CSTR水力学模型数值求解方法探讨

Discussion on the Numerical Solution of CSTR Hydrological Model

CSTR模型是河流水质模拟的常用模型之一,其中水力学模型是影响CSTR模型数值稳定性的关键因素,但迄今为止对CSTR水力学模型数值稳定性鲜有充分的讨论.以赣江朝阳水厂至八一桥北段为例,采用实测数据,分单箱积分和整体积分2种方式,讨论了Runge-Kutta-Felberg方法(RKF)、经典四阶Runge-Kutta方法(RK4)和二级四阶隐式Runge-Kutta方法(RK2)的数值稳定性、模拟精度和时间效率.结果表明,与国际上目前常用的单箱积分相比,整体积分具有更好的稳定性.3种Runge-Kutta方法的稳定性排序是RKF<RK4<RK2;时间效率的排序是RKF<RK2<RK4.采用基于整体积分的经典四阶Runge-Kutta方法求解CSTR水力学模型具有较好的优越性.

The Continuously Stirred Tank Reactor （CSTR） Model is one of the most commonly used river water quality models in the world. The hydrological model plays a key role in the model＇s numerical stability, but this problem has not been fully discussed until now. With the river section from Chaoyang Water Plant to Bayi Bridge in Ganjiang River as an example, based on the field observations, the numerical stability, accuracy and efficiency of Runge-Kutta-Felberg （RKF）, classical Runge-Kutta （RK4） and implicit Runge-Kutta （RK2） were compared by tank-by-tank integration and whole river integration respectively. It shows that although the tank-by-tank method is used much extensively, the stability of the whole integration is superior to the tank-by-tank integration. The stability of the three Runge-Kutta methods is in the order of RKF〈 RK4 〈 RK2, and efficiency is RKF〈 RK2 〈 RK4. It is concluded that the classic four-order Runge-Kutta method based on the whole river integration is suitable for the numerical solution of CSTR hydrological model.