求解二维浅水波方程的移动网格旋转通量法

为提高求解二维浅水波方程数值算法的分辨率,拟构造求解该方程的新算法:基于移动网格法,选用熵稳定数值通量函数,利用旋转不变性得到混合数值通量.该算法中,浅水波方程的数值求解和依据解的特性进行自适应疏密分布的网格计算过程交错进行.利用变分原理进行网格重构,新网格上的物理量采用二阶精度的守恒型插值公式计算,最终采用三阶强稳定Runge-Kutta法与满足热力学第二定律的熵稳定格式实现浅水波方程的数值求解.数值结果表明,新算法具有良好的间断捕捉能力,分辨率高.

Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method

In order to improve the resolution of the numerical algorithm for solving the 2D shal low water wave equation,a new algorithm was proposed based on the moving-grid method,with the entropy stable numerical flux function and by means of the mixed numerical flux ob tained through the rotating invariance.The numerical solution of the shallow water wave equa tion and the grid computation process based on the characteristics of the solution were inter leaved.The variational principle was used to reconstruct the mesh,and the physical quantity on the new mesh was computed with the 2nd-order precision conservation interpolation formula.The 3rd-order strongly stable Runge-Kutta method and the entropy stable format satisfying the 2nd law of thermodynamics were used to numerically solve the shallow water wave equation.The numerical results show that,the new algorithm has good discontinuity capture ability and high resolution.