Xây dựng mô hình mô phỏng dòng chảy và truyền chất hai chiều, ứng dụng cho vùng vịnh Hạ Long

DAI HOC
QUOC GIA
HA
NQI
Trudng
Dai hoc Khoa hoc
Tir
nhien
XkY
DUNG
MO HINH
MO PHONG
DONG
CHAY
VA TRUYEN
CHAT HAI
CHKU,
VTNG DUNG
CHO YUNG
VINH
HA LONG
MQ
SO:
QT.06.34
Chu Iri 3S
kcii:
TS Phung
Dang
Hie'u
CQC
thcinh vien

thorn
gio:
ThS
Phqm
Hodng Lam
CN
Trdn Dvcc Trvt
OAI
HOC QUOC GIA HA
NO:
TRUNG
T.Ar/
THONG
TIN THU '"^^
DT /
64^
HA
NOI
- 2005
BAO CAO TOM TAT
D£
TAI
1.
Ten de
tai:
Xay
dung m6 hinh mo phdng ddng chay va
truydn
chat hai
chieu,

Ihig
dung cho
viing
vinh Ha Long
2.
Ma
sd:
QT.06.34
3.
Chu
tri
de tai: TS
Phiing
Dang Hieu
4.
Cac can bo
tham
gia:
1) ThS Pham Hoang
Lam
2) CN Trdn
Dixc
Trur
5. Muc tieu va not dung nghien
curu:
1) Muc tieu:
- Xay dung dugc mo hinh so m6 phdng ddng chay va truyen chat dang hai
chidu
sir
dung

h6
phuong trinh
nude
nong phi tuyen va phuong trinh
truydn
tai khuech tan.
-
LSig
dung
tinh
loan
thir
nghiem cho
viing
vinh Ha Long.
2) Npi dung:
a)
xay
dung mo hinh so mo phong ddng chay va
truydn
chat hai chieu
- Nghien
cihi
thuat toan thich hop sai phan giai he phuong trinh nude nong hai
chi6u.
Lap
chuong trinh may tinh.
- Nghien cuu thuat toan thich hop sai phan giai he phuong trinh truyen chat. Lap
chuong trinh may tinh.
- Tinh toan va kiem nghiem mo hinh so theo cac

di6u
kien
ly
thuyet va thuc te.
b)
Ung
dung mo hinh tinh toan
thir
nghiem cho
viing
vinh Ha Long
- Thu thap va so hoa trudng dp sau
viing
vinh Ha Long; thu thap cac sd lieu
v6
thuy trieu va gid
viing
bien ven bd Quang Ninh.
- ung dung mo hinh tinh toan
thir
nghiem cho viing vinh Ha Long theo cac kich
ban.
- Phan
tich
ket qua, danh gia mo hinh va viet bao cao long ket, nop san pham,
nghiem thu.
6. Cac ket qua dat dugc:
1) Da
utig
dung phuong phap

CIP
(Constraint Interpolation Profile) hien dai cd dp
chinh
xac bac ba va phat
trie'n
mot phuong phap sai phan
an
vao viec sai phan hoa giai
11
h6
phuong
trinh nude ndng
phi
tuy^n
cho bai toan ddng chay. Viet thanh cong chuong
trinh
may
tinh
m6 phdng ddng chay sinh ra do gid va do thuy
trilu.
Tinh toan thu
nghidm
va
ki^m chung md hinh
cho cac dieu kien
ly
thuyet cd nghiem giai tich va
kilm chiing
trong trudng hop dieu kien thuc te
ciia

bai toan
truydn
trieu Bien Dong.
K^t
qua cho
tha^y
phuong phap CIP
sir
dung d day cho bai toan mo phdng ddng chay la
r^t
hop ly va cd d6 chinh xac kha cao. Mo hinh
chiing
to kha nang ung dung tot cho
cac
viing bi^n
nong ven bd.
2) Da
xay
dung thanh cong chuong trinh
truyin
tai va khuech tan vat cha't su
dung phuong phap
th^
tich huu han vdi so do TVD (Total Variation Diminishing) cd
dp chinh xac bac hai. Viet thanh cong chuong trinh may tinh va kiem
chung
mo hinh
cho cac bai toan ly thuyet cd nghiem giai
tich.
Ket qua cho thay phuong phap TVD

siJ
dung d day cd dp chinh xac cao hon nhieu so vdi mot sd phuong phap sai phan truyen
thdng hay dugc
sir
dung nhu UPWIND bac mot hay Lax-Wendrof. Mo hinh cho phep
md
phdng qua
trinh truydn
tai khuech tan vat cha't dudi tac dpng cua ddng chay trung
binh.
3) Da thu thap va sd hoa dia hinh viing vinh Ha Long tren
ludi
vuong gdc trong
toa dp
D6
Cac vdi budc ludi 250 m
x
250 m. Thu thap va phan tich nhung sd lieu
v6
tdc dp gid va hudng gid viing ven bd Quang Ninh, sd lieu
thiiy
tridu.
LSig
dung mo
hinh m6 phdng he thdng ddng chay gay ra do gid trung binh
mija
Dong va
miia
He va
do tac dpng

ciaa
thuy trieu trong cac chu ky
trilu len
va xudng
Idn.
Mo phdng
Ian
truyen vat cha't dugc thuc hien tren
n6n
ddng chay long hop ca gid va thuy
tri^u
vdi gia
thiet chat chi thi
bin
vung khong phan huy va cd
sir
cd mo trudng thai ra tai mot sd
di^m
gia dinh. Cac ket qua cho ra cac
bu'c
tranh phan bd trudng ddng chay va phan bd
nong dp cha't 6
nhilm
khi cd tac dpng
ciia
cac yeu td dpng
lire
la gid va thuy trieu.
4) Ndi chung md hinh xay dung trong
di

tai da dap
ihig
dugc yeu cau
v6
mo
phdng ddng chay va truyen chat vdi dp chinh xac dang tin cay va cd kha nang urng
dung de nghien
cihi
cho cac viing bien ven bd khac. Ket qua ung dung
tinh
toan cho
viing vinh Ha Long, Quang Ninh cho thay ro kha nang ung dung
ciia
md hinh da phat
trien.
5) Dang dugc mot bai bao tren tap
chi
khoa hpc Dai hoc Qudc Gia.
7.
Tinh hinh
kinh
phi
cua de tai
Tdng
kinh phi dugc cap: 20.000.000 ddng
Da nhan: 20.000.000 ddng
Da thanh toan: 20.000.000 dong
111
XAC
NHAN

CUA BAN CHU
NHlfiM
KHOA
CHU TRI
D£
TAX
(^>^>t^-^^
PGS. TS Pham Van
Hudn
TS Phung Ddng Hieu
XAC NHAN CUA
TRU^ONG
OHO
HIEU
TRUONU
GS.TS.^^rfin/
^/^/^
IV
ABSTRACT
1.
Project title: Development of a numerical 2-D model based on the shallow
water equation and convection-diffusion equation for the application to the Halong Bay
2.
Code number: QT.06.34
3.
Project Leader: Dr. Phung Dang Hieu
4-
Members: 1) M. Sc. Pham Hoang Lam
2) B.Sc. Tran
Due

