Quelques modèles diffusifs capillaires de type KortewegSome diffusive capillary models of Korteweg type. |
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Authors: | Didier Bresch Benoît Desjardins |
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Affiliation: | 1. LMC-IMAG UMR5223, 51, rue des mathématiques, B.P. 53, 38041 Grenoble, France;2. CEA/DIF, B.P. 12, 91680 Bruyères le Châtel, France;3. DMA E.N.S. Ulm, 45, rue d''Ulm, 75230 Paris cedex 05, France |
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Abstract: | The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004). |
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Keywords: | Mécanique des fluides numérique Modèles d'interface diffuse Modèles de type Korteweg Estimations d'énergie Modèles compressibles Computational fluid mechanics Diffuse interface models Korteweg models Energy estimates Compressible flows |
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