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A Pressure Difference Adaptive Rotating Entropy Stable Scheme forTwo Dimensional Riemann Problems

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 作者 单位 邮编 郭依琳 长安大学 理学院 710064 郑素佩* 长安大学 理学院 710064 陈梦莹 长安大学 理学院 刘佳豪 长安大学 理学院

Euler方程是计算流体力学中描述流体运动的基本方程之一，间断解的存在是该类方程数值求解算法构造的一个难点。为得到二维Euler方程Riemann问题的高分辨率数值结果，本文构造了一种压差型自适应旋转熵稳定格式。利用方程的旋转不变性，将边界外法向量分解到两个正交方向，在每个方向上采用熵稳定格式。两分量方向的确定与旋转角有关，本文通过引入压力函数使格式的旋转角根据局部的压力变化进行自适应改变，熵稳定格式的分辨率可通过自适应旋转角的引入而改善。数值算例表明该格式的数值结果对称性好且分辨率高。

The Euler equation is one of the fundamental equations describing fluid motion in Computational Fluid Dynamics, and the existence of discontinuous solutions poses challenges in constructing numerical algorithms for solving this type of equation. To achieve high-resolution numerical results for the Riemann problem of the two-dimensional Euler equation, this paper constructs a pressure-difference adaptive rotating entropy stable scheme. Utilizing the rotating invariance of the equations, the normal vector outside the boundary is decomposed into two orthogonal directions, and an entropy stable scheme is implemented in each direction. The determination of the direction of the two components relies on the rotation angle, In this paper, a pressure function is introduced to adaptively adjust the rotation angle of the scheme based on local pressure variations, The resolution of the entropy stable scheme is enhanced by introducing the adaptive rotation angle. Numerical examples show that the numerical results obtained by this scheme exhibit good symmetry and high resolution.
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