MATHEMATIcAL MODELS IN AIR QUALITY PROBLEMS Jean Roux ...
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Transcript of MATHEMATIcAL MODELS IN AIR QUALITY PROBLEMS Jean Roux ...
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xi+ 1
2
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2
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H
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y
z
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North
East
South
West
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/ #(,x
FW
4,0/FE ! (- " ': " ,! #"%$& 4,0/(' ) ! 9#(,
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an+1ijk = an
ijk −∆t∆xi
(FE (An)− FW (An))− ∆t∆yj
(FN (An)− FS (An))− . . .
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(FH (An)− FL (An))
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t0 < t1 < . . . < tn < . . . < tN = t0 + T,¨ å ®ÒÏ©
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hn = tn+1 − tn ; h = max0≤n≤N−1
hn.¨ å ® Ê ©
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¨ å ®öÍy©k−1
k2M2 −→ P
¨ å ®ÒÑ©êRUÃU
k′sUÃUÃt«v UvPUfâv¥TPyUP
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dC1
dt= −(k1CX)C1 + (k−1CX)C2
dC2
dt= (k1CX)C1 − (k−1CX + k2)C2
¨ å ®ÒÕ©
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dt= P1 − L1C1,
êRUP1 = (k−1CX)C2
PL1 = k1CX .
¨ å ®ÒÛ©
9ÓßBê Fv§1¡3GFfPUU[vfF"U*FTPst«vvi
dCi
dt= Pi − LiCi;
¨ å ®Ë ©
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dCi
dt= Pi( ~C)− Li( ~C)Ci.
¨ å ®ËËB©
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d ~C(t)
dt= f(t, ~C(t)) = P (t, ~C(t))− L(t, ~C(t)) ~C(t),
¨ å ®ËBÏ©
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P (t, ~C(t))¾UP
L(t, ~C(t))
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yi+1 = F (yi+1) = (I + hiγL(ti+1, yi+1))−1(Yi + hiγP (ti+1, yi+1)),
¨ å ®Ë Ê ©
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Yi =
2∑
j=1
aij,2yi+1−j =
(c + 1)2yi − yi−1
(c2 + 2c),
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êRUc = ti−ti−1
ti+1−ti
Pγ = c+1
c+2
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yi+1
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yi+1
¨_Uf)ti+1
©'Ö¹tyi
¨_Fti©P^
yi−1
¨aGFti−1
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γ = 23
PYi = 4yi−yi−1
3ß7v¡Uc = 1®;×vtÖ¹tê?3
yi+1 = (I + hi
2
3L(ti+1, yi+1))
−1(4
3yi −
1
3yi−1 + hi
2
3P (ti+1, yi+1)),
¨ å ®ËBç©
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itfUv/:[URt¤*^v«7UFfP*f#«3PUPKFUfùv)PÂ+BêRyêpPt ¡nÜ
Fd,i = −ud,ici
¡nRPÖF+ê?v¥R[/Ù¤PvêRUci
fU+v^vvyUFUfPÖF^fpTPU«7vffÁUf*f¤v:
ud,i
fF^"^v«7UFfP¾f[vì¤P® ×fPvnì¤Áv:ÂP*)¤:Uvtfß7vFt¡Ì*UUf¥TP^vP3PÌP¤Z¨ vU¤ Óf 1 Ê Û ©ßy¤
ud,i =1
Ra + Rb,i + Rc,i.
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×'Pvtn^¤[3Ra = (cDv)−1 Pv¡fFÖ¹UôFUPÌ*v[)vvyRÖ¹)yF¡
cD¨¹U Ê Û ©pPF^êRU«7v
vFfBê?v¥hf¤v®
vUÌFh [ÓP^ÃP öÕ U§1¡3PU ëìfP3PÂUUf¥TP^vRb,i
fvPf¡ÙGFv"P
Rb,i =2
ku∗
(Sci
Pr
),
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êRUSci
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kU;PUP
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Rc,i
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Rc,iFtP'UÖ¹Utv¾U Û ®3+)UfnÖ¹UFítv
öÏPÍ ®
? HD @ @ A@ ! *PUt¡)F3GF'êRf 3fZ 1BêRs®×¦Â¢¨a¦;¡t«vP vyUUÖ¹¢"v¡ëÓPÌ ¾vF3tvtFF©hÓF¢í¢íçZ¨ Í ©ÓTJk¡tvíÖ¹k h÷¥¢¦ Ó¦®£¤UPUëùvP1FPs^Ff?Pv¡fFvUvÂêRUF+¡«yêRKF[ÂF ÂP9vp)UnPF^ª#ªÂ¢&)F^n¨_tvnvKFfP Ê ®ÒÏn® Ê ©pv«7v^fÌÃTP9t«vvv®÷ìÃUÓUtv¡^vvP«¡nFf^ÌíFf)P:ª#ªÂ¢ P ÂPð9vKF[Pt¡Uâ^¤¾Ö¹P tv¡^vvâUKÖ ìUfBê TP=U«7vfv®?yFUPt¤FFhtfùvP1FPêRf^v)«7vyUv:1v¥FP=êRffÂP?TvUvKF¤íÖ¹U F)KFUÌPef«¡n:ß¡^'Pv¡fF U^Ö¹tv)JPtß3PÙv®J×'vvtFP¥¤PUkPvtUfvP/tvUPf¡^UfPÖF)[vÂÖ¹?KFUÌP¤)P^«f¡^UfPtPÖDF/Uvy¨DF3fF^PtÖ¹PF¦Â¢Ý¨_P¢í¢íç©â h÷¥¢Ã¦ Ó¦ÌUT©i® #tFPPU ¡[Ü^Pt+Pv¡fFêRF"3ttÓU^vÓP««tyPT¾¨¹UUÌf3sÎ+n^¡B)Un3©K® #v¥FfvPpF¡^Uß¡vy) ÜnfÌíFP«fPv F"ßP¡3P¥¤yëìÙ¤Pv¤®4×Ö¹U¡ÙUf
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ÌUPfyFvt®;÷ì"T)n^vsf¡)s:^¡Unì¤K(z)
fRvPf¡ÙUvPØ
K(z) = kwsz(1−z
h)2,
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êRUwsfRtUf9UfÌPvßy¤UÙPtì¤*Ö¹t¡ÙP®
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ws =u∗
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,¨açn® å ©
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ws = (u3∗ + 2.8εw3
∗)1
3 ,¨açn®ÐçP©
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h):LhU£ß¡í9vÌPU¨¹U£ß¡í9vÌPUZfkJvPU¡^U
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R(z) = g(θ(z)− θ0)(z − z0)
θ(z)(V (z) + Vmin),
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êRUz0
f;F^ht¡Ì^vU?vÌy:Vmin = 0.1ms−1 f?)fJ[êRJt«vJPUÂÖ¹;U
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√u2(z) + v2(z)
fU*tfùyTPêR«t3ff
z¨u(z)P
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FU)PP
LPtÓtv«fPvßy¤*Uh)[ 3FU)
P = P +Ph +Pv
PL = P +Lh +Lv
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div(~V ~C)P^U Ê vn¤'^¡U
FUdiv(w ~C)®
Ph
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Ph
P^Lh PêPUê 1fÌfZÏ:7Ö¹PP
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an+1i,j = an
i,j −∆t
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∆yj
(FN (An)− FS (An)) .¨açn®öÛy©
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Surface Ozone [ug/m3] 08/08/2003 14hUT
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