Tru
5. Aims and contents of project:
1) Aims:
- Development of a numerical 2-D model based on the shallow water equation
and convection-diffusion equation.
- Application of the model to the study of tide-induced currents and wind-
induced currents, the transportation of tracer in the Halong Bay.
2) Contents:
a) Development of a numerical 2-D model
- Development and application of a finite difference scheme for solving the
shallow water equation. Development of a computer program.
- Development and application of a finite volume TVD scheme for solving the
conveetion-diffution equation. Development of
a
computer program.
- Verification of the numerical model with some analytical and practical
conditions.
b) Application of the model to the study of tide-induced currents and wind-
induced currents, the transportation of tracer in the Halong Bay
- Collection and digitization of the bathymetry of Halong Bay; Collection of wind
and tidal data in the near-shore area of Quang Ninh.
- Application of the model to the simulation of tide-induced, wind-induced
currents in the Halong Bay. Simulation of the propagation and distribution of pollution
(tracer) based on some scenarios.
- Analysing and assessing the simulated results in order to give conclusions and
writing the final report.
6. Results:
1) The CIP (Constraint Interpolation Profile) method and a implicit finite
difference scheme have been applied to the developement of a numerical model based
on the shallow water equation. A numerical computer program has been successfully

developped for the simulation of wind and tide induced currents. Computation has been
carried out using the numerical model for the caseses of analiytical and practical
problems. Computed results show that the application of CIP method for the simulation
of shallow water currents is fairly accurate. The numerical model can be applied to the
near-shore shalow seas.
2) A numerical model based on the convection-diffusion equation using the TVD
(Total Variation Diminishing) scheme has been successfully developed. A computer
program has developed. Some numerical tests with analytical conditions show that the
TVD method used here is more accurate than the conventional methods such as
Upwind first order or Lax-Wendrof. The numerical model is capable of simulation of
the advection and diffusion processes of suspended materials under the driven action of
the depth averaged currents.
3) Collection and digitization of the bathymetry in the Halong have been done for
an orthogonal mesh with the same mesh size in x and y direction 250 m. The wind and
tidal data in the near shore area of Quang Ninh also were collected. Then, the
numerical model was applied to the simulation of wind induced currents resulted by
the averaged wind in the sommer and winter; and by the tide. Simulation of
propagation and distribution of suspended materials initiated at some locations under
the depth averaged currents induced separately by wind and tide, and by both wind and
tide was also carried out. Simulated resuhs showed resonable pictures of the water
current and pollution concentration distribution.
4) In general, the numerical model developed in this study meets the requirement
on the simulation of depth averaged currents and pollution propogation with an
acceptable accuracy and the model can be applied to other areas of shallow sea.
5) Results of the study were published as an article on the Journal of Science,
VNU.
VI
MUC LUC
Mdd^u
2

Chuong 1. Md hinh md phdng ddng chay hai
chilu
4
1.1
H6
phuong trinh ca ban va cac
di6u
kien bien 4
1.2 Phuong phap sai phan theo so
dd
CIP cho he phuong trinh
nude
nong 5
1.3 Kiem
chung
md hinh sd'theo cac bai toan ly thuyet va thuc te 10
1.4
Nhan
xet 16
Chuong 2. Mo hinh mo phdng
truydn
chat hai
chi6u
17
2.1 He phuong trinh
coban vacac didu
kien bien 17
2.2 He phuong trinh dudi dang rdi rac
sir
dung phuong phap TVD 17

2.3 Kiem chung mo hinh sd theo cac bai toan ly thuyet 18
Chuong 3: Ung dung md hinh cho vung vinh Ha Long 26
3.1 Gidi thieu viing nghien
cuxi
26
3.2
Sdlieu sijrdung
trong nghien cuu 35
3.3 Ket qua mo phdng 35
Ket
luan
va kien nghi 51
Tai lieu tham khao 53
Phuluc
54
Tom tat cac cong trinh NCKH cua ca nhan (Miu 1) 55
Scientific Project
(Mlu
2) 56
Phieu dang ky ket qua nghien cuu KH-CN 57
MODAU
O
nhidm
moi trudng bien hien dang la va'n
dl
dugc quan tarn ciia
hSu
het cac
qudc gia cd bien tren the gidi. Vdi nhu
c^u

phat trien kinh te hudng vao tiem nang
ciia
bi^n
da ngay cang gia tang ap
lire v6 6 nhilm
moi trudng bien ndi chung va d
nhilm
mdi
trudng vung ven bien ndi rieng. Chinh vi
le
dd, viec phat trien kinh te
ciia
mdt
viing ludn
dugc ddi hoi dat trong bdi canh phat
tri^n
ben vung. Trong dd viec danh gia
tac ddng
ciia
boat dpng kinh te dan sinh
d6'n
thay doi moi trudng ddi hoi phai dugc
thuc
hidn
mdt each nghiem
tiic
de cd
nhirng chien
luge phat trien cung nhu qui hoach
phat trien dudi

sir
quan ly tdng
th^
sao cho
vira
dap ung dugc nhu cau phat trien tat yeu
cua kinh te xa hoi, vira dam bao giam thieu dugc tac hai cho moi trudng
tir
nhien vd'n
cd.
Hiu
het cac qudc gia phat trien va dang phat trien cd bien (nhu: My, Nhat ban,
Anh, Ha
Ian,
Mexico, Trung Qudc,
v.v.)
d6u
da va dang thuc hien cac
dir
an khao sat,
danh gia va du bao bien dpng moi trudng
nham
dua ra cac canh bao, cac thong tin trp
giiip
cho he thdng ra chinh sach,
phue
vu cho qui hoach phat trien kinh te cua cac viing
bi^n
va ven bien quan trong (Peterlin va nnk, 2005
[10];

Lozano va nnk, 2005 [7]; Lau,
2005 [8]). Trong dd viec md phdng va danh gia muc dp
Ian
truyen chat d
nhi6m
trong
mot viing nude cu the la mot trong nhung mat xich quan trpng trong cac chuong trinh
quan ly tich hgp phuc vu cho viec xir dung hop ly tai nguyen va phat trien ben
vimg
d
h^u
het cac qudc gia tren the gidi trong dd c6 Viet Nam.
Cac cong cu md phdng thuy dpng
lire
va
Ian truydn
vat cha't noi chung va cac chat
d
nhilm
ndi rieng (COD, BOD, TSS, ) da va dang dupe rat nhieu trung tam nghien
cull cd uy
tin
tren the gidi phat trien va cho ra cac san
phfa
thuong mai cd gia tri cao
dap ung dugc cac nhu cau ung dung trong quan ly va
sir
dung hgp
ly
ngudn

nude
cung
nhu trg
giiip
cho qui hoach phat trien kinh te. Cac san pham cong cu phan mem dai
dien nhu SMS
(ciia
My), MINLAKE (cua My), MIKE 21 (cua Dan mach). Dd la
nhung cong cu hiru ich de ting dung tren thuc te.
0
nude
ta cac chuyen gia ve mo hinh hoa va md phong loan hpc tren may tinh
cac qua trinh thuy dpng
lire
hpc va
Ian
truyen cac cha't d
nhidm
da va dang dan tiep can
dugc
nhimg
thanh tuu khoa hpc hien dai tien tien tren the gidi. He phuong trinh
nude
nong phi tuyen hai
chi6u
da dugc
nhi^u
tac giai sir dung de md phdng bai toan ddng
chay hai
chi^u

