基于局部时间步长方法的潮流数值模型研究及应用

为了准确快速地模拟潮流过程,将局部时间步长(LTS)方法应用于基于黎曼近似解通量——有限体积法的浅水模型。LTS方法和传统整体最小时间步长方法的计算性能对比表明,两种方法的计算结果定量差异远小于模拟值与实测值之间相对误差;但由于LTS方法对每个网格采用了与稳定性条件相适应的尽可能大的时间步长,计算效率大幅度提高。本模型计算所得渤海、黄海、东海的潮流传播过程、潮汐调和常数的空间分布、无潮点位置,以及长江口和杭州湾区域的潮流过程与已有认识和实测资料吻合良好。

Numerical simulation of tidal flows based on the local-time step approach

To accurately and rapidly simulate tidal flows, we applied the local time step approach (LTS approach) in a approximate Riemann solver-based finite-volume shallow water model. Comparative studies between the present local-time-step (LTS) approach and the traditional global-minimum (Gmi) time step approach show that the LTS approach results in negligible relative errors but brings significant reduction in the computational cost due to the use of the locally allowable maximum time step for each computational cell. The computed spatial distribution of tidal harmonic constants and the location of nodal points in the Bohai Sea, the Yellow Sea, the East China Sea are consistent with previous understanding/results. The computed tidal water level, tidal velocity and direction in the Yangtze estuary and Hangzhou Bay agree with the measured data quite well.