
    DOI: 10.1007/978-3-642-33134-3_76
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