基于AUSM^+-UP格式的有限体积模型及其在钱塘江河口的应用

Finite volume model for solving discontinuous shallow water flow with AUSM^+-UP schemes

通过引入空气动力学计算领域中发展起来的AUSM+-UP格式,建立了基于非结构网格的有限体积法求解二维间断浅水流动的数学模型。模型通过变量重构和梯度限制将空间精度提高到二阶,同时使用单元节点水深计算压力项以实现源项平衡,并对动边界进行特殊处理。最后模拟了两个经典的水力学算例和钱塘江河口潮流运动实例,结果表明模型不仅保持了AUSM+-UP格式的各种优点,而且在实际应用中具有良好的精度及适用性。

AUSM ＋ -UP schemes are used to develop a finite-volume numerical model on unstructured grids for solution of the 2D shallow-water flow equations. Combining these schemes with multi-dimensional gradient reconstruction and slope limiting techniques for calculation of the inviscid fluxes, a second-order accuracy in space is achieved. Calculation of pressure term based on flow depths at the cell vertices is well balanced with source terms, and the drying-wetting moving boundary is specifically handled. The accuracy and applicability of this model is verified with two test problems and a real tidal flow case of the Qiantang river.