Abstract:The problems with complex boundary shapes, such as natural river channels, lakes, estuaries and bays, were solved by using the boundary curve fitting methods. Arbitrary orthogonal curvilinear grid was established to overcome the computational difficulties caused by those complex boundaries. Then, a set of derived equations in the arbitrary curvilinear coordinates, including 2D shallow water equation, turbulence kinetic energy equation and dissipation rate equation etc. were numerically discreted by the finite difference method. In addition, the 2D shallow water equation was numerically solved within the computational domain by using the alternating direction implicit (ADI) difference scheme. In order to verify the reliability and correctness of the method, the De Vriend's 180° plane curve flume experiment model was adopted as an example to implement the numerical simulations. Finally, the simulation outcomes are in excellent agreement with that experimental results with a maximum error as large as approximate 10-2, indicating that the numerical method in this paper is reasonable and feasible. Hence, the method will provide an efficient way for calculating hydrodynamics of water bodies with arbitrary complex boundaries, such as natural river channels and lakes.
[1]Thompson J F, Warsi Z U A, Mastin C W. Boundaryfitted coordinate systems for numerical solution of partial differential equations:A review[J]. Journal of Computational Physics, 1982,47(1):1-108.[2]Stelling G S. On the construction of computational methods for shallow water flow problems[D]. Delft, the Netherlands: Delft University of Technology,1983.[3]王船海,程文辉. 河道二维非恒定流场计算方法研究[J]. 水利学报,1991(1):10-18.Wang Chuanhai, Cheng Wenhui. The calculation of two dimensional unsteady flow pattern in natural rivers[J]. Journal of Hydraulic Engineering, 1991(1):10-18. (in Chinese)[4]De Vriend H J. Mathematical model of steady flow in curved shallow channels[J]. Journal of Hydraulic Research, 1977,15(1):37-54.[5]王如云, 张东生, 张长宽,等. 曲线坐标网格下二维涌波数值模拟的TVD型格式[J]. 水利学报,2002(10):72-77.Wang Ruyun, Zhang Dongsheng, Zhang Changkuan, et al. Application of TVD scheme to numerical simulation of 2D surge in curvilinear coordinates[J]. Journal of Hydraulic Engineering, 2002(10):72-77.(in Chinese)[6]黄炳彬,方红卫,刘斌. 复杂边界水流数学模型的斜对角笛卡儿方法[J]. 水动力学研究与进展:A辑, 2003,18(6):679-685.Huang Bingbin,Fang Hongwei, Liu Bin. Diagonal Cartesian method for numerical simulation of flow with complex boundary[J]. Journal of Hydrodynamics: Ser A, 2003,18(6):679-685. (in Chinese)[7]吴修广,沈永明,郑永红,等. 非正交曲线坐标下二维水流计算的SIMPLEC算法[J]. 水利学报,2003(2):25-30,37.Wu Xiuguang, Shen Yongming, Zheng Yonghong, et al. 2D flow SIMPLEC algorithm in nonorthogonal curvilinear coordinates[J]. Journal of Hydraulic Engineering, 2003(2):25-30,37.(in Chinese)[8]Shi Fengyan, Kirby Js T. Curvilinear parabolic approximation for surface wave transformation with wavecurrent interaction[J]. Journal of Computational Physics Archive, 2005,204(2):562-586.