用TVD格式预测溃坝洪水波的演进

Dam break flood wave routing by using TVD scheme

溃坝洪水波通常为迅变或间断流动,同时兼有急流和缓流、压缩波和稀疏波等流态。常用的求解圣维南方程组的差分方法常遭失败,或不稳定,或数值解含有振动,或间断被抹平而分辨率低。本文利用气体动力学中新近提出的TVD格式求解获得成功。 文中介绍了一阶及二阶、显及隐、对称及逆风TVD格式的有关算法。以简单的一阶TVD显格式为对象,结合洪水演进问题,详细分析了其内在机制及优良性能,说明它既具有逆风格式及中心格式的性能,又能及时对水位或流量过程的峰谷作出响应,保持解在间断处陡峭而在其两侧无振动。文中最后通过一个概化为黎曼问题的瞬时溃坝模型,以及一座高坝的假想迅溃实例,将该格式与LF格式、LW格式的计算结果作比较,充分显示了该格式在预测一般洪水及溃坝洪水波演进方面的前景。

Dam-break flood waves often vary rapidly or even discontinuously, with both rapid and tranquil flow behaviors, as well as both compression and rarefaction waves. Finite difference methods commonly used for solving the Saint-Venant equations often failin dam-break flood wave routing on account of nonlinear instability, parasite oscillation and smearing of discontinuities. In this papera TVD scheme is utilized to solve this oroblem with success.Relevant algorithms with first or second order, explicit or implicit, symmetric or biased TVD schemes are introduced. A detailed analysis of flood routing problem solved by simple first-order explicit TVD scheme is given to show the intrinsic mechanism and its good performance. It has been proved that the TVD scheme not only has the features of both upwind and centred schemes, but also can make quick response to the occurrence of peaks and hollows in the hydrograph, so that discontinuities can preserve sharpness and no oscillation would generate in the vicinity.A comparison of the results obtained with an instantaneous dam-break model formulated as a Riemann problem by using the TVD scheme, Lax-Friedrichs scheme, Lax-Wendroff scheme, and a case study about the hypothetical rapid break of a high dam in China are presented. The results show that the TVD scheme has broad prospects in its application to both natural flood and dambreak flood wave routing.