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Original article
502
NEFT FILTRATSIYA MASALASINI IKKI O`LCHOVLI MASALASI ALGORITMI
Naziroza Elmera Shodmonovna
Toshkent axborot texnologiyalari universteti
Texnika fanlari dotsenti professor
Hoshimov Donobek
Toshkent axborot texnologiyalari universteti
2-kurs tayanch doktoranti
E-mail:
hoshimovdonobek@gmail.com
Annotatsiya:
Ushbu ilmiy maqolada neftning filtratsiya(sizish) masalasi yechilgan, algoritmi
tuzilgan.
Kalit so`zlari:
Neft masalalari, sonli usullar, matematik model, g`ovak muhit, progonka usuli.
Ushbu maqolada aytiladigan algoritmda ko`ndalang kesm sximasi va haydash usuli g`oyasiga
asoslangan bo`ladi. Qisqacha aytganda haydash usuli g`oyasi chap va o`ng haydash usuli
go`yasidek bo`ladi. Bundan kelib chiqadiki ikki oqimga parallellashtirish imkonini beradi.
Bunday holatda chekli ayirmali usul ikkita oqim o`rtasida ikkiga bo`linadi va birinchisi
1
k
i
yo`nalishida ikkinchisi
k
i k
yo`nalishida (bu yerda
(
1) / 2
k
k
=
+
, k toq son). Bu yerda
k
- oldinga siljishning ikkita shoxlari yuqorida va pastda tutashadigan tenglamaning soni.
Bundan kelib chiqadi qarama- qarshi yo`nalishda birinchi navbatda uning oldinga siljishi amalga
oshiriladi- koyefitsentlar yuqoridan pastga hisoblanadi:
Usulning algoritmi quyidagicha progonka koefitsentlari topish usuliga o`xshash:
1. Oldinga haydash ishga tushiriladi (to‘g‘ri yurish bilan):
1
0
0
1
0
0
=b /c ,
=f /c ,
a
b
=a /c ,
=f /c .
N
N
N
N
N
N
x
h
2. Oldinga yurish quyidagi formulalarni hisoblash orqali ketma-ket bajariladi:
1
i
i
i i
=b /(c -a ), i=1, 2, ... , m-1.
i
a
a
+
1
i
i i
i
i i
=(f +a )/(c -a ), i=1, 2, ... , m-1.
i
b
b
a
+
i
i i+1
=a /(c -b
), i=N-1, N-2, ... m .
i
i
x
x
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Original article
503
i+1
i
i i+1
=(f +b
)/(c -b
), i=N-1, N-2, ... m .
i
i
i
h
h
x
3. Teskari haydash ishga tushiriladi:
m
m m
m m
=( +
)/(1-
) .
m
p
h x b
x b
1
m
m m
m m
=( +
)/(1-
) .
m
p
b a h
x b
-
4. Teskari haydashda quyidagi formulalar ketma-ket bajariladi:
i+1
1
i+1
=(
+
) , i=m-2, ... , 1, 0 .
i
i
p
p
a
b
+
1
i+1
i+1
=(
+
) , i=m, m+1, ... , N-1.
i
i
p
p
x
h
+
To‘g‘ridan-to‘g‘ri harakat formulalarida bir xil ifoda bilan bo‘linish juftlari mavjud. Ularni
o‘zaro hisoblab, keyingi qadamda ushbu raqamlarga ko‘paytirish orqali almashtirish mumkin.
Odatda berilgan orqaga o‘tish formulalarida
1
m
p
-
komponenti uchun formula yo‘q, bu esa
keyinroq teskari ishda hisoblanadi. Biroq, bu o‘zgaruvchilar soni juft bo‘lgan taqdirda ham
grafikning kritik yo‘lini uzaytiradi,
1
m
p
-
ni hisoblashni
m
y
allaqachon hisoblangan paytgacha
kechiktiradi, ikkala komponent bir vaqtning o‘zida bir-biridan deyarli mustaqil ravishda
hisoblanishi mumkin va o‘zgaruvchilarning soni toq bo‘lsa, “tutashish nuqtasida” hisob-kitoblar
uchun koeffitsiyentlarning bitta qo‘shimcha hisobini “yuqorida” yoki “pastda” kutish kerak.
Shuning uchun keyingi manbalarda toq sonli noma’lumlar uchun maqbulroq formulalar berilgan.
Ularda teskari harakatning boshlanishi quyidagi formula bilan almashtiriladi (bizning
belgilashimizda):
m
m m+1
m m
m
m m
m m+1
=(f +b
+a
)/(c -a
-b
)
m
p
h
b
a
x
Endi ikki o‘lchovli masalalar uchun parabolik tipdagi tenglamalarni hisoblashning parallel
algoritmini ko‘rib chiqamiz. Bu yerda ma’lumki, chekli farqli tenglamalar uchun ko‘ndalang-
kesim sxemalar qo‘llaniladi. Parallel hisoblash jarayonini tashkil qilish uchun l+0,5 yarim vaqt
qatlami, qarama-qarshi ishning hisoblash maydoni 1-nuqtadan
�
gacha va m-nuqtadan
�
nuqtaga qadar ikki qismga bo‘linadi.
