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建立了一种在非规则结构化网格上求解平面二维浅水流动的有限体积方法。通过采用地形在离散网格内双线性变化及离散网格界面间地形连续的地形逼近方法和应用可以有效处理间断问题的Roe格式来离散浅水方程中的对流项,并通过VanLeer提出的状态插值法提高格式精度。在计算原始变量在网格内的插值梯度时,采用最小二乘方法求变量的最优梯度代替差分计算梯度,从而可采用任意形状的不规则四边形网格离散计算域。计算实例表明,该方法能够计算间断问题并能够处理各种复杂流态的过渡,具有较好适应性和计算精度,能够满足不同实际问题的计算要求。
A finite volume method for solving two-dimensional planar shallow water flow on an irregular structured grid is established. The convection term in the shallow water equation is discretized by using the terrain approximation method with bilinear changes in the discrete grid and the continuous terrain approximation between discrete grid interfaces and the Roe scheme which can effectively deal with the discontinuous problems. Law to improve the format accuracy. When calculating the interpolation gradient of the original variable in the grid, the optimal gradient of the least square method is used to calculate the gradient instead of the differential gradient, so the random quadrangular mesh with arbitrary shape can be used to discretize the computational domain. The calculation example shows that this method can calculate the discontinuity problem and can handle the transition of complex flow regimes. It has good adaptability and computational accuracy, and can meet the computational requirements of different practical problems.