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1        •2        ߝh3         

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2   ϺͨWWϵ Ϻ200030  3BWľϵB116023

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ЈD̖ TV131.4     īIRaA

1ǰ

    Sˮͭh̆}ҪMМ\ˮӷֵӋuɞҪֶmȻS\ˮһ㆖}Ӌ^gs߅ȏs\ˮ}оڌֵӋ㷽Ҫ^̎ڰlչ֮Ά}оһֱPעҪn}ҪČWgrֵ͹̑ñ

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ӵĿƷһͨ^oˮСºLٶNavier-StokesMƽõĜ\ˮ䌑غʽ

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Ħ½  ʽ_

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3        weTVDʽ

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    ᘌԪi(Ȳ^ )(1a)ʽMзeõeʽķ

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ʽA^ edl߅ ĻLn߅ ⷨλ߅ ėlνMʽ˵2헿Ԍ

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߅L k߅ⷨͨ

    OUچԪȲֲ׃Mһxɢ(3)ʽõwe

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M

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    F(U)G(U)D׃D׃Q ɸČ5ʽ

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    ӛ(7)ʽҶ˞ t

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ÃɲRunge-KuttaxɢʽrgҲ_Aõ

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    ÿһԪÿһ߅ͨMTVDʽo(猦چԪiĵ1߅)

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ʽ ԪildžԪ1ĵlgƽýMTVDʽMвֵ

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ԪildžԪ1ĵlٶȵgƽ Ԫ׃ֵgƽ īI[8]MUSCL

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0.138Ӌ㝢βrھRcR֮gRˮʼcεˮ^󣨝ףr˲Æ΅ tڸɵוr˲p ԱډַķŤF

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ʾԪildžԪ1֮gľx

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(1)    _߅ҕB_[6]

(2)    ̱߅,

   c߅غϵ߅

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ʾ䷨ͨоͨ˜ˡ12ʾԪbʾ߅ăȲԪ(D1ʾ)ӋԪĎ׺γߴΠӋвҪ

5        ֵA

5.1   180   

    180cֱL2400m΃돽քe300m900m600mַλ2240 mֱ̎Oˮքe10m0.1mֲϵ0.02һJƽС3tҕ鏊ƽȞ1.0@Ȼڏ

    Ӌ㷽@ԓȫβĔֵģMYӋvr100s300s470sõˮٶȈքeʾڈD2D3͈D4?J?_ʼrβƽֱξMM돝β\ܵɰ̱ڵٷˮλֲl׃ˮλԸڃȂˮλǰ˵wٶȿƫxMڅ@xԼ^ľMƽֱκ@N׃upСvLһΕrg@NeuʧɰwԎ׺ͬIJߺٶMwMٶԿ@ЩcеČY[14]һµ


Dȝӵˮcٶ??/span>t=100s


Dȝӵˮcٶ??/span>t=300s


Dȝӵˮcٶ??/span>t=470s

5.2  90pֲ֧

һ90ֲַλ920m̎]ʼˮλ10mˮλ2m0.01mքe׺͸ɵֲϵȡ0.02D5(a)(b)քeӋ㝢Q100sr׺͸ɵ׵ĝβˮؓ΂wڽR̎ԄM|̈́ٷγ֧ڽDž^ˮλ׃uc̎dzs, ڲͬˮrµҲ@eɵוr@ȻȝוrСƽ̹


Dpֲ֧βˮ澀 (D҈Dɵ)

5.3  45ֲ֧

һ45ֲ֧ɗlQֲķ֧cӵ45ӵL2300m,400m֧ӵ300mַλ900m̎ͬȡˮ10mˮ2m0.01mֲϵ0.02Ӌ㝢Q40s80srˮȞ0.2rˮλֵD6ʾˮȞ0.001rˮλֵD7?J?β\cβκͲMٶڲͬˮȕrƵڽDž^uR̎βμMٶȅs^eСˮrcˮθƽڵ_R֮̎ǰMٶԿ


