Parallel pressure projection stabilized finite element algorithms based on two-grid discretizations for incompressible flows

ABSTRACT

Based on two-grid discretizations, three parallel pressure projection stabilized finite element algorithms are investigated and compared for solving the steady-state incompressible Navier–Stokes equations. In these parallel stabilized algorithms, a global stabilized nonlinear problem is first solved by Oseen iterative method on a coarse grid, and then local stabilized and linearized problems are independently solved on overlapping local fine grid, where the stabilization terms are based on two local Gauss integrations for the coarse and fine grid problems. Theoretical results show that with appropriate scalings of the algorithmic parameters, the proposed algorithms can yield an optimal convergence rate. Some numerical examples are also provided to verify the correctness of theoretical predictions and demonstrate the high efficiency of the algorithms.

KEYWORDS:

• Navier–Stokes equations
• two-grid discretizations
• parallel algorithm
• finite element
• pressure projection stabilization

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 76D05
• 65N55
• 65N30

Acknowledgements

The authors would like to express their deep gratitude to the anonymous reviewers for their valuable comments and suggestions, which led to an improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Science Foundation of China (No. 11361016), the Basic and Frontier Explore Program of Chongqing Municipality, China (No. cstc2016jcyjA0348) and Fundamental Research Funds for the Central Universities (No. XDJK2018B032).