双时间步法在二维浅水方程求解中的应用  

Application of dual time-step algorithm for 2-D shallow water equations

作　　者：喻海军[1] 黄国如[1,2] 武传号 

机构地区：[1]华南理工大学土木与交通学院,广东广州510640 [2]华南理工大学亚热带建筑科学国家重点实验室,广东广州510640

出　　处：《水科学进展》2014年第4期542-549,共8页Advances in Water Science

基　　金：水利部公益性行业科研专项经费资助项目(201301093);华南理工大学亚热带建筑科学国家重点实验室自主研究课题项目(2014ZC09)~~

摘　　要：针对传统算法效率低的问题,将隐式双时间步法应用于求解二维浅水方程,建立了非结构网格下高效的有限体积模型。在应用双时间步法时,虚拟时间层中的定常问题采用高效的隐式LU-SGS(Lower-Upper Symmetric Gauss-Seidel)方法进行迭代求解。通过模拟计算4个典型算例以及与传统显式算法进行比较,对模型精度、效率及处理实际问题能力进行检验,分析了时间步长、内迭代次数对模型性能的影响。结果表明,双时间步法放宽了稳定性对时间步长的限制,时间步长可取到显式格式10倍以上,计算耗时减少了50%以上,模型具有良好精度与适应性,具有较好的推广应用价值。Aiming at the problem of low efficiency of traditional explicit schemes, an efficient finite volume scheme is proposed by applying an implicit dual time-step algorithm to discretize the two-dimensional shallow water equations on unstructured grids. An implicit non-linear lower-upper symmetric Gauss-Seidel （LU-SGS） solution algorithm is used as the iteration solver for the inner steady problems. The model＇s accuracy, efficiency, and capability of dealing with practical problems are validated through its application to four typical examples and comparison with an explicit algorithm. In addition, the effects of physical time step and maximum iteration number on the model＇s accuracy and efficiency are assessed. Numerical results from the test examples show that the dual time-step approach eases the restrictions on the sizes of time steps, which can be more than 10 times that of explicit algorithms, and that the reduction in run-time can be more than 50%. The proposed model is found to be accurate and efficient, thus having a good potential for popularization.

关 键 词：双时间步法 二维浅水方程 有限体积法 非结构网格 

分 类 号：TV131[水利工程—水力学及河流动力学]