Low Mach Number Flames

OMpuletir-aStocralSeplRitetiancgtiTnegchWnaivqeusesAfnodr

ApplicationtoLowMachNumberFlames
withComplexChemistry

S.Descombes
2
T.Dumont
1
,J.Beaulaurier
3
F.Laurent-Nègre
3
V.Louvet
1
M.Massot
3

1
CamilleJordanInstitute-ClaudeBernardLyon1University-France
2
J.DieudonnéLaboratory,Nice-SophiaAntipolisUniversity-France
3
EM2CLaboratory-EcoleCentraleParis-France

12thInternationalConferenceonNumericalCombustion

noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpS
4

Conclusion

3

LaminarPremixedCounter-Flowflamessimulations
Premixedcounter-flowflamesmodel
Applicationofsplittingmethod:chemicalcorrection
NumericalResults

2

Operatorsplittingandstiffness
Aimofsplittingmethods
Standardnumericalanalysisofoperatorsplitting
Stiffnesscomesintoplay

ContextandMotivation
ApplicationBackground
Numericalandcomputationaldifficulties
NumericalStrategies

1

Outline

noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpS
noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpS4

Conclusion

3

LaminarPremixedCounter-Flowflamessimulations
Premixedcounter-flowflamesmodel
Applicationofsplittingmethod:chemicalcorrection
NumericalResults

2

Operatorsplittingandstiffness
Aimofsplittingmethods
Standardnumericalanalysisofoperatorsplitting
Stiffnesscomesintoplay

ContextandMotivation
ApplicationBackground
Numericalandcomputationaldifficulties
NumericalStrategies

1

Outline

vlovniscimanyD)stnatullop,scimanyd,seitilibatsnI(noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLroChemical“waves”
(spiralwaves,scrollwaves,...)
,
exampleinmedicine

fFlames

s→,complexchemistry
→,→,

eApplicationBackground:Numericalsimulation
ofunsteadyreactivephenomena

uqinhceTgnittilpSsmelborpselacs-itlumecapsdnaemiTstneidarghgihhtiwnoituloS:snoitcaerdnaseicepsynamgni
smelborpstneidar:snoitcaerdnaseicepsynamgnivlovniscimanyD)stnatullop,scimanyd,seitilibatsnI(noisulcnInstationnarities(S.Ducruix,S.Candel,N.Tran,EM2C)

oFlames

CChemical“waves”
(spiralwaves,scrollwaves,...)
,
exampleinmedicine

s→,complexchemistry
,
→
Solutionwith
highg
,
→
Timeandspace
multi-scales

tApplicationBackground:Numericalsimulation
ofunsteadyreactivephenomena

luserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpS
tlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpSPotassiumionsduringstroke(T.Dumont,ICJ)

Chemical“waves”
(spiralwaves,scrollwaves,...)
,
exampleinmedicine

Flames

→,complexchemistry
,
→
Solutionwith
highg
,
→
Timeandspace
multi-scales

ApplicationBackground:Numericalsimulation
ofunsteadyreactivephenomena

smelborpstneidar:snoitcaerdnaseicepsynamgnivlovniscimanyD)stnatullop,scimanyd,seitilibatsnI(noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSsei
noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpSChemical“waves”
(spiralwaves,scrollwaves,...)
,
exampleinmedicine

Flames

→,complexchemistry
,
→
Solutionwith
highg
,
→
Timeandspace
multi-scales

ApplicationBackground:Numericalsimulation
ofunsteadyreactivephenomena

smelborpstneidar:snoitcaerdnaseicepsynamgnivlovniscimanyD)stnatullop,scimanyd,seitilibatsnI(
elacsegralaevlosotelbarevlosdetacidedrofdeeNnoisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnResolvingalargescalespectrum
→,spectrumandlargespatialgradientsonmulti-dimensional
configuration

iSpatialStiffness

tDifficulties
tobetreated:

tNumericalandcomputationaldifficulties

ilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpS
NhcaMwoLrofseuqinhceTgnittilpSnoitarugfinoclanoisnemid-itlumnostneidarglaitapsegralSpatialStiffness

dDifficulties
tobetreated:

nNumericalandcomputationaldifficulties

aResolvingalargescalespectrum

murtcepselacsegralaevlosotelbarevlosdetacidedrofdeeN→,noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmu
noisulcnoCstluserlaciremuNnoitcerroclacimehc:gnittilpSnoitasiledoMsnoitalumissemalFwolF-retnuoCdeximerPranimaLssenffitSsisylanadradnatSgnittilpsfomiAgnittilpSseigetartSseitlucfifiDlaciremuNdnuorgkcaBtxetnoCsemalFrebmuNhcaMwoLrofseuqinhceTgnittilpS→,spectrumandlargespatialgradientsonmulti-dimensional
configuration

PagodaFlame(D.Durox,S.Ducruix,S.Candel)

Resolvingalargescalespectrum

SpatialStiffness

Difficulties
tobetreated:

Numericalandcomputationaldifficulties

elacsegralaevlosotelbarevlosdetacidedrofdeeN