微极Navier-Stokes方程的一种二阶时间步算法

A Second-Order Time-Step Algorithm for the Micropolar Navier-Stokes Equations

摘要: 针对微极Navier-Stokes方程(MNSE)，我们提出了一种新的二阶时间步算法。对MNSE中的非线性项进行了线性化处理，并在线速度、压力和角速度的离散解中加入了“曲率稳定”项，旨在改进常用的“速率稳定”。该方法不仅克服了阻力产生的数值不稳定，并且在不增加计算复杂性的情况下将解的精度从一阶提高到二阶。然后我们给出了算法的无条件稳定性。最后，通过数值实验验证了预测的收敛速度。

Abstract: We propose a new second-order time-step algorithm for the micropolar Navier-Stokes equations (MNSE). The nonlinear term in MNSE is linearized, and the term “curvature stabilization” is added to the discrete solutions of online velocity, pressure and angular velocity, which aims to improve the commonly used “rate stabilization”. This method not only overcomes the numerical instability caused by resistance, but also improves the accuracy of the solution from the first order to the second order without increasing the computational complexity. And then we give the unconditional stability of the algorithm. Finally, the predicted convergence rate is verified by numerical experiments.