Zhao Yanzi, Feng Xinlong
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
Entropy (Basel). 2022 Sep 23;24(10):1338. doi: 10.3390/e24101338.
In this paper, an effective numerical algorithm for the Stokes equation of a curved surface is presented and analyzed. The velocity field was decoupled from the pressure by the standard velocity correction projection method, and the penalty term was introduced to make the velocity satisfy the tangential condition. The first-order backward Euler scheme and second-order BDF scheme are used to discretize the time separately, and the stability of the two schemes is analyzed. The mixed finite element pair (P2,P1) is applied to discretization of space. Finally, numerical examples are given to verify the accuracy and effectiveness of the proposed method.
本文提出并分析了一种用于曲面斯托克斯方程的有效数值算法。通过标准速度修正投影法将速度场与压力解耦，并引入惩罚项以使速度满足切向条件。分别采用一阶向后欧拉格式和二阶BDF格式对时间进行离散，并分析了两种格式的稳定性。采用混合有限元对(P2,P1)对空间进行离散。最后，通过数值算例验证了所提方法的准确性和有效性。
