非规则网格下二维浅水流动的数值模拟

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。

Numerical simulation of 2-D shallow-water flow on irregular grids

A numerical model for solving the 2-D shallow-water flow on irregular grids is described. The model based on finite-wlume method adopts the Roe's approximate Riemann solver to deal with the advection terms in the shallow-water equations. A bilinear approximation for the topography in a discrete cell is introduced to preclude the restrictions on the Roe's scheme duo to bed slope. And a modified MUSQ, technique is combined to obtain an increased accuracy. Instead of unilateral difference method,the least square method is used to find the gradient of the primitive variables so that irregular grids can be used. The results of several examples show that the model is capable of treating discontinuities and flow transients,and is good accuracy as well as performance for different applications.