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Semi-Lagrangian Particle Methods for Hyperbolic Equations

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Theory, Numerics and Applications of Hyperbolic Problems I (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 236))

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Abstract

Particle methods with remeshing of particles at each time step can be seen as forward semi-Lagrangian conservative methods for advection-dominated problems, and must be analyzed as such. In this article, we investigate the links between these methods and finite-difference methods and present convergence results as well as techniques to control their oscillations. We emphasize the role of the size of the time step and show that large time steps, only limited by the flow strain, can lead to significant gains in both computational cost and accuracy. Our analysis is illustrated by numerical simulations in level set methods and in fluid mechanics for compressible and incompressible flows.

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Author information

Authors and Affiliations

  1. University Grenoble Alpes and Institut Universitaire de France, Grenoble, France

    Georges-Henri Cottet

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  1. Georges-Henri Cottet
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Correspondence to Georges-Henri Cottet .

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Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Cottet, GH. (2018). Semi-Lagrangian Particle Methods for Hyperbolic Equations. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_31

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