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Numerical Mathematics and Advanced Applications 2011 pp 209–217Cite as

Curvature Calculations for the Level-Set Method

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Abstract

The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set function where the derivative is discontinuous. Thus the standard discretization scheme is not suitable. Three discretization schemes are outlined that are shown to perform better than the standard discretization on two selected test cases.

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Acknowledgements

The authors acknowledge Bernhard Müller (Norwegian University of Science and Technology) and Svend Tollak Munkejord (SINTEF Energy Research) for valuable feedback on the manuscript.

This work was financed through the Enabling Low-Emission LNG Systems project, and the authors acknowledge the contributions of GDF SUEZ, Statoil and the Petromaks programme of the Research Council of Norway (193062/S60).

Author information

Authors and Affiliations

  1. Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes veg 2, NO-7491, Trondheim, Norway

    K. Y. Lervåg

  2. SINTEF Energy Research, Sem Sælands veg 11, NO-7465, Trondheim, Norway

    Å. Ervik

Authors
  1. K. Y. Lervåg
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  2. Å. Ervik
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Corresponding author

Correspondence to K. Y. Lervåg .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Leicester, Leicester, LE!1 7RH, United Kingdom

    Andrea Cangiani

  2. , Department of Mathematics, University of Leicester, Leicester, LE1 7RL, United Kingdom

    Ruslan L. Davidchack

  3. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Emmanuil Georgoulis

  4. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Alexander N. Gorban

  5. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Jeremy Levesley

  6. , School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

    Michael V. Tretyakov

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Lervåg, K.Y., Ervik, Å. (2013). Curvature Calculations for the Level-Set Method. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_23

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