| 参 考 文 献 [1] Harten A. High resolution schemes for hyperbolic conservation laws, J. Comp. Phys., 1983, 49: 357-393. [2] 胡四一、谭维炎，用TVD格式预测溃坝洪水波的演进，水利学报，1989，(7)：1－11. [3] 陶建华, 张卫东. 总变差不增格式计算一维、二维溃坝波. 天津大学学报, 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] 王嘉松, 倪汉根, 金生, 李鉴初，用TVD显隐格式模拟溃坝波的演进与反射，水利学报，1998，（5）：7-11. [6] 王嘉松, 倪汉根, 金生，二维溃坝波传播和绕流特性的高精度数值模拟，水利学报，1998，（10）：1-6. [7] 王嘉松, 倪汉根, 金生，二维溃坝问题的高分辨率数值模拟，上海交通大学学报，1999，（10）：1213－1216. [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] 谭维炎, 胡四一，二维浅水流动的一种普适的高性能格式—有限体积Osher格式，水科学进展，1991，(3)：154-161. [11] Zhao D H, Shen H W, Lai J S and Tabios Ⅲ 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 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 180°strong bend, a 90°bifurcation and a 45°three 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 |
