浅水波方程混合旋转通量旋转角的研究

Study on the Rotation Angle of Mixed Rotational Flux in the Shallow Water Equation

摘要: 本文在浅水波方程的混合旋转通量的基础上，对通量旋转角进行分析及研究。在单元界面法向方向采用具有良好鲁棒性且可消除红斑现象的HLL格式，在单元界面切线方向上采用满足热力学第二定律的熵稳定格式，两者进行结合，时间方向采用三阶强稳定Runge-Kutta方法，得到混合旋转通量算法。基于Euler方程通过压力加权函数定义旋转角度的策略，对浅水波方程混合旋转通量的旋转角给出不同的方案并进行数值实验，验证算法的有效性，确定最佳旋转角度。

Abstract: Based on the mixed rotational flux of the shallow water equations, this paper conducts an analysis and research on the flux rotation angle. For the normal direction of the element interface, the HLL scheme—characterized by excellent robustness and the ability to eliminate the “red spot” phenomenon is adopted; for the tangential direction of the element interface, an entropy-stable scheme that satisfies the second law of thermodynamics is used. By combining these two schemes and applying the third-order strongly stable Runge-Kutta method in the time direction, a mixed rotational flux algorithm is derived. Drawing on the strategy of defining the rotation angle via a pressure-weighted function based on the Euler equations, different schemes for the rotation angle of the mixed rotational flux in the shallow water equations are proposed. Numerical experiments are carried out to verify the effectiveness of the algorithm and determine the optimal rotation angle.