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.
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)