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SUMMARY:Diffuse interfaces modelling - Richard Saurel\, Aix-Marseille Univ
 ersity\, IUSTI - SMASH Group\, France
DTSTART:20101123T130000Z
DTEND:20101123T140000Z
UID:TALK27530@talks.cam.ac.uk
CONTACT:Louise Mortimer
DESCRIPTION:Diffuse interfaces are a consequence of numerical diffusion at
  contact discontinuities separating various materials. They appear with an
 y Eulerian hyperbolic solver and result in computational mixture cells. Th
 is has serious consequences on the thermodynamic state computation as the 
 equations of state of the fluids in contact are discontinuous. To circumve
 nt this difficulty artificial mixture cells were considered as true multip
 hase mixtures with stiff mechanical relaxation effects (Saurel and Abgrall
 \, 1999). This method was simplified by Kapila et al. (2001) with the help
  of asymptotic analysis\, resulting in a single velocity\, single pressure
  but multi-temperature flow model. This model present serious difficulties
  for its numerical resolution\, as one of the equations is non-conservativ
 e\, but is an excellent candidate to solve mixture cells as well as pure f
 luids.\n\nIn the presence of shocks\, jump conditions have to be provided.
  They have been determined in Saurel et al. (2007) in the weak shock limit
 . When compared against experiments for both weak and strong shocks\, exce
 llent agreement was observed. These relations are accepted as closure rela
 tions for the Kapila et al. (2001) model in the presence of shocks.\n\nMas
 s transfer modeling in this model was addressed in Saurel et al. (2008)\, 
 in the context of evaporation and flashing fronts. With the help of corres
 ponding heat and mass transfer terms\, it was possible to deal with high s
 peed cavitating flows.\n\nOppositely to the previous example of endothermi
 c phase transition\, when exothermic effects are considered as for example
  with high energetic materials\, detonation waves appear. With the help of
  the shock relations and governing equations inside the reaction zone\, ge
 neralized Chapman-Jouguet conditions are obtained as well as detonation wa
 ve structure of heterogenous explosives (Petitpas et al.\, 2009). \n\nWith
  the same multiphase flow model\, solved at each mesh point with the same 
 numerical scheme is it thus possible to deal with:\n\n-	material interface
 s dynamics\, eventually in the presence of surface tension (Perigaud and S
 aurel\, 2005) and hyper-elastic solids (Favrie et al.\, 2009)\,\n\n-	shock
 s and detonation waves in heterogeneous energetic materials\,\n\n-	phase t
 ransition fronts.\n\nMore recently\, dynamic powders compaction including 
 irreversible effects has been considered (Saurel et al.\, 2010) in the sam
 e theoretical frame. In addition\, gas permeation effects have been restor
 ed\, resulting in velocity drift effects in the Kapila et al. (2001) model
 . Slight velocity disequilibrium effects can thus be considered\, extendin
 g diffuse interface modeling capabilities to fluids mixing and extra physi
 cs.\n\nKapila A.\, Menikoff R.\, Bdzil J.\, Son S.\, Stewart D. (2001) Two
 -phase modeling of DDT in granular materials: reduced equations\, Physics 
 of Fluids\, 13\, pp. 3002-3024\n\nPerigaud G.\, Saurel R. (2005) A compres
 sible flow model with capillary effects\, Journal of Computational Physics
 \, 209\, pp. 139-178\n\nSaurel R. and Abgrall R. (1999) A multiphase Godun
 ov method for compressible multifluid and multiphase flows. Journal of Com
 putational Physics\, 150\, pp 425-467\n\nSaurel R.\, Petitpas F.\, Abgrall
  R. (2008)\, Modelling phase transition in metastable liquids. Application
  to cavitating and flashing flows\, Journal of Fluid Mechanics\, 607: 313-
 350\n\nFavrie N.\, Gavrilyuk S. and Saurel R. (2009) Solid-fluid diffuse i
 nterface model in cases of extreme deformations. Journal of Computational 
 Physics\, vol. 228\, Issue 16(1)\, pp 6037-6077\n\nPetitpas F.\, Saurel R.
 \, Franquet E. and Chinnayya A. (2009) Modelling detonation waves in conde
 nsed energetic materials: Multiphase CJ conditions and multidimensional co
 mputations. Shock Waves\, Vol. 19\, Number 5\, pp. 377-401\n\nSaurel R.\, 
 Petitpas F. and Berry R.A. (2009) Simple and efficient relaxation methods 
 for interfaces separating compressible fluids\, cavitating flows and shock
 s in multiphase mixtures. Journal of Computational Physics 228\, pp 1678-1
 712\n\nSaurel R.\, Favrie N.\, Petitpas F.\, Lallemand M.H. and Gavrilyuk 
 S. (2010) Modelling irreversible dynamic compaction of powders. Journal of
  Fluid Mechanics\, in press\n
LOCATION:Rutherford Seminar Room\, Cavendish Laboratory
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