基于未确知信息的环状河网水质数学模型研究

以圣维南方程组、对流扩散方程以及未确知信息理论为基础,建立了环状河网一维水动力与未确知水质数学模型。采用Preissman四点隐格式法对圣维南方程组进行离散和采用显式差分对对流扩散方程进行离散,对河网水动力与水质分别进行了合理的编码,并考虑了泵闸等控制工程、降雨径流的影响,采用河网的三级解法编制河网非恒定流的计算程序求解各断面的水位Z和流量Q,实现了水动力和水质两模块之间的数据连接,且对微分形式的水质模型运用未确知数学理论进行了含有两个未确知参数的水质计算,从而不仅能获得污染物浓度区间值,还能得到相应的可信度。实例研究表明,建立的河网水动力模型和未确知信息的水质模型是可靠的,可以用于河网水质治理工程的数值模拟研究和水环境评估。

Water quality mathematical model for looping river network based on uncertain information

Based on the Saint-Venant equations,the advection-diffusion equation and the uncertain mathematics theory,both a one-dimensional hydrodynamic model and a uncertain water quality mathematical model are established.The Preissmann implicit four-point scheme is used to solve the Saint-Venant equations,and the explicit scheme is used to solve the advection-equation.Two reasonable computational codings of hydrodynamic and water quality for the river network are conducted.The model considers the controlling projects of pump and brake,rainfall-runoff.The Computer program of the unsteady flow is compiled by using the three-level solution method for river network to solve the water level and the discharge at different cross sections.The data connection of the two sub-model is realized.The differential water quality model is computed based on the uncertain mathematics theory,including two unascertained parameters at the first time.According to the model proposed,both the interval values of pollutant concentration and the respective corresponding veliability can be obtained directly.The case shows that the hydrodynamic model and the uncertain water quality model for looping river network are reliable and can be applied to water quality regulation project and the water environmental assessment.