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Two-level defect-correction stabilized algorithms for the simulation of 2D/3D steady Navier-Stokes equations with damping
Applied Numerical Mathematics ( IF 2.8 ) Pub Date : 2021-01-20 , DOI: 10.1016/j.apnum.2021.01.008
Bo Zheng , Yueqiang Shang

By combining the defect-correction method with the two-level discretization strategy and the local pressure projection stabilized method, this paper presents and studies two kinds of two-level defect-correction stabilized algorithms for the simulation of 2D/3D steady Navier-Stokes equations with damping, where the lowest equal-order P1P1 finite elements are used for the velocity and pressure approximations. In the proposed algorithms, an artificial viscosity stabilized nonlinear Navier-Stokes problem with damping is first solved in the coarse grid defect step, and then corrections are computed in the fine grid correction step by solving a linear problem based on Oseen-type and Newton-type iterations, respectively. Under the uniqueness condition, stability of the proposed algorithms is analyzed, and optimal error estimates of the approximate solutions are deduced. The correctness of the theoretical predictions and the effectiveness of the proposed algorithms are illustrated by some 2D and 3D numerical results.



中文翻译:

两级缺陷校正稳定算法,用于模拟带有阻尼的2D / 3D稳定Navier-Stokes方程

通过将缺陷校正方法与两级离散化策略和局部压力投影稳定化方法相结合,提出并研究了两种两级缺陷校正稳定化算法,用于2D / 3D稳态Navier-Stokes方程的仿真。带阻尼,最低等次 P1个-P1个有限元用于速度和压力的近似。在提出的算法中,首先在粗网格缺陷步骤中解决了带有阻尼的人工黏性稳定非线性Navier-Stokes问题,然后在精细网格校正步骤中通过解决基于Oseen型和Newton-类型迭代。在唯一性条件下,分析了所提算法的稳定性,推导了近似解的最优误差估计。一些2D和3D数值结果说明了理论预测的正确性和所提出算法的有效性。

更新日期:2021-01-20
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