Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

Abstract : The modelling of diffusive terms in particle methods is a delicate mat-ter and several models were proposed in the literature to take such terms into account. The Diffusion Velocity Method (DVM), originally designed for the dif-fusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier-Stokes equations, in their incompressible, velocity-vorticity formulation. The inte-gration of a Large Eddy Simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expres-sion of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.
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Computational and Applied Mathematics, Springer Verlag, 2016, 35 (2), pp.447-473. 〈10.1007/s40314-014-0200-5〉
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Paul Mycek, Grégory Pinon, Grégory Germain, Elie Rivoalen. Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations. Computational and Applied Mathematics, Springer Verlag, 2016, 35 (2), pp.447-473. 〈10.1007/s40314-014-0200-5〉. 〈hal-01087854〉

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