trung binh theo dp sau nhu bai toan thuy trieu, bai toan ddng chay do
gio.
Tuy nhien cac tac gia chu yeu don gian hoa he phuong trinh thanh dang tuyen
tinh
hoa nhu
Nguyln
Ngpc Thuy (1969), Dang Cong Minh (1975) [1, 2] hoac giai phuong
trinh
nude
nong
d^y
dii
nhung vdi cac so dd toan don gian nhu UPWIND bac 1 hoac
sai phan trung tam cd dp chinh xac khong cao. Ddi vdi bai toan truyen tai vat chat thi
va'n
dt
con khd hon la vdi cac so dd toan don gian thi viec ton tai cac nghiem sd khong
that
(thi
du nghiem am, hoac
nhiiu
sd) la va'n de thudng gap. Do vay viec phat trien
mdt md
hinh
md phdng ddng chay va
chuydn
cha't hai
chi6u
dang tin
cay

cho
viing
ven
bd la
v^n
di cin thiet phuc vu cho nghien cuu
ciing
nhu qui hoach moi trudng trong
cac viing
nude
ven bd.
Muc tieu
ciia
dd tai la phat trien va ung dung thanh cong cac so dd sd tien tien cd
dd chinh xac cao vao
xay
dung mo hinh sd md phdng dugc ddng chay va truyen chat
hai
chi^u
trong viing ven bd dudi tac dpng ciia gid va thuy
tridu.
Sau dd ung dung tinh
toan thii nghiem cho viing vinh Ha Long.
Ngoai
phSn
md
ddu,
ket luan va kien nghi, tai
li6u
tham khao, npi dung bao cao

cua
d^
tai dugc trinh bay trong ba chuong:
Chuong 1 : Md hinh ddng chay hai
chidu.
Trong chuong nay trinh bay co sd ly
thuyet, he phuong trinh
xua^t
phat, cac dieu kien bien
ciia
md hinh md phdng ddng chay
hai
chi6u
cd tinh den anh hudng
ciia
gid. Trinh bay tdm
luge
phuong phap sai phan cd
dd chinh xac cao CIP (Constrained Interpolation Profile); phuong phap sai phan an
dang SMAC va
each
ung dung rdi rac hoa giai he phuong trinh
nude
nong phi tuyen.
Cac bai toan kiem nghiem md hinh dudi dang ly thuyet va thuc
tiln
cung
dupe
trinh
bay

nham
khang dinh tinh on dinh, dung dan cua md hinh so.
Chuong 2 : Md hinh
truyin
cha't hai
chidu.
Trong chuong nay trinh bay he
phuong trinh md ta qua trinh
truyen
tai va khuech tan vat chat hai chieu dudi tac dpng
cua ddng chay nen. Md ta cac
dilu
kien bien. Trinh bay phuong phap sai phan dang
TVD cd dp chinh xac bac hai va
ling
dung rdi rac hoa giai he phuong trinh xuat phat.
Md
hinh
sd dugc kiem chung thdng qua cac bai toan co ban cd nghiem giai tich nham
kiem nghiem kha nang mo phdng qua trinh
truydn
tai vat chat
ciia
md hinh.
Chuong 3: Ung dung md hinh cho viing vinh Ha Long. Chuong nay trinh bay tom
lupe
viing nghien cun,
di6u
kien gid, thuy treu, dia hinh.
Lira

chpn cac sd lieu dau vao
de md phdng. Cac ket qua mo phdng
Ian truyen
vat chat gia dinh khong bi phan huy
theo thdi gian theo cac kich ban dudi tac dpng
ciia
gid va thuy trieu. Cac nhan xet
v6
ket qua nghien cun.
De tai nay dupe hoan thanh vdi
sir
hd trp kinh
phi
tir
phia
Dai hpc Qudc gia
(DHQG) Ha Ndi,
sir giiip
do
ciia
Ban Khoa hpc & Cong nghe, DHQG, Phong Khoa
hpc Cdng nghe, trudng Dai hpc Khoa hpc
Tir
nhien,
sir
ung ho nhiet tinh
ciia
Hoi ddng
Khoa hpc Trai da't, DHQG HN,
ciia

Ban chu nhiem khoa
Khi
tugng Thuy van va Hai
duong hpc, cung nhu su ddng gop y kien
eiia
cac nha khoa hpc, cac ddng nghiep tham
gia di tai va tap the can bd cua Bp mdn Hai duong hpc. Nhan day
chiing
tdi xin chan
thanh cam on nhimg giiip do qui bau dd.
CHUONG 1:
MO HINH MO PHONG DONG CHAY HAI
CHltv
LI
H£
PHUONG TRINH CO BAN VA CAC
Difiu
KI$N
BifiN
He phuong trinh xuat phat
diroc sir
dung trong phat trien md hinh la he phuong
trinh
nude
ndng phi tuyen, bao gom :
Phuong trinh bao toan dpng
lugng
du
du du
-

dC
—
+
u—
+
v
fv =
-S^A-
dt dx
dy
dx p{h
+ 0
dv dv dv
^ dC
1
—
+ u
—
+ v
—
+
fu
= -2
-^-
+
dt dx
dy
dy
p{h
+

0
Phuong trinh bao toan khdi
lupng
dC
,
d(h
+ Ou , d(h + Ov ^
k'rlh^^^
dt
trong dd
dx
dx
•'
dx
(
du^
I
dx.
dy
d
+
—
dy
1
dy
(
du]
(
dv]
'J,

—
(LI)
(1.2)
(1.3)
(1.4)
(1.5)
w,v:
cac thanh phan van tdc trung binh dp sau theo cac hudng ox
va.
oy\
f:
tham sd
Coriolis;
(^
:
dao dpng muc nude; p
:
mat dp
nude;
h :
dp
sau
nude;
u^:
he sd nhdt rdi.
T^Ty
la cac thanh phan ung suat gio tren mat theo
true
x va true
y,

chung
dupe
xac
dinh theo cdng thuc sau:
T:
=P^C,^\W\W/, T].=P^C\W\W^,^
(1.6)
trong dd
p^
la mat dp khong
khi;
w la vector van tdc gid. He sd
C,
dugc xac dinh
theo Smith & Banke (1975) nhu sau :
C.
(0.63 +
0.066|W^|)xlO^
|fF|<20m/5
\w\>2t)mls
(2.28+
0.033(1^^^1-20))
X
10"
Cac thanh phan ung suat ma sat day
dupe
xac dinh theo cdng thuc sau:
CLU^JU
+ V
h

r^
I 2
2
Tj
= p
Cf,vyju
+
v^
(1.7)
He sd ma sat
Q
dugc xac dinh theo cdng thuc
C,
(h
+
cy
Ai^
0.0264
H6
phuong trinh tren cho phep md phdng ddng chay cd chu ky dai trong viing
nude
ndng bao gom ca ddng chay phat sinh do
thiiy triSu
va do gid.
Cac
diiu
kien bien dugc sir dung trong md hinh nhu sau:
Bi6n
cung: sir dung dieu kien khong tha'm,
ture

la thanh phan van tdc theo phuong
phap tuyen vdi mat
bi6n
bi triet tieu.
Bidn
long: dieu kien bien phat xa
tir
do cho sdng dai dugc
sir
dung. Khi dd gia tri
van tdc
thang
gdc vdi bien dugc xac dinh theo cdng thirc
a-^
(1.8)
Bi6n
Idng
cho dao done thuy trieu: dao dpng muc nude dugc tinh theo cac hang
sd dieu hoa cho tren bien.
1.2
PHUONG PHAP
SAI
PHAN THEO SO DO
CIP
CHO
H£
PHUONG TRINH
NU6C
NONG
Va'n