Dֲ֧βˮλֵ Dt=40s҈Dt=80s


Dֲ֧ɵβˮλֵ Dt=40s҈Dt=80s

6 YZ

߽оĻA߅ΆԪldžԪxؓPϵÎĽMTVDʽRunge-Kuttaքegxɢ͕rgxɢ˜\ˮ̵߅ΆԪweTVDʽβӋṩ˸߷ֱ߾ȵĔֵֶ״ᘌ180ӵ90Լ45ֲӵA˝βM^ʾڏsӵ؄eǾЏֲȻrβļ׃mȻᘌβǺ㶨ɱg}оAҊĵķԷƏVгˮSFһĺ㶨cǺ㶨\ˮ}Ӌ

      I

[1]     Harten A. High resolution schemes for hyperbolic conservation laws, J. Comp. Phys., 1983, 49: 357-393.

[2]     һTSTVDʽAyκˮMˮW1989(7)111.

[3]     սA, l|. ׃ʽӋһSSβ. WW, 1993, (1): 7~15.

[4]     Yang J Y, Hsu C A and Chang S H. Computations of free surface flows, Part 1: 1D dam-break flow. J. Hydr. Res. , 1993, 31(1): 19-34.

[5]     , ߝh, , bTVD@[ʽģMβMcˮW199857-11.

[6]     , ߝh, Sβ@Եĸ߾ȔֵģMˮW1998101-6.

[7]     , ߝh, SΆ}ĸ߷ֱʔֵģMϺͨWW19991012131216.

[8]     Wang Jia-song and Ni Han-gen. A high resolution finite-volume method for solving the shallow water equations. J. Hydrodynamics, Ser. B., 2000, (1): 35-41.

[9]     Wang Jia-song, Ni Han-gen and He You-sheng. Finite-difference TVD scheme for computation of dam-break problems. J. Hydr. Eng., ASCE, 2000, 126(4): 253-262.

[10]  TS, һS\ˮӵһNmĸܸʽweOsherʽˮƌWMչ1991(3)154-161.

[11]  Zhao D H, Shen H W, Lai J S and Tabios G Q. Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling, J. Hydr. Eng., ASCE, 1996, 122: 692-702.

[12]  Anastansiou K and Chan C T. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. Inter. J. Numer. Meth. Fluids, 1997, 24: 1225-1245.

[13]  Mingham C G and Causon D M. High-resolution finite-volume method for shallow water flows. J. Hydr. Eng., ASCE, 1998, 124(6): 605~614.

[14]  Bell S W, Elliot R C and Chaudhry M A. Experimental results of two-dimensional dam-break flows. J. Hydr. Res., 1992, 30(2): 225-252.

Numerical simulation of dam-break flows in bend and furcated channels

           Wang Jia-song1        He You-sheng1         Ni Han-gen2

(1.Shanghai Jiaotong University, Shanghai 200030;  2. Dalian University of Technology, Dalian 116023) 

Abstract  A high-resolution finite-volume method for solving the conservative shallow water equations is presented in this paper. The method is based upon extending the finite-difference TVD scheme to finite-volume method considering the corresponding relationships between elements and nodes. A second-order hybrid TVD scheme with an optimum-selected limiter and a two-step Runge-Kutta method are utilized to discretize the integral type of the shallow water equations over arbitrary quadrilateral cells. The dam-break flows are simulated for the first time considering the cases in channels with a 180strong bend, a 90bifurcation and a 45three branches. The complex characteristics of velocity and water elevation changes at both banks of the curved sections, auto-reassignment of discharges and momentum as well as vortices and super-elevation near the corner of embranchment regions in the furcated channels are displayed. The effects of wetting bed and drying bed are discussed simultaneously.

 Key words  shallow water equations, finite-volume method, bend channel, furcated channel, dam-break Bores


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