115435843-phan-tich-động-lực-học-dong-chảy-chất-lỏng-bằng-phương-phap-meshless

8/12/2019 115435843-Phan-tich-ng-lc-hc-dong-chy-cht-lng-bng-phng-phap-MESHLESS

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~ , p O I f i~~ N~~.{fa tO GIAo Dl)C vA BA o TAO

TRUONG D~I HOC SU PH~M KY THU~ T A: ~ ~THANH PHO HO CHI MINH

LUAN VAN THAC .KS NGUYEN DUY HUNG

PHAN TicH DONG r.uc HQC DONG CHACHAT LONG BANG PHUONG PHAp MESHLESSChuyen nganh:Ma sf) nganh:

Cong Nght$ Ch~ T;lO May605204

HQ va Ten hoc vien:Nguoi huong d:n:

KS. Nguyen Duy HungTS. Nguyen Hoai Son

S K 002386TH U V IE N TR rJc t G D H ~PKTI_.___o _ __ 0.- .. _ .. _-

Tp. H6 Chi Minh, thang 11 nam 2009


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TOM TAT

Smoothed Particle Method (SPH) la mot phuong phap khong lucri dSgiai cac phuong trinh vi phan tirng phan. Day la phuong phap Lagrange thufrntuy duoc phat trien nr nhtrng narn cua thap nien 70 dn nay, cling la mot trongnhfrng phuong phap chat dim khong lucri (Meshfree Particle Method) lau doinhk Cling voi nhtrng cai tin lien tuc thi dQ chinh xac, dQ 6n dinh va tinhnrong thich cua phuong phap SPH dat dn mire dQ tin c~y cho cac trng dungtrong ky thuat.

Trong d tai nay, phuong phap SPH duoc su dung d phan tich dQng hrch9Cdong chay ch~t long hai chieu. Nn tang cua SPH la ly thuyet noi suy vacac dinh lu~t bao toan cua dQng lire h9C ch~t long trong moi tnrong lien tucduoc thS hien diroi dang cac phirong trinh vi phan rung phan duoc chuyen vaotrong cac ch~t dim dang hat bang cac phuong trinh tich phan thong qua viecsu dung ham nQi suy. Khi tinh toan, cac thong tin chi duoc bit dn a dang roirac tung diem vi vay gia tri cua cac tich phan nhu t6ng tren toan bQ cac ch~tdiSm Ian can.

Trong luan van nay, phuong phap SPH duoc irng dung dS phan tichtrang thai dong chay cac bai toan: dong chay Poiseuille, dong chay Couette vabai toan va d~p. Kt qua thu duoc trong phan tich cac bai toan tren voi nhtrngham nhan ill khac nhau, kich thuoc lucri khac nhau, ban kinh nhan nr khac nhause duoc so sanh voi loi giai giai tich hoac kt qua thi nghiem.


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ABSTRACT

Smoothed Particle Hydrodynamic (SPH) method is a meshless methodfor solving partial differential equations. The SPH is a purely Lagrangianmethod developed during the seventies as one of the oldest Meshfree ParticleMethods (MPM), is quickly approaching its mature stage. With the continuingimprovements and modifications, the accuracy, stability and adaptivity of themodel have reached an acceptable level for practical engineering applications.

In this master thesis, a meshless approach to the analysis of dynamictwo-dimensional fluid problems by the Smoothed Particle Hydrodynamic(SPH) method is presented. The foundation of SPH is interpolation theory. Theconservation laws of continuum fluid dynamics, in the form of partialdifferential equations, are transformed into their particle forms by integralequations through the use of an interpolation function usually known as kernel.Computationally, information is known only at discrete points, so that theintegrals are evaluated as sums over neighboring points.

In this study, SPH is applied to dynamic analysis: flow Poiseuille, flowCouette and break dam problem will be computed in this paper. The results areobtained for a two-dimensional problem using different SPH kernel functions,different mesh-size, and different kernel radius compared with the results ofexact methods or resulft of experimental.


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MUCLUCLoi earn an i

T om tat iiM uc luc iv

Chuong I: G iO i thieu 11 1 Tong quan 11.1.1 Tinh hinh nghien ciru va irng dung phuong phap Meshless tren th gioi .. 21.1.2 Tinh hinh nghien ciru va irng dung phirong phap Meshless a Viet Narn ... 4

11 M f I ~ 5\Ie leu cua u~nvan 1 2 D e cuong lu~n van 5Chuong II: Coo sO' l y thuyet phuong trioh Navier - Stokes cho bai toan dQng

luc hoc hru chat 72 1 G iO i thi~u 72.2 Thi~t l~p phuong trinh Navier - Stokes dang LagrangeError Bookmark not defined.

2.2.1 Phuong phap khoi kiern scat va phirong phap khoi chat long vo cung be................................................. : 7

2.2.2 Phuong trinh lien tuc 102.2.3 Phuong trinh d(>ng hrong 112.2.4 Phuong trinh nang hrong 13

Chuong III: Phuong phap SPH 143.1 Gi6'i thieu 14

3.1.1 SPH trong v~t ly thien th~ 143.1.2 Phuong phap SPH trong co h9C v~t r~n 153.1.3 Phuong phap SPH trong h9C chfrt long 17

3 2 Ly thuy t phuong ph p SPH 193.2.1 Dinh nghia chfrt diem trong SPH 193.2.2 Tich phan n(>i suy 19


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3.2.3 Ham nhan t u 203.2.4 Chon ham nhan t u 21

. 3.2.5 Chon ban kinh nhan ill h 243.2.6 Chinh ly ap sufit ao 25

3 3 r ic h phan thiri gian 283.4 BU'O'ctho; gian 303.4.1 Diu kien CFL (Courant - Fredreichs - Lewy stability condition) 303.4.2 Diu kien hrc quan tinh 303.4.3 Diu kien hJC nhot 303.5 J)i~u ki~n bien 31

3.5.1 Gioi thieu cac loai dieu kien bien [17] 313.5.2 Diu kien bien dong hrc hoc (Dynamic boundary conditions) 32

ChU'O'DgV: Cong tlnrc SPH cho phurrng trinh Navier - Stokes 364 1 G i6 i t ~u 364.2 Cong tlnrc SPH cho phuong trinh N avier - Stokes 36

4.~.1 Phuong trinh dong hrong 364.2.2 Phuong trinh lien tuc 394.2.3 Phuong trinh trang thai 394.2.4 Phuong trinh nang hrong 414.2.5 Chuyen dong cua chfit diem 41

4.3 Giai thuat phuong phap SPH cho bai toan phan tich dQng 11 c hoc cht long 4 2

Chuong V: Ap dung 4351 GiOi thi~u 435 2 Bai toan dong chay Poiseuille 43

5.2.1 Mo hinh va thong s6 phan tich 435.2.2 Phan tich k~t qua 46

5 3 Bai toan dong chay Couette 505.3.1 Mo hinh va thong s6 phan tich 505.3.2 Phan tich k~t qua 51


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5 4 Ba toan V d~ P 565.4.1 Mo hinh va thong s phan tich 565.4.2 Phan tich k~t qua 575 5 K et lu~n 68

Chuong VI: Ket lu~n va hurmg phat trien 706 1 K et lu~n 70

6 2 Hmrng phat trien .................................................................................................. 7 2


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115435843-phan-tich-động-lực-học-dong-chảy-chất-lỏng-bằng-phương-phap-meshless

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