A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions

Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-homogeneous Dirichlet boundary conditions are considered...

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Bibliographic Details
Published in:Advances in computational mathematics Vol. 50; no. 1; p. 3
Main Authors: Zheng, Bo, Shang, Yueqiang
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2024
Springer Nature B.V
Subjects:
Algorithms
Boundary conditions
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Defects
Fluid flow
High Reynolds number
Incompressible flow
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Multiscale analysis
Reynolds number
Stability analysis
Stiffness matrix
Visualization
Defect-correction method
Two-grid method
Variational multiscale method
Stabilized finite element method
76D05
65N55
65N30
Navier-Stokes equations
ISSN:1019-7168, 1572-9044
Online Access:Get full text
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Summary:Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-homogeneous Dirichlet boundary conditions are considered and high Reynolds numbers are allowed. In this developed algorithm, we first solve an artificial viscosity stabilized nonlinear problem on a coarse grid in a defect step and then correct the resulting residual by solving two stabilized and linearized problems on a fine grid in correction steps. While the fine grid correction problems have the same stiffness matrices with only different right-hand sides. We use a variational multiscale method to stabilize the system, making the algorithm has a broad range of potential applications in the simulation of high Reynolds number flows. Under the weak uniqueness condition, we give a stability analysis of the present algorithm, analyze the error bounds of the approximate solutions, and derive the algorithmic parameter scalings. Finally, we perform