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Semi-implicit Level Set Method with Inflow-Based Gradient in a Polyhedron Mesh

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Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (FVCA 2017)

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Abstract

In this paper , a semi-implicit method is proposed to solve a propagation in a normal direction with a cell-centered finite volume method. An inflow-based gradient is used to discretize the magnitude of the gradient and it brings the second order upwind difference in an evenly spaced one dimensional domain. In three dimensional domain, we numerically verify that the proposed scheme is second order. The implementation is straightforwardly combined with a conventional finite volume code and 1-ring face neighborhood for parallel computation. An experimental order of convergence and a comparison of wall clock time between semi-implicit and explicit method are illustrated by numerical examples.

The original version of the book was revised: Missed out corrections have been updated. The erratum to the book is available at https://doi/org/10.1007/978-3-319-57394-6_58

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Acknowledgements

The work was supported by grants VEGA 1/0808/15, VEGA 1/0728/15, APVV-0522-15.

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Authors and Affiliations

  1. AVL LIST GmbH, Hans-List-Platz 1, 8020, Graz, Austria

    Jooyoung Hahn & Branislav Basara

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Radlinskeho 11, 810 05, Bratislava, Slovakia

    Karol Mikula & Peter Frolkovič

Authors
  1. Jooyoung Hahn
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  2. Karol Mikula
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  3. Peter Frolkovič
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  4. Branislav Basara
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Corresponding author

Correspondence to Jooyoung Hahn .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Hahn, J., Mikula, K., Frolkovič, P., Basara, B. (2017). Semi-implicit Level Set Method with Inflow-Based Gradient in a Polyhedron Mesh. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_9

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