含底坡项浅水方程的一种数值求解方法  

Numerical approximation of the shallow-water equations with bed slope source term

作　　者：朱德军[1] 陈永灿[1] 刘昭伟[1] 李钟顺[1] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《水科学进展》2012年第6期796-801,共6页Advances in Water Science

基　　金：国家自然科学基金重点资助项目(51039002);清华大学自主科研计划(20101081780)~~

摘　　要：激波捕捉格式能处理含强间断的浅水方程,因为必须采用关于守恒变量的守恒形式方程,作为水流实际驱动力的水位梯度项被分解为压力梯度项和底坡项,如果离散格式不能很好地平衡这两项的作用,将导致不准确的结果。基于理论推导,提出了一种新方法,在单元内部采用非守恒形式,保留水位梯度项,在界面处采用守恒格式捕捉间断。利用4个具有代表性的算例对提出的方法进行了验证,结果表明,该方法能够处理变化地形上的强间断和流态变化,并能够准确捕捉扰动的传播过程。Shock-capturing schemes are capable of solving the shallow-water equations with strong discontinuities. However, since the conservative form equations are employed, the water surface gradient term is split into two terms, the gradient of pressure and the bed slope source term. Nonphysical results will be produced if the latter two terms are not well balanced. Based on theoretical analysis a novel algorithm is proposed in this paper. The non-conservative form equations are utilized inside cells in the algorithm, which retains the water surface gradient term. While the con- servative form equations of the conservative variables are utilized at cell interfaces to capture discontinuities. The pro- posed algorithm is verified using four benchmark problems, and the results demonstrate that it can successfully treat strong discontinuities and transcritical flows over varied topography, and it can also accurately reproduce the propaga- tion of small perturbations.

关 键 词：浅水方程 底坡项 间断 

分 类 号：TV122.4[水利工程—水文学及水资源]