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A Method to Solve Hamilton–Jacobi Type Equation on Unstructured Meshes

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Abstract

A new method is developed to approximate a first-order Hamilton–Jacobi equation. The constant motion of an interface in the normal direction is of interest. The interface is captured with the help of a “Level-Set” function approximated through a finite-volume Godunov-type scheme. Contrarily to most computational approaches that consider smooth Level-Set functions, the present one considers sharp “Level-Set”, the numerical diffusion being controlled with the help of the Overbee limiter (Chiapolino et al. in J Comput Phys 340:389–417, 2017). The method requires gradient computation that is addressed through the least squares approximation. Multidimensional results on fixed unstructured meshes are provided and checked against analytical solutions. Geometrical properties such as interfacial area and volume computation are addressed as well. Results show excellent agreement with the exact solutions.

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All data related to the corresponding computational results are given in the manuscript.

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Acknowledgements

The authors are very grateful to Jeaniffer Vides for numerous helpful discussions that definitely helped to improve the quality of this work. This work has been partly funded by Eurenco that is gratefully acknowledged.

Funding

Part of this work has been funded by Eurenco that is gratefully acknowledged.

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Authors and Affiliations

  1. RS2N, Chemin de Gaumin, 83640, Saint-Zacharie, France

    Alexandre Chiapolino, François Fraysse & Richard Saurel

  2. CNRS, Centrale Marseille, LMA, Aix Marseille Univ, Marseille, France

    Richard Saurel

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  1. Alexandre Chiapolino
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Correspondence to Alexandre Chiapolino.

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Chiapolino, A., Fraysse, F. & Saurel, R. A Method to Solve Hamilton–Jacobi Type Equation on Unstructured Meshes. J Sci Comput 88, 7 (2021). https://doi.org/10.1007/s10915-021-01517-9

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  • DOI: https://doi.org/10.1007/s10915-021-01517-9

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