曲线坐标网格下二维涌波数值模拟的TVD型格式

针对水动力学中的涌波现象导出二维曲线坐标系下的守恒型方程，然后利用算子分裂法和TVD差分格式思想构造出计算格式，在此基础上建立起由实际流场区域至方形计算区域的全局同胚映射，对急流过缩窄河道产生的涌波结构进行数值模拟，结果表明，本文的数值方法能够很好地模拟附体涌波、交叉涌波等复杂结构现象，所得波系结构和有关物理量与理论分析结果非常吻合，表明本文的数值方法对于模拟水动力学中的涌波现象是可行的。

Application of TVD scheme to numerical simulation of 2-D surge in curvilinear coordinates

The TVD scheme is designed for numerical simulation of 2-D surge with curvilinear coordinates meshes.The basic concept of this method is to establish the conservation equation for shallow water wave in 2-D curvilinear coordinate system and then to construct the computational scheme by using the split operator method and TVD scheme.Before using this scheme to simulate the practical flow field,a global homeomorphic mapping must be established to transform the flow field into a square computational field.The numerical simulation of the surge generated by a narrowed channel shows that the proposed method is feasible to the calculation of complicated flow such as attached surge,cross surge and etc.The calculated wave construction and relevant physical variants are in good agreement with the theoretical analysis.