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CATEGORIES:Laboratory for Scientific Computing
SUMMARY:Diffuse interfaces modelling - Richard Saurel\, Ai
x-Marseille University\, IUSTI - SMASH Group\, Fra
nce
DTSTART;TZID=Europe/London:20101123T130000
DTEND;TZID=Europe/London:20101123T140000
UID:TALK27530AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/27530
DESCRIPTION:Diffuse interfaces are a consequence of numerical
diffusion at contact discontinuities separating va
rious materials. They appear with any Eulerian hyp
erbolic solver and result in computational mixture
cells. This has serious consequences on the therm
odynamic state computation as the equations of sta
te of the fluids in contact are discontinuous. To
circumvent this difficulty artificial mixture cell
s were considered as true multiphase mixtures with
stiff mechanical relaxation effects (Saurel and A
bgrall\, 1999). This method was simplified by Kapi
la et al. (2001) with the help of asymptotic analy
sis\, resulting in a single velocity\, single pres
sure but multi-temperature flow model. This model
present serious difficulties for its numerical res
olution\, as one of the equations is non-conservat
ive\, but is an excellent candidate to solve mixtu
re cells as well as pure fluids.\n\nIn the presenc
e 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 ex
periments for both weak and strong shocks\, excell
ent agreement was observed. These relations are ac
cepted as closure relations for the Kapila et al.
(2001) model in the presence of shocks.\n\nMass tr
ansfer modeling in this model was addressed in Sau
rel et al. (2008)\, in the context of evaporation
and flashing fronts. With the help of correspondin
g heat and mass transfer terms\, it was possible t
o deal with high speed cavitating flows.\n\nOpposi
tely to the previous example of endothermic phase
transition\, when exothermic effects are considere
d as for example with high energetic materials\, d
etonation waves appear. With the help of the shock
relations and governing equations inside the reac
tion zone\, generalized Chapman-Jouguet conditions
are obtained as well as detonation wave structure
of heterogenous explosives (Petitpas et al.\, 200
9). \n\nWith the same multiphase flow model\, solv
ed at each mesh point with the same numerical sche
me is it thus possible to deal with:\n\n- material
interfaces dynamics\, eventually in the presence
of surface tension (Perigaud and Saurel\, 2005) an
d hyper-elastic solids (Favrie et al.\, 2009)\,\n\
n- shocks and detonation waves in heterogeneous en
ergetic materials\,\n\n- phase transition fronts.\
n\nMore recently\, dynamic powders compaction incl
uding irreversible effects has been considered (Sa
urel et al.\, 2010) in the same theoretical frame.
In addition\, gas permeation effects have been re
stored\, resulting in velocity drift effects in th
e Kapila et al. (2001) model. Slight velocity dise
quilibrium effects can thus be considered\, extend
ing diffuse interface modeling capabilities to flu
ids mixing and extra physics.\n\nKapila A.\, Menik
off R.\, Bdzil J.\, Son S.\, Stewart D. (2001) Two
-phase modeling of DDT in granular materials: redu
ced equations\, Physics of Fluids\, 13\, pp. 3002-
3024\n\nPerigaud G.\, Saurel R. (2005) A compressi
ble flow model with capillary effects\, Journal of
Computational Physics\, 209\, pp. 139-178\n\nSaur
el R. and Abgrall R. (1999) A multiphase Godunov m
ethod for compressible multifluid and multiphase f
lows. Journal of Computational Physics\, 150\, pp
425-467\n\nSaurel R.\, Petitpas F.\, Abgrall R. (2
008)\, Modelling phase transition in metastable li
quids. Application to cavitating and flashing flow
s\, Journal of Fluid Mechanics\, 607: 313-350\n\nF
avrie N.\, Gavrilyuk S. and Saurel R. (2009) Solid
-fluid diffuse interface 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. (200
9) Modelling detonation waves in condensed energet
ic materials: Multiphase CJ conditions and multidi
mensional computations. Shock Waves\, Vol. 19\, Nu
mber 5\, pp. 377-401\n\nSaurel R.\, Petitpas F. an
d Berry R.A. (2009) Simple and efficient relaxatio
n methods for interfaces separating compressible f
luids\, cavitating flows and shocks in multiphase
mixtures. Journal of Computational Physics 228\, p
p 1678-1712\n\nSaurel R.\, Favrie N.\, Petitpas F.
\, Lallemand M.H. and Gavrilyuk S. (2010) Modellin
g irreversible dynamic compaction of powders. Jour
nal of Fluid Mechanics\, in press\n
LOCATION:Rutherford Seminar Room\, Cavendish Laboratory
CONTACT:Louise Mortimer
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