d6
kha quan trpng trong viec giai sd he phuong trinh nude ndng phi tuyen la
xa'p xi dugc tot thanh phan binh
luu
phi tuyen. Thuc te giai sd cho thay neu xap xi cac
thanh
ph^n
phi tuyen nay bang cac so do sai phan trung tam cd dp chinh xac bac hai thi
thudng dan den cac
nhilu
gia trong ket qua gia sd trong trudng hgp tdn tai cac gradient
Idn ciia
muc
nude
hay ddng chay. De khac phuc va'n
d^
nay mot trong nhung phep sai
phan thudng dupe sir dung do la phuong phap upwind bac mot hay so dd Quick bac ba
ket hop vdi so do nhdt nhan tao.
Gan day mot sd phuong phap sai phan mdi ket hgp giira hai phuong phap
Lagrangian va
Euler
cd dp chinh xac cao da dupe nhdm tac gia Yabe va Aoki (1991)
[11] cong bd cd ten la CIP (Constrained Interpolation Profile). Phuong phap nay da
dugc chiing minh la co dp chinh xac bac ba va xap
xi
rat tot cho cac thanh phan truyen
tai phi tuyen. Thi du ve mot sd nghien cun
sir
dung phuong phap CIP da xuat ban nhu

nghien
cihi
tuong tac sdng va cong trinh ngam (Hieu va Tanimoto, 2006) [9] hay
nghien ciin thuy trieu Quang Ninh (Hieu, 2006)
[3].
Trong nghien cun nay, phuong
phap CIP dugc sir dung de xap xi thanh phan binh luu phi tuyen trong phuong trinh
chuyen dpng cua he phuong trinh
nude
nong.
Dudi day trinh bay tdm tat tu tudng va npi dung
ciia
phuong phap CIP (chi tiet
xem Yabe va Aoki, 1991)
[11].
1.2.1 Tdm
tdt
phuong phap CIP
Tren thuc te hau het cae qua trinh vat ly thudng
diln
ra trong mdi trudng lien tue
nhung giai sd cac qua trinh dd ta phai thuc hien rdi rac hda
mi6n
tinh toan. Muc tieu co
ban
CLia
thuat giai sd la khdi phuc nhung thong tin bi mat (hay bi bd qua) giira cac
diem rdi rac dd. Da sd cac so do sd trudc day
d6u
khong quan tam den nghiem thuc

phan bd ben trong
6
ludi va do dd
mii'c
dp chi tiet quan tam la d
miJc
kich thudc
ludi
chia
(Ax,Ay).
Phuong phap CIP do Yabe va Aoki (1991)
[11]
trinh bay da cd gang di
xay
dung phan bd
nghidm
trong d ludi sao cho
g^n
dung nhat vdi phan bd nghiem thuc
cua phuong trinh md ta vdi mot sd phep ap dat cu the. De
di6n
ta phuong phap CIP ta
xet mdt phuong
trinh truydn
tai dang sau :
dt dx
(1.9)
Khi van tdc u la hang sd thi phuong trinh (1.9) md ta chuyen ddng tinh tien don
gian ciia trudng / vdi tdc dp u
.

Dang phan bd ban dau (xem dudng
liin
net tren hinh
1.1 a) di chuyen thanh dudng
dut
net trong trudng hgp bieu
diln
lien tuc (xem hinh
1.1a).
Tai thdi diem nay nghiem tai cac diem ludi dugc ky hieu la cae
cham
trdn va nd
gidng nhu nghiem dung tai cac
di^m
dd. Tuy nhi6n neu ta
loai
bd dudng durt net nhu
tr6n
hinh Lib
thi thdng tin ve hinh dang (profile)
ciia
nghiem ben trong d ludi bi mat
va raft khd tudng tugng ra dung profile nghiem, khi dd mot each rat tu nhien ta cd the
tudng tugng ra dang profile
ciia nghifm
nhu dudng lien net tren hinh
Lie.
Nhu the
khuech tan sd cd the phat sinh khi ta xay dung dang profile cua nghiem bang phep ndi
suy tuyen tinh mac

dii
ta da dua tren cac nghiem
diing
tai cac diem ludi (hinh
Lie).
Qua trinh ndi suy nay dugc thuc hien trong so dd Upwind (ngugc ddng) bac 1. Mat
khac neu ta xap
xi
npi suy bang ham bac hai thi se gap phai ket qua
la
cac gia tri ndi
suy vugt qua gia tri that, qua trinh npi suy nay dupe thuc hien trong cac so dd Lax-
Wendroff hay trong so do Leith.
uAt
gradient
Hinh
1.1: Nguyen ly cua
phucmg
phap CIP. (a) duong
li^n
net la duong ban
dau,
duong dut net
la
nghiem
dung sau
budc thcfi
gian
At;
(b) nghiem tai tung

die'm rdi
rac; (c) khi noi suy tuyen
tinh,
xuat
hifin
khuech tan so; (d) so do CIP: dao ham khong gian cung di
chuydn
va profile
ciia
nghiem
trong o ludi
dugc
khoi phuc.
Dieu gi da lam nghiem kem chinh xac di? Dd la do ta da bd qua co che phan bd
nghiem phia trong d ludi va ta da di theo cac nghiem tron. Do dd ta thay phuong phap
dua dang phan bd nghiem thuc vao trong
6
ludi la rat quan trpng. Phuong phap CIP da
dua ra
each
xap xi phan bd nghiem thuc trong 6 ludi nhu sau :
Trudc
h6't l£y
dao ham phuong trinh (1.9) theo bien x ta thu dugc :
^
+ 3 =
-^^
(1.10)
dt dx dx
Trong dd g

=
df
Idx
la dao ham khong gian
ciia
/. Trong trudng hgp don gian
nh^t
u
=
const
thi
phuong trinh (1.10) gidng nhu (1.9) la md ta
chuye'n
ddng cua dao
ham khdng gian theo van tdc
u.
Bang each
siir
dung phuong trinh nay ta cd the duoi
theo cac tien trien thdi gian cua / va
g
dua tren phuong trinh co sd
(1.9).
Neu g tinh
dupe va di chuyen nhu trinh bay bang mui ten tren hinh
Lid,
thi ta de dang sir dung
cac dao ham g nay de hinh dung ra phan bd nghiem va dudng profile se gan dung vdi
dudng ban
d^u

(nghiem
diing)
hon rat
nhidu
Neu ca hai gia tri
ciia
/ va g
dupe
cho trudc tai hai diem ludi thi dang profile
cua nghiem cd the dupe npi suy bang mdt da thuc bac ba (Nakamura va nnk, 2001):
F:{x)
=
a,X'+b,X'+g:X
+
f;
(1.11)
trong dd
g:+g:,
2{f:-f:^)
+
''' ""'
(1.12)
Ax' Ax,'
3(/;-r) 2g:+g:^)
Ax.'
Ax,
(1.13)
^.
=^,up-X,
iup =

