一种新的浅水方程黏性项计算格式的研究与应用

Derivation and application of a new numerical scheme of viscous term in shallow water equation

用浅水方程模拟某些紊流特性很强的流动时,紊动黏性项对数值解的稳定性和合理性至关重要。为提高浅水方程中黏性项的计算精度,首先对前人提出的两种计算格式进行精度分析,在此基础上提出了一种具有更高精度的计算格式。这种方法从有限体积法的特点出发,用单元形心的流速直接计算流速梯度,比使用奥高公式具有更高的精度。通过3个典型算例的比较,验证了该方法具有更好的数值稳定性,同时也证明了此格式能比较合理地反映平均水深流动问题中的一些紊流现象,在工程上具有较好的应用价值。

Viscous term is crucial to the stability and rationality of numerical solution when shallow water equation is used to simulate some flow patterns with strong turbulence characteristics. In order to improve the computational accuracy of viscous term, in this paper, two conventional numerical schemes are firstly analyzed, and based on which a new one with better accuracy is proposed. Inheriting from the nature of the finite volume method, this method directly calculates the velocity gradients by using the velocity at gird central point, which can achieve higher accuracy than Gauss formula. Three case studies fully proved that this method possesses better numerical stability, as well as the capability to reflect the basic rules of the turbulence in depth - aver- aged flow, being worth applying to some engineering practices.