自适应大时间步长格式在一维浅水方程中应用

针对一维浅水方程提出了一种自适应大时间步长格式，具有较高计算精度和计算效率。在本格式中，依据波头与波尾传播速度差的绝对值，确定稀疏波近似波数。当波头与波尾速度相近时，稀疏波采用双波近似，以提高计算效率；当波头与波尾速度差距较大时，稀疏波采用十波近似，以获得较高计算精度。同时通过数值结果对比发现随机选取法（random choice method，RCM）可以有效抑制平台区域的震荡，但随着courant friedrichs lewy（CFL）数和时间的增加，RCM对间断处短波震荡抑制效果逐渐减弱。

Application of Adaptive Large Time Step Pattern in One-Dimensional Shallow Water Equations

In order to achieve higher computational accuracy and efficiency, an adaptive large time step (LTS) scheme relative to the one-dimensional shallow water equation is proposed in the present study. In this scheme, the approximate wave number of the rarefaction wave is determined in accordance with the absolute value of the velocity difference between head and tail of the wave. When the wave head is close to the wave tail, double wave approximation is employed by rarefaction wave to improve the calculation efficiency. On the other hand, when the wave head is far from the wave tail, ten wave approximation is adopted by the rarefaction wave to obtain higher calculation accuracy. At the same time, the comparison of numerical results shows that RCM method can effectively suppress the shock in the platform area, but with the increase of CFL number, RCM method has less effect on the short-wave shock suppression at the discontinuity.