/-sgn(w,)
X
=
x-x,
sgn(w)
la ham lay da'u
ciia w
. x la tpa dp
phia
ngupc ddng cua diem xet sau budc
thdi gian
A/.
Nhu vay profile tai budc thdi gian
(« +
l)
d^
dang thu dugc bang
each
dich chuyen profile di mot doan
w^A/
(tuong tu nhu phuong phap Lagrangian) vi the
/"*'
=F"{x,
-u,At)
va
g;^'
=dF"{x,
-w,A/)/^.
Do dd ta cd :
fr'=ci,^!^b,^'+g:^,+f:

(LI4)
gr'=3a,^,^+2Z),^,+g;
(1.15)
Trong dd
<f,
=-u^At.
Nhu the phuong phap CIP sir dung phap tinh tien Lagrangian tren
ndn
ludi Euler
va do dd nd thupc vao dang phuong phap Semi-Lagrangian.
Thirc
te tinh toan sir dung
phuong phap CIP da cho thay vdi phuong phap CIP hien cd the sir dung vdi sd Courant
- Friedrichs - Lewy (CFL) kha
Idn
ma so d6 van rat on dinh.
1.2.1 Ung dung phuong phap CIP cho he phuong trinh
nude
ndng
Vdi he phuong trinh nude ndng ta co the bieu
di6n
tong quat dudi dang nhu sau:
7
^^u^^^^^G
(1.16)
dt dx dy
trong dd G bao
gdm
cac sd hang cdn
lai

ciia phuong trinh chuyen ddng (gradient muc
nude,
ung
su^ft
gid, ung sua't day,
lire
Coriolis,
lire
nhdt).
Sir dung thuat toan tach ta tim nghiem
ciia
phuong trinh (1.16) theo hai budc
(Yabe va
Aoki, 1991):
Budc A: Pha truyen tai (Advection phase)
df df df
^ .,.
-^ +
u^^
+
v^^
= 0
(1.17)
dt dx dy
Budc B: Pha khdng
truy6n
tai (Non-Advection phase)
^ = G
(1.18)
dt

Sau khi budc A dupe giai cho pha
truyen
tai thi budc B dugc
tinh
toan cho pha
khong
truydn
tai dua tren cac gia tri vira
tinh
tir budc A. Trong budc A ta sir dung
nghidm
giai tich
dja
phuong
ciia
phuong trinh (1.17) dudi dang Lagrangian:
f{x,,y,J + At) = f{x^,^y^„J)
(1.19)
vdi
x^„
=x,
+^,
y^„
=y,
+;;,
^ =
-w,A/,
rj = -v,At
Nhu
the phuong trinh (1.19) cd the thu dupe bieu

thurc
hien theo cdng
thure
(1.14)
va bang each diing so do CIP nay
luan
chuyen cho timg hudng ox va oy cho bai toan
hai
chidu.
Sau khi tim dugc
f"*^'
= f{x,,y ,t+
At) a budc 1 thi gia tri
ciia /
tai budc thdi
gian n
+1
that bao ham ca cac ddng gdp
ciia
cac yeu td khdng thupc pha
truyen
tai se
dugc giai theo phuong trinh
(1.18)
la:
/r'
=fr''
+GAt
(1.20)
Ddi vdi ham gradient g

ciia
/
(tii'c
la
— =
g^,—
=
g ) cung duoc thuc hien
dx
dy
tuong tu nhu ham / nhung sir dung cong thuc CIP phuong trinh (1.15).
Trong nghien cuu nay de tang tinh on dinh
eiia
bai toan trong budc giai phuong
trinh (1.19) va phuong trinh lien tuc da sir dung phep sai phan an
nhu
sau:
Trudc het ta
lira
chpn vi tri cac bien dat tren he ludi so le: cac bien
w,
v dugc dat
tai cae canh
ciia
d ludi
chu*
nhat con bien
^ dupe
xac dinh tai tam
ciia

d ludi (nhu so dd
Akagawa-C). Phuong trinh (1.1) va (1.2) dugc viet lai dudi dang don gian nhu sau:
^ =
-F(u,v,h, )-g^
(1.21)
dt dx
— =
-G(M,v,/i, )-g^
dt dy
(1.22)
trong dd ham F va G
chu:a
dung cac thanh
ph^n
cdn lai trong phuong trinh (1.1) va
(L2).
Ta sir dung phep sai phan tuong tu nhu phuong phap SMAC (Simplified Marker
and Cell Method) cho phuong trinh (1.21) va (1.22). Ddi vdi budc thdi gian cho trudc
n trudng
van
tdc du doan cho budc thdi gian tiep theo
dupe
xac dinh hien thdng qua
cac phuong trinh ddng lupng gpi la budc 1
,("+!)•
w"
A-At
g
.("-^D*
-,,"

=
v"
+
Ar
dC
dx
dt;"
dy
F{u,v,h, )
-G(M.V,/?, )
(1.23)
(1.24)
Chi sd dau sao d tren cho biet trudng van tdc du doan ban dau (predicted velocity)
d budc thdi gian
«
+1.
Trudng van tdc du doan nay sai lech so vdi trudng van tdc thuc
do cd
sir
thay ddi
ciia
dao dpng muc nude
A^
d thdi diem mdi, do dd van tdc d thdi
di^m n +1
dupe xac dinh tir trudng van tdc du doan ban
di\x\
„< •,,,,
_^^j
V

=
V
(n+D*
+
A^
dAC
dy )
va
r^'=r+A<-
(1.25)
(1.26)
(1.27)
Tir phuong trinh bao toan khdi lugng thay neu nhan cac ve cua phuong trinh
(1.25),
(1.26) vdi dai lugng
{hA-Q
va lay dao ham tuong ung theo x va theo y roi
cdng lai ta thu dugc phuong trinh Poisson cho gia sd
At^
nhu sau:
dt
r^^in.vr
H dv
(-1)-/^N
dx dy
^gAt^l-in'-^
^
^dx\
dx
oy

d( ^dAC
oy
(1.28)
trong
dd H
= {h +
(;")
Neu
la'y
xap xi sai phan cho dao ham thdi gian
eiia ^
va sir dung phuong trinh
(1.27) ta thu dugc phuong trinh sau:
At
^
\dx\
dx
d_
dy
H
dA£_
dy
cu H
c^-'"^"'//'
dx dy
(1.29)
Sai phan hoa phuong trinh (1.29) cho cac dao ham khdng gian tren ludi so le vdi
^n
la dp tang muc
nude AC

ta thu dugc mot he phuong trinh dai sd tuyen tinh vdi ma
tran ddi xiing cd he sd tren dudng cheo chinh xac dinh duong. He phuong trinh dai sd
tuyen tinh nay cd the giai lap bang phuong phap SOR hay CG rat hieu qua. Trong
nghiSn
cun nay da sir dung phuong phap BiCGSTAB (Bi-Conjugate Gradient
ciia
van
derVort(1992).
Vdi phep sai phan nhu tren, ta cd the tdm luge qui trinh tim nghiem nhu sau:
Budc 1: tinh toan trudng van tdc du doan ban dau sir dung phuong trinh (8) va (9).
Trong dd cac thanh
ph^n
binh luu phi tuyen, nhdt, coriolis va ma sat dupe xac dinh
theo cac so dd tuy chon, d day da sir dung phuong phap xap xi CIP cua Yabe va Aoki
(1991) [3].
Budc 2: giai he phuong trinh dai sd tuyen tinh cho
A^
tir phuong trinh (1.29) vdi
cac gia
tri
H
va
w'"^"',
v*"^"*
da biet tir budc 1.
Budc 3: cac gia tri
w"*',
v"^'
va
4'"*'

