非结构网格上浅水方程的LU-SGS隐式算法

LU-SGS scheme for shallow water equation computation on unstructured grids

针对浅水数值模拟的特点,建立了可以在非结构网格上求解浅水方程的LU-SGS隐式算法.对复杂地形的底坡项进行了修正,并利用淹没节点法处理移动边界问题.利用算例对此隐式算法进行了模拟验证,并与Roe显式算法进行了比较.结果表明,隐式算法可以有效地缩短计算时间,具有良好的计算和收敛效果.长江口实际潮流模拟结果也证明了此隐式算法处理实际浅水问题的能力.

An implicit LU-SGS scheme for two-dimensional shallow water equation computation on unstructured grids was presented. A sloping method was employed for topographic treatment. The submerged-node method （SNM） was used to deal with the problems concerning the moving boundary. Two examples were calculated and the results were compared with those computed by the explicit Roe scheme. It is shown that this scheme greatly reduces calculation time and has good efficiency and convergence. The results of a numerical simulation of the Yangtze River Estuary further demonstrate that the scheme is accurate and efficient.