浅水方程的间断有限元解法  

DG FEM for Shallow Water Equations

作　　者：韩涛[1] 逄勇[1] 翟金波[1] 安婷[2] 

机构地区：[1]河海大学环境科学与工程学院,南京210098 [2]河海大学水文水资源与水利工程科学国家重点实验室,南京210098

出　　处：《中国农村水利水电》2007年第9期23-25,29,共4页China Rural Water and Hydropower

基　　金：国家自然科学基金(50579015)

摘　　要：基于间断迦疗金有限元方法建立了求解二维、深度平均浅水方程的模型,该模型由浅水方程这一系列双曲方程组按照守恒律推导而得。通过在某一单元积分方程组并乘以基函数可以得到一个弱解,并假设未知量为间断分布的多项式逐个单元求解。由于间断有限元的本质具有局部特征,因此很容易通过提高插值多项式的次数来提高模拟精度。同时,间断有限元又具有局部守恒特征,可以结合数值通量来模拟高流动梯度问题。最后,给出了了间断有限元的内江数值模拟结果。A discontinuous Galerkin （DG） finite element method is utilized to solve the two-dimensional depth-integrated shallow water equations （SWEs）. These hyperbolic equations are derived following the laws of conservation. A weak solution is obtained by integrating the equations over a single element, and approximating the unknown variables by discontinuous polynomials. Because of its local nature of discontinuous FEM, the DG method can easily improve the simulation precision through increasing the polynomial order of approximation. The discontinuous FEM is also ‘locally conservative＇, so it is possible to simulate high velocity gradient through integrating numerical flux. Finally, numerical simulation results on Nei River using discontinuous FEM are Presented.

关 键 词：浅水方程 间断有限元 通量 黎曼算子 守恒 

分 类 号：O352[理学—流体力学] O241.82[理学—力学]