通量向量分裂格式及有限体积法在水流模拟中的应用

Application of FVS and FVM to Water Flow Simulation

有限体积法（FVM）的方程是对控制体写出的积分形式的物理恒律．该法将计算域划分成若干不规则形状的控制体，对每个控制体分别进行水量和动量平衡计算，得出各控制体边界沿法向输入或输出的流量和动量通量，然后便可计算出时段末各控制体的平均水深和流速．该法的主要特色在于以高精度的通量向量分裂格式（FVS），通过求解局部黎曼问题来估算各网格边界上的法向通量．我们将以有限体积法为基础的二维水流模型应用于长江江苏段潮流数值模拟．同时，根据长江江苏段受弯道影响的特点对模型进行了一定的改进．结果证明：有限控制体积法（FVM）配合通量向量分裂格式（FVS）是一种具有高解析度的数值方法．

：The basic equation of the finite volume method， FVM， is obtained using the divergence theorem after being integrated． In FVM the unstructured mesh is used to represent the computational domain． Firstly， the mass and momentum fluxes through each side of every cell are calculated according to the balance theory． Then， the water elevation and depth-averaged velocity of each cell are obained at the end of each time interval． Two-dimensional unsteady flow model is based on the finite volume method． One of the attractive features of this model is to treat the calculation of the mass and momentum flux across each side of elements as a local Rieman problem that is solved using the flux vector splitting scheme（FVS）． The sample applications of this model have shown fairly satisfactory results，which include simulating the flow in Yangtze River reach of Jiangsu Province． Additionally，the model is improved to simulate the flow affected remarkably by river meander．