任意曲线坐标系下二维浅水方程的数值模拟

采用拟合边界曲线的方法来构造天然河道、湖泊、港口河口以及海湾的复杂边界问题,建立任意正交曲线网格以克服由于复杂边界而引起的计算困难.在此基础上,推导出任意曲线坐标系下的二维浅水方程、湍流动能方程和湍流动能耗散方程;应用有限差分方法对该方程组进行数值离散,并用交错方向隐式格式实现在计算区域内对任意曲线坐标系下的二维浅水方程进行数值求解.为了验证在任意曲线坐标系下二维浅水方程数值求解方法的可靠性、正确性,以DeVriend的180°平面弯道水槽试验物理模型为例进行数值模拟,结果表明,数值计算的结果和DeVriend的试验结果相当吻合,最大绝对误差值约为10^-2,因此,数值计算方法合理可行,可为任意复杂边界的天然河道、湖泊等水域的水动力研究提供有效的计算方法.

Numerical simulation of 2D shallow water equation in arbitrary curvilinear coordinates

The problems with complex boundary shapes,such as natural river channels,lakes,estua-ries and bays,were solved by using the boundary curve fitting methods.Arbitrary orthogonal curvili-near 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.