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对于浅水动边界(干湿边界)问题的数值模拟而言,保证水量守恒和复杂地形上单元半干(湿)处理是两大难题。该文在单元中心格式有限体积法的基础之上,提出了一个新的干湿边界判别方法:通过定义单元边界的干湿特性来判别单元本身的干湿特性。采用该判别方法,结合高效的HLLC黎曼算子计算模型通量,对二维浅水非恒定流问题的计算结果表明,这种判别方法既可以保证质量守恒,对复杂地形具有很高的自适应性;同时对间断流的单元半干(湿)处理简易高效。
For the numerical simulation of the shallow-water boundary (wet-dry boundary) problem, it is two major problems to ensure the water conservation and the semi-dry treatment of the unit on the complex terrain. Based on the finite volume method of cell center format, a new wet-dry boundary method is proposed in this paper. The wet-dry characteristics of the cell itself are determined by defining the wet-dry properties of cell boundaries. By using the discriminant method and the efficient HLLC Riemann operator to calculate the model fluxes, the calculation results of two-dimensional shallow water unsteady flow show that the method can not only ensure the mass conservation but also have high adaptability to complex terrains While semi-dry (wet) treatment of discontinuous flow is simple and efficient.