河流流场数值模拟初始场误差发展研究

为分析河流初始场误差对计算结果的影响,利用小扰动方法推导了流动模拟过程中初始场误差发展的控制方程,并依照湖泊假潮的形式得到了方程的分析解。理论结果表明,在通常的边界条件下,初始场误差相当于在流动中附加了一个虚拟的长波,这种波动以驻波的形式存在于河流中,波长是河段长度的4倍,波周期可用梅立恩公式近似估计。在底摩擦的作用下,误差波将会迅速衰减直至消失,充分显示了流场的强耗散特性。通过数值计算实例验证了理论分析的结果。

Study on the evolution of initial field error in the simulation of river flow

In order to estimate the influence of the initial field error on the fiver simulation, the governing equation is developed by the small perturbation method in this paper. The analytical solution to the equation is derived according to the form of the seiche wave. The theoretical result shows that the initial field error is equivalent to an extra numerical wave imposed on the simulated fiver. The numerical wave exists as standing wave, whose length is four times of the simulated fiver length. Its period can be estimated by the Merian formula, where the friction impact can be neglected. The error wave disappears quickly, which reveals the strong dissipation of the velocity field. The analysis is validated by a numerical simulation in a natural river.