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在采用浅水方程的洪水模拟中,经典的交替方向隐式格式(ADI)被认为不能用来计算跨临界流。这种格式会在自由水面和流速急剧变化的地方产生非物理振荡。然而,实际中这种格式仍然被广泛应用于商业计算软件。为了能够用ADI格式在模拟跨临界流时能够得到稳定的数值结果,修改动量修正系数(Boussinesq系数)这种数值处理方法能够部分地减轻ADI模型在模拟跨临界流时遇到的困难。该文通过对一维恒定流条件下的高速明渠流动问题的数值模拟,以及二维英国Boscastle地区洪水波的数值模拟,系统地评估了这种数值处理方法对模型计算的影响,并对比了ADI和具有激波捕捉能力的TVD-Mac Cormack模型的计算结果。结果表明,随着动量修正系数的减小,可以有效抑制ADI格式产生的数值振荡,但同时会降低水深的预测值。这些结果有助于评估数值格式在模拟跨临界流动时的准确性。
In flood modeling using the shallow water equations, the classical Alternating Direction Implicit Format (ADI) is considered not to be used to calculate transcritical flows. This format creates non-physical oscillations where the free surface and the velocity of flow vary dramatically. However, in practice, this format is still widely used in commercial computing software. In order to be able to obtain stable numerical results in simulating transcritical flow in ADI format, the numerical processing method of modifying the momentum correction coefficient (Boussinesq coefficient) can partially alleviate the difficulties of ADI model in simulating transcritical flow. This paper systematically evaluates the effect of this numerical method on the model calculation through numerical simulation of the high speed open channel flow under one-dimensional constant flow conditions and the numerical simulation of two-dimensional Boscastle flood in the UK. And TVD-Mac Cormack model with shock-capture capability. The results show that with the reduction of the momentum correction coefficient, the numerical oscillation produced by ADI format can be effectively suppressed, but at the same time, the prediction value of water depth will be reduced. These results help to evaluate the accuracy of the numerical format when simulating transcritical flow.