d budc thdi gian can tim dupe xac dinh tir
phuong trinh (1.25), (1.26) va (1.27).
Budc 4: gan cac gia tri budc thdi gian
n +1
cho budc n rdi tiep tuc qui trinh cho
cac budc thdi gian tiep theo.
1.3
KI^M
CHUNG
M6
HINH SO THEO
BAI
TOAN
LV
THUYET VA
THlTC TE
Tr6n thuc te tinh toan
nhi6u
khi gap nhung trudng hgp tdn tai cac gradient muc
nude
Idn,
thi du nhu cac front
nude
tran len cac viing dat thap
(nude
dang d cac bai
tri^u,
sdng nude dang do bao
v.v.),
do dd viec kiem tra xem kha nang mo phdng cua

mo hinh toan mo ta d tren cd sir dung phuong phap CIP ddi vdi cac trudng hpp cd
gradient
Idn ciia
muc
nude
la rat can thiet. De thuc hien dieu nay bai toan sdng vo dap
dupe sir dung lam dieu kien kiem tra
thu*
nhat.
Muc tieu
ciia
md hinh la mo phong ddng chay trong viing ven bd do dd viec kiem
tra kha nang md phdng sdng dai
ciia
mo hinh cung la van di dugc dat ra. Yeu cau quan
trpng
ciia
md hinh sd la phai md ta
dupe
tuong tac phi tuyen
ciia
sdng dai va hon nira
phai bao toan nang lupng
ciia
cac sdng dai nay d
miic
dp chap nhan
dupe.
De thuc hien
kiem nghiem cho muc tieu dat ra thi bai toan sdng truyen trong kenh thing kin mot

d£u,
trong kenh gia thiet khdng co ma sat, khong cd
lire
coriolis, sdng dung hoan toan
dugc gia thiet va sir dung lam bai toan kiem tra
thii
hai.
Bai toan thu: ba diing de kiem nghiem kha nang md phdng thiiy trieu vdi dieu kien
thuc te
ciia
Bien Ddng.
Tinh
toan dugc thuc hien cho truyen trieu tren Bien Dong va
ket qua dugc so sanh vdi sd lieu muc nude thuc do d mot sd tram hai van ven bien.
1.3.1 Kiem chung vdi bai toan vd dap
Trudc tien, md hinh sd dupe kiem nghiem qua viec mo phdng sd bai toan vo
dap.
Day la mot trong nhung bai toan kinh dien diing de kiem tra cac mo hinh sd rat
hun hieu. Bai toan dupe gia thiet la co hai viing nude d thdi diem ban dau cd dp cao cot
nude la
/?,
d phia trai va
K dphia
phai
(h^>h._).
TiJc
thi, vach ngan giira hai viing nude
dupe rut bd, do tac dung
eiia lire
trpng trudng

nude tir phia
trai tran sang
phi'a
phai. Bai
toan nay cd nghiem giai tich cho
sir
bien dang va di chuyen
ciia
cot
nude.
Viec md
10
phdng qua trinh nay la kha khd ddi vdi md hinh nude ndng khi sir dung phuong phap
sai phan
hiiu
han do ton tai gradient
Idn
tai diem ngan
each
hai viing nude.
Di
kiim
tra so dd toan trong md hinh sd d day da sir dung
viing
nude chu nhat cd
dd dai 1000 m, dp cao
h^
=3m d phia trai va
/z2=lm
d phia phai, hai viing nude cd dp

rdng bang nhau la 500m (xem hinh 1.2). Ket qua md phdng sd va nghiem giai
tich
cho
thdi
di^m
50 giay sau khi dap ngan giira hai viing
nude
bi vo, dugc trinh bay tren hinh
2.
Hinh
2 cho tha'y cac nghiem sd sir dung cac so do khac nhau cho cac ket qua rat
khac nhau va khac vdi nghiem giai
tich,
trong dd nghiem sd cua phuong phap sai phan
in
six
dung trong nghien cun nay ket hgp vdi so do CIP (xem hinh 1.3) cho ket qua
gdn
triing
vdi phan bd cua nghiem giai tich. Hon
nira
cae
nhidu
gia do so dd sd khdng xuat
hien tai cac diem front cua cot
nude.
Diiu nay cho ta mdt co sd tin cap de tin tudng vao
su
6n
dinh va kha nang ung dung

ciia
md hinh cho cac bai toan thuc te.
£3
c
E
o
Q
100 200
300
400 500 600
Khoang each
ngang (m)
700 800
900
1000
Hinh 1.2: Phan
bo'cot nU6c
tai
thdi
diem ban dau.
c
E
o
s
O
1
Nghiem giai
tich
Nghiem so (Linear)
Nghiem so (Upwind)

Nghiem so (CIP)
100 200 300 400 500 600
Khoang
each
ngang (m)
700 800 900 1000
Hinh 1.3: So sanh ket qua mo phong so'va nghiem giai
tich
trUdng
hop bai toan vd dap sau khoang
thoi
gian 50
giay.
11
1.3.2 Kiem
chumg
vdi trudng hgp sdng dai dumg trong kenh thang
Do bai toan thuy trieu la mdt bai toan md phdng
Ian truydn
sdng dai nen nhat
thi^^t
phai
ki^m nghi6m
md hinh toan ddi vdi trudng hgp sdng dung. Day la mot trong
nhirng bai toan kiem nghiem don gian nhung lai ra't
hihi
hieu trong viec kiem tra tinh
bao toan nang lugng
eiia
so do sd. Bai toan dat ra la khi cd mot sdng dai truyen vao

mot kenh thang cd dp sau khdng doi, kin mot dau. Gia thiet phan xa hoan toan va
khdng cd tac dung
ciia luc
coriolis thi do ket hgp
ciia
sdng tdi va sdng phan xa, trudng
sdng dung se
xu£t
hien trong kenh vdi cac diem nut va diem bung phan bd theo qui
luat.
Neu suy giam sd cua md hinh sd la nhd thi tai cac diem bung ta phai thu dupe cac
dao ddng cd
bidn
dd it nha't la ga'p hai
Ian
bien dp
eiia
sdng tdi. Tai cac diem nut cd cac
dao ddng nhd. Neu tinh phi
tuyd'n
dupe md phdng tot thi cac dao ddng tai diem nut
khdng bi triet tieu ma se xuat hien song thir ca'p cd
t^n
sd ga'p hai \in
t^n
sd
ciia
song
tdi.
Vdi bai toan kiem tra

thur
hai nay, kenh din dugc chpn cd dp dai /=1000 m, dp
rdng b =50m, dp sau
h
=10m, sdng tdi cd chu ky
r=30s,
bien dp A =20cm. Viing kenh
dugc chia thanh cac ludi hinh chir nhat 2,5m x 2,5m. Bien tai cudi kenh dugc chpn la
bien khdng tha'm (phan xa toan
phdn).
Thdi gian tich phan dupe chpn la 250s du de
sdng truyen het hai
Ian
chieu dai kenh. Cac ket qua md phdng dao dpng muc nude tai
cac
di^m
bung va diem nut (each nhau xen ke bang mot phan tu dp dai sdng
L x
T^fgh
dupe trinh bay tren cac hinh 1.4 va hinh 1.5.
- Dao dpng tai bien
Dao dong tai diem bung
T
r
100 150
Thoi
gian (s)
Hinh 1.4: Dao
dpng mUc nu6c
tai diem bung (diem ngay