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Original article
504
1.1-rasm.l+0.5 vaqt qatlami uchun parallel hisoblash algortm sxemasi.
Ushbu parallel hisoblash sxemasida har bir yo‘nalishda x
i
o‘zgaruvchisi orqaga qarab,
(
1,2,..., )
j
y j
m
=
o‘zgaruvchisi bo‘ylab harakatlanadi va
(
,
1,..., )
j
y j m m
m
=
-
ga parallel
bo‘ladi.
Algoritmik sxemadagi ishlatilgan belgilar quyidagilarni ko‘rsatadi:
m - y o‘zgaruvchisi bo‘yicha nuqtalar soni;
n - x o‘zgaruvchisi bo‘yicha nuqtalar soni;
uh - Uchrashuv-haydash usulining qo‘llanilishi(Vstrechnay pragonka);
m
- y o‘qi yo‘nalishdagi markaziy nuqta
1
2
m
m
=
+
;
ISSN: 3030-3931, Impact factor: 7,241
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Original article
505
n
- x o‘qi yo‘nalishidagi markaziy nuqta
1
2
n
n
=
+
.
1.2-rasm. l+1 vaqt qatlami uchun parallel xisoblash.
Bu yerda ham hisoblash sxemasi (l+1 vaqt qatlami uchun) ko‘ndalang kesim sxemasi bo‘yicha
amalga oshiriladi. Ushbu parallel hisoblash sxemasida har bir yo‘nalishda y
i
o‘zgaruvchisi
orqaga qarab,
( 1,2,..., )
i
x i
n
=
o‘zgaruvchisi bo‘ylab harakatlanadi va
(
,
1,..., )
i
x i n n
n
=
-
ga parallel bo‘ladi.
ISSN: 3030-3931, Impact factor: 7,241
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Original article
506
ISSN: 3030-3931, Impact factor: 7,241
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Original article
507
1.3-rasm. Ko`ndalang kesmning parallel xisoblash blok sximasi.
ISSN: 3030-3931, Impact factor: 7,241
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Original article
508
Parallel xisoblashda haydash usulidan foydalanish ko`proq progonka usuli koeffitsentlarini
topishga o`xshaydi. Koeffitsentlar bunda ham avval to`g`ri so`ngra teskari tartibda topib boriladi.
Bu yerda parallel hisoblash algirtlarining ishlatilishiga asosiy sabab esa ikkala jarayonda tizimda
parallel hisoblansa jarayonda natijaga erishish tezroq amalga oshiriladi. Jarayonni vaqtni
hisoblashning o`rni judayam muhimroq chunki ushbu jarayonda reyal jarayonlarda natijalarni
olish muhim o`rin tutadi. Reyal natijalarni tezkorlik bilan taqdim etsa jarayon uchun xulosa
berish shuncha tezroq amalga oshiriladi.
Xulosa:
Ushbu jarayon progonka usuliga o`xshash jarayon bo`lganligi sababli oshkormas
hollarda sonli yechimlar olish uchun juda qo`l keladi. Bunda jarayonning yechimlari parallel
ravishda pastdan tepaga va tepadan pastga qarab bajarilganligi sababli jarayonni amalga
oshirishda parallel hisoblash algoritmidan foydalandik oxirida. Ushbu jarayon reyal vaqtlarda
ko`proq vaqtdan yutish uchun juda qo`l keladi. Bunda vaqtdan yutishda jarayonlar parallel
ravishda bajariladi.
Foydalanilgan adabiyotlar:
1.
Nazirova, E.Sh. Numerical modeling of oil filtration processes in multi-layer porous
media with dynamic connection between layers. Descend. Muhammad Al-Khorezmi 4(6), 10–14
(2018)Google Scholar.
2.
Ne’matov A., Ismailov Sh.R. “Beqaror yer osti suvlarining filtratsiya masalasini
yechishning parallel hisoblash algoritmi” //
Мақола
// Халқаро Илмий Форум 2023 йил 13
январ
3.
Ne’matov A.A. , Nazirova E.Sh. , Sadikov R.T. 2021 On numerical method for modeling
oil filtration problems in piecewise-inhomogeneous porous medium. https://iopscience. iop.
org/article/10. 1088/1757-899X/1032/1/012018
4.
Ne’matov A.A., Nazirova E.Sh., Sadikov R.T., I.Nabiyev 2021 One-Dimensional
Mathematical Model and a Numerical Solution Accounting Sedimentation of Clay Particles in
Process of Oil Filtering in Porous Medium. https://link. springer. com/chapter/10. 1007%2F978-
3-030-68449-5_35
5.
Xujayorov, B. X.; Maxmudov, J. M.; Usmanov, A. I.; and Saidov, B. O. (2020) "A
problem of solute transport in a cylindrical porous media with a fractal structure taking into
account adsorption phenomena," Scientific Journal of Samarkand University: Vol. 2020 , Article
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