一维浅水方程组的间断有限元计算

根据间断有限元法的基本原理,选用正交化基函数,构造求解一维浅水方程的计算格式。采用这种算法并对浅水方程的底坡源项按水面梯度法进行处理,可以获得较高精度的模拟结果。对二个模型算例的数值模拟结果表明:该算法对拟恒定流和非恒定流模拟都有较高的分辨率,具有处理间断问题的锐利波形能力,适合浅水流动的数值模拟。

Discontinuous finite-element method for one-dimensional shallow water equations

According to the principle of discontinuous finite-element method and selection of orthogonal basis shape functions,the computational scheme is developed for the shallow water equations.The bottom slope source terms is treated with surface gradient method so as to obtain the high-order accuracy result in the scheme.The simulation of three examples shows that the method has high-resolution when it is applied in unsteady and quasi-steady flows with the sharp wave in discontinuous problems and suitable to computation of the shallow water flows.