一种Godunov算法及其在非平底流污染物传输中的应用  

Application of a Godunov-Type Algorithm to the Pollutant Transport with Irregular Bedslope

作　　者：杨金波[1] 段文刚[1] 黄国兵[1] 李订芳[2] 

机构地区：[1]长江科学院水力学研究所,武汉430010 [2]武汉大学数学与统计学院,武汉430072

出　　处：《长江科学院院报》2013年第8期97-101,共5页Journal of Changjiang River Scientific Research Institute

基　　金：国家自然科学基金资助项目(11102027);中央级基本科研业务费项目(CKSF2011014/SL;CKSF2013025/SL;CKSF2012010/SL)

摘　　要：采用和谐的加权平均通量(Weighted Average Flux,简称WAF)算法,研究了浅水波方程的间断解及污染物传输问题。该算法采用WAF格式和HLLC Riemann求解器近似单元边界数值通量,中心差分格式离散地形源项,然后理论上证明了该算法是和谐的。最后利用WAF算法对非平底地形上浅水波间断解及污染物传输问题进行数值计算,精确地捕捉到了间断解和污染物运动过程,结果表明该算法满足守恒性,具有高分辨率、无振荡及捕捉污染物运动边界的能力。A well-balanced weighted average flux （WAF） scheme is proposed for the nonhomogeneous shallow water equations with pollutant transport. The water surface elevation and water discharge are used as the conserved varia- bles in the shallow water equations, while the conserved variables and the bed elevation are set on the staggered mesh. Here, the WAF scheme combined with the HLLC Riemann solver is directly performed for the nonhomoge- neous shallow water equations with pollutant transport, and the spatial second order central difference approximation is applied to source terms. Then, it＇ s proved that the extended WAF scheme is harmonious in theory. Finally, several numerical tests about the steady and nonsteady flows over the irregular bottom or with the wet/dry front are simulated. The results obviously suggest that the WAF scheme is a well-balanced, robust, efficient, and practical scheme with high resolution.

关 键 词：浅水波方程 WAF格式 溃坝 污染物传输 

分 类 号：X51[环境科学与工程—环境工程]