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Communication Dans Un Congrès Année : 2016

Semi-Lagrangian particle methods for hyperbolic problems

Georges-Henri Cottet

Résumé

Particle methods are often associated with frequent remeshing to maintain the regularity of the particle distribution and the accuracy of the method. In that case particle methods can be seen as forward, conservative, semi-lagrangian methods. In the case of systems, pressure terms are separated from advection terms and semi-lagrangian particle methods are a particular case of flux splitting methods. For CFL numbers smaller than one, they can also be interpreted as finite-volume methods. In the linear case, the related finite-volume methods are rather classical (e.g. Lax-Wendroff or Beam-Warming schemes) but in the non-linear case one obtains less conventional methods, in particular with good entropy properties. On the other hand, the analogy with finite-volume methods allows to borrow from the finite-volume world several technics that can be translated into particle remeshing schemes. Among these technics, limiters allow to deriveTVD particle methods for which convergence can be proved, at least in the scalar case, whereas convergence for totally grid-free particles (e.g. the so-called SPH methods) remains an essentially open question. However, the main practical interest of particle methods lies in the possibility to use non-CFL constrained time-steps, a possibility which still remains largely unexplored for non-linear systems. In this talk I will address these questions. I will also discuss the derivation of high order methods for linear hyperbolic equations and their application for the Direct Numerical Simulation of turbulent transport.
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Dates et versions

hal-01353330 , version 1 (05-12-2016)

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  • HAL Id : hal-01353330 , version 1

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Georges-Henri Cottet. Semi-Lagrangian particle methods for hyperbolic problems. XVI International Conference on Hyperbolic Problems (HYP 2016), Aug 2016, Aix-la-Chapelle, Germany. pp.395-411. ⟨hal-01353330⟩
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