phia tru6c tu6ng
diing) va dao
dong song t6i
Hinh 1.4 trinh bay dao dpng
ciia
muc nude tai diem bung ngay
phia
trudc tudng
diing va dao dpng cua sdng tdi tai bien vao dau kenh. Tren
hinh
ve ta thay, sau mot
khoang thdi gian khoang 100 giay song truyen tdi tudng va hien tuong phan xa xuat
hien. Dao dpng tai diem sat tudng co bien dp gap hai
Ian
bien dp sdng tdi va on
djnh
sau mot khoang thdi gian rat
ngdn.
Sau khoang 200 giay, sdng phan xa tir tudng ket
hgp vdi sdng tdi tai bien va tao thanh mot song ket hpp, luc nay dao dpng
ciia
sdng tai
12
bidn
khdng cdn la dao dpng cua rieng sdng tdi
nira,
ta cd the thay rd
sir
bien ddi
ciia

dudng
dtJt
net
trdn
hinh
1.4
cua dao ddng tai bien.
0.4
^
02
-0.2 •
-0.4
Dao dpng tai bien
Dao dpng tai diem nut
50
-1—
100
T
•
150
200 250
Thai gian (s)
Hinh 1.5: Dao dong
mUc nu6c
tai diem nut
(each tUdng
mot khoang
5L/4)
va dao dong tai
bien.

Hinh 1.5 trinh bay dao dpng cua muc nude tai diem each tudng mdt khoang 5/4
dd dai sdng tdi
^,
tuong ung vdi diem
gdn
diem
niit.
Ta tha'y sau khi sdng tdi di qua
mot khoang thdi gian ngin co 130 giay thi sdng phan xa tir tudng quay lai gap sdng tdi
tai
dilm
nay va tao thanh sdng ket hpp cd dao ddng nho hon rat
nhidu
dao ddng cua
sdng tdi. Dae biet ta cd the quan sat thay dao dpng cd tan sd cao tai diem nay do
sir
ket
hpp phi tuy6'n giira sdng tdi va sdng phan xa chinh vi vay cac dao dpng muc nude van
tdn tai d diem niit.
Nhu vay md hinh sd cd the mo phdng tot trudng hpp
Ian
truyen song dai va md
phdng dugc cac tuong tac giira cae sdng vdi
sir
suy giam sd khong dang ke. Ket qua
nay cho phep ta tin tudng vao md hinh de cd the ap dung cho cac bai toan
truyen
sdng
dai tren thuc te.
1.3.3 Kiem chumg vdi bai toan thuy trieu Bien Ddng

Md hinh sd da kiem nghiem d tren dugc ap dung tinh toan thir cho truyen trieu
trong Bien Ddng. Viing bien dupe chia thanh cac ludi hinh vudng vdi
Ax
=1/5 dp
Ay =1/5
dp, cac true dupe chpn xap xi hudng theo kinh tuyen va
vi
tuyen tren he toa dp
Di Cac. Bien ciing dupe xap xi vdi
didu
kien thong lupng bang khdng. Cac bien long
dupe cho cac dao dpng muc
nude
theo cac hang sd dieu hoa
ciia
4 sdng chinh. Cd ba
bien long dugc sir dung cho mo hinh la eo Dai Loan, eo Basi va eo Malaea. Cae hang
sd
di6u
hoa tren cac eo bien nay dugc lay theo bang thuy trieu Admiralty Tidal Tables
[6].
Cac toa dp diem la'y hang sd
dilu
hoa va cac bien dupe trinh bay trong bang 1.1.
13
Bang 1.1:
Cdc bifin
long va cac hang s6
6iiu
hoa

DM
Loan
Basi
Malaea
VTdp
23033,
21^58'
rir
Kinh do
119033,
120M5'
108''59'
M2
H(cm)
87
26
26
G"
326
188
125
S2
H(cin)
23
11
5
G°
15
214
199

Kl
H(cm)
25
23
14
G"
278
262
66
01
H(cm)
21
18
16
G"
236
224
10
Hinh
1.6 trinh bay trudng van tdc ddng trung binh tai luc 10 gid ngay
12
thang 2 nam
1988.
Hinh 1.6:
TrUcJng
dong ehay trieu mo phong tren bien Dong
(luc 0 gid ngay
12/2/1988;
mien
tinh dUdc

chia thanh
1116
theo kinh dp v6i
bu6c lu6i
1/5
do va 116
6
theo
vi
do v6i
bu6c lu6i
1/5
dp;
go'c (0,0) tai toa dp
(0,8'N;98,8°E))
14
S
-1
.
ft'
'/1 .1
V
•/ I ,"/ I •/
f
"ft
,7
I
'A
'1
Tinh

toan
ThiJc
do
f\
./s^.
A
.7
\
;/
_ _, _
50
100
150 200 250
Thdi gian (gio)
300 350 400
Hinh 1.7: Dao dpng
mUc nu6c
tai
khu vUc
Hon Da'u
(bit
dau tir 0 gid ngay 01/1/1988; Tpa
dp:
VI
dp
20"41'N,
kinh dp
106'^49'E)
300
Thdi gian (gid)

600
Hinh 1.8: Dao dong
mUc nu6c
do trieu
tai
Qui
Nhdn
(bit
dau
tijf
0 gid 15/5/2002; Toa dp:
VI
dp
13*'45'N,
kinh dp
109n3'E
)
Tren cac hinh
1.7 va 1.8
trinh bay
so
sanh dao dpng muc nude giira tinh toan theo
md hinh
va
thuc
do tai hai
tram
hai van Hdn Dau va Qui
Nhon.
Tren hinh

ve ta
thay
dao dpng muc nude tinh toan kha
phii
hgp vdi
sd
lieu thuc do. Dao dpng muc
nude
the
hien
rd
tinh nhat trieu
diu
a khu
virc
Hon Dau va xu the
thay
doi
ciia
dao
dpng
muc
nude
tinh toan
rat
phii
hgp vdi thuc te. Tren hinh
ve so
sanh
ta

cung thay
cd
sir
sai khac
nho
vi
bien
dp
tri6u
giira
md
phdng
sd va sd
lieu thuc
do,
nguyen nhan
co the
giai
thich
do vi tri lay ket qua md
phdng
sai
lech
kha
Idn
so vdi vi tri co sd
lieu
vi
ludi
la

1/5
dp va hon
nira
do
ludi
md
phdng
eon kha thd nen
chua
md ta
dupe
het
nhimg
anh
hudng
phi
tuyen
cua
viing nude ndng
va
sir
thay
ddi dia
hinh
phu'e
tap
len
dao
dpng
muc

nude
trilu.
Ndi
chung
md
hinh
da mo
phdng
dupe
kha
chinh
xac dao
dpng
ciia
tri^u
tren Bien Ddng.
15
1.4
NHi^N
XET
Cac
k6t
qua
ki^m
chung md hinh cho mot sd bai toan ly thuyet va thuc te da
chung td phuong phap sd sir dung de phat trien md hinh la rat
phii
hgp. Md hinh cd kha
nang md phdng tot sdng dai trong vimg ven bd va ddng chay hai
chi6u

trong viing bien
ndng. Ket qua kiem chung d tren cho ta su tin tudng vao kha nang ung dung
ciia
md
hinh cho cac bai toan thuc l6.
16
CHirONG
2:
MO HINH MO PHONG
TRUYEN
CHAT HAI
CHl£u
2.1 H$
PHl/ONG
TRINH CO BAN VA CAC
DI^U
KI£N
BIEN
He phuong trinh co ban dugc sir dung de phat trien md hinh md phdng
Ian
truyen
vat cha't trong nude la he phuong trinh truyen tai va khuech tan vat chat dudi dang hai
chi^u.
H^
phuong trinh dugc viet nhu sau
:
dC
dC dC d
(^
dC\

d
A-U—
+
v—
=
— D.
— +
'
dy
^Q-oC
(2.1)
dt
dx dy
dx\
dx)
dy
Trong dd
C(x,y,r)
la
ndng dp vat cha't trong nude;
D^,
Dy
la
he sd khuech tan
theo phuong cac true tpa dd;
Q
la ham ngudn;
a
la he sd phan huy.
Cac dieu kien bien dupe sir dung la: tai bien cung cho rang thdng lupng truyen tai

vudng gdc vdi bien bang khdng; tai bien md truyen tai tu do va khuech tan tu do.
2.2
H£
PHl/ONG TRINH
DUdi
DANG
ROI
RAC
SIT
DUNG PHl/ONG PHAP TVD
He phuong trinh (2.1) tuy don gian song de thu dupe nghiem sd hgp ly va ed dp
chinh xac cao lai khdng phai
la
van de don gian chut nao. Thuc
te
tinh toan cho thay
neu
sijr
dung cac so dd toan thong thudng cd dp chinh xac hon bac 1 cho thanh
ph^n
truy6n
tai thi trong khdng gian nghiem thudng ton tai cae
nhilu
gia tao ra cac nghiem
am hay cac nghiem vugt qua cao so vdi nghiem dung. De giai quyet van de nay thi mdt
sd tac gia da di sir dung so do ngugc ddng bac 1 de giai. Tuy nhien phuong phap ngupc
dong (Upwind) bac
1
nay lai
mdc

phai
sir
khuech tan
sd
rat
Idn
lam cho nghiem
sd
thudng nhd hon
nhidu
so vdi thuc va viing phan bd thi rdng hon. De khac phuc van de
nay trong nghien cun nay chiing toi di sir dung so do FLUX-LIMITING cd dang TVD
vdi dp chinh xac bac 2 nhung khong
gay nhi^u
sd. Dudi day trinh bay so dd toan nay.
De don gian xet phuong trinh
truyen
tai mot
chilu
dang bao toan sau
^ + ^^^ = 0
(2.2)
dt
dx
Khi dd bieu thuc sai phan cd the viet dudi dang sau
cr'=c:-^[F:^,,,-F,%,,)
(2.3)
So dd Flux-Limiting
di
xac dinh cac ham Flux

F^^i
^
va
F,%:-^
theo cong
thu:c
sau
:
17
OAI HOC QUOC GIA
uh
Nr>'
TRUNG
^•-^^
^H
^;G
'ir
.Hi:
;.
F,:,n
=^-?(/.,
-/,) +
^(-^)(/,.
-/,) (2.4)
2 2 2 Ax
Vdi
cc =
sign{ii^^^,2)\
0(r)
la ham gidi han (Limiter) thda man bieu

thu:c
<^{r)
= 0
neu
r<0
0(r) = min(2i-,l)
neu
0<r<l
(2.5)
0(r) =
min(r,
2) neu r
> 1
Trong dd tham sd r dupe xac dinh theo bieu thure
Ddi vdi trudng hpp cd thanh
ph^n
khuech tan tham gia vao phuong trinh xuat
phat thi sau khi giai phuong trinh (2.3) theo so dd TVD rdi se them bieu
thu'e
sai phan
trung tam bac hai thdng thudng cho thanh phan khuech tan. Cdn ddi vdi bai toan hai
chieu
thi
ta sir dung phuong phap tach, tire la ta di giai luan chuyen cho hai hudng x va
hudng y dudi dang bai toan mot chieu. Ket qua
eiia
phep giai cho
chilu
thii: nhat se la
ban dau cho phep giai d

ehilu
thur hai. Phuong phap trinh bay d tren tuy don gian
nhung lai ra't hiru hieu. Dudi day se trinh bay mot sd kiem chung cho bai toan
truyen
tai va khuech tan vat cha't cd nghiem giai tich.
2.3
KI^M
CHCNG
M6 HINH SO THEO CAC BAI TOAN
L^
THUYET
Tren thuc te qua trinh
truyen
tai va khuech tan vat chat lien quan den hai
di6u
kien ban dau chinh: mot la phan bd vat chat cd gradient
Idn
cua nong dp theo khdng
gian tren mot pham vi hep (d gin ngudn thai - tuong ung vdi bai toan shock); hai la
phan bd vat chat cd gradient khdng
Idn
va phan bd trong pham vi rpng (d xa ngudn thai
- tuong ung vdi bai toan smooth). Do dd mot so d6 toan tot phai md phdng
dupe
tot ca
hai trudng hpp tren, cac nghiem sd khdng vi pham ban chat vat ly
ciia
hien tugng dugc
md ta (chang han vat cha't bi am, hay
nhilu

sd gia).
Dudi day se trinh bay cae kiem nghiem mo hinh vdi cae bai toan shock va smooth
neu tren cho cac trudng hgp mot
chilu
va hai
ehilu.
2.3.1 Bai toan mot chieu
a) Bai toan Smooth
Dieu kien ban dau
ciia
bai toan la eo mot ngudn vat chat phan bd dudi dang tron
tren nin ddng chay cd van tdc
U
=0.75m/s. Gia sir he sd khuech tan bang khdng. Ta di
m6 phong
sir
di chuyen cua ngudn vat chat nay. Hinh 2.1 trinh bay phan bd ban dau
ciia
vat chat. Vdi dieu kien cho thi do khdng cd khuech tan nen dang phan bd n6ng dp
ban
dIu
phai
giii*
nguyen va chi tinh tien di theo trudng van tdc. Do dd ta
d6
dang tim
dupe nghiem giai tich.
10
8
^

6
•^
5
4
u
2
0
-2
U=0.75m/s;
he
s6 khuech tan D = 0.
20
40 60 80 100
120 140 160 180 200
x(m)
Hinh
2.1:
Phan
b6'
n6ng
d6 6
thai
die'm
ban diu co dang
ircm
(van
toe
U=0.15m/s\
he
s6'

khue'ch lan D=0.)
200
Hinh
2.2: phan bo n6ng dp theo thai gian tinh theo so d6 Upwind
(tnJcfng
hop phan bd' ban dau tran)
— Lax-Wendrof
o
Giai
tich
x(m)
Hinh
2.3: phan bo ndng 66 theo thcfi gian tinh theo so do Lax-Wendrof
(truong
hop phan bo ban dau tron)
Ket qua md phdng so sanh vdi nghiem giai tich trinh bay tren hinh 2.2 khi sir
dung so dd Upwind thdng thudng, hinh 2.3 ket qua sir dung so d6 Lax-Wendroff va
hinh 2.4 la cua so dd Flux-Limiting TVD. Ta thay vdi so dd Upwind suy giam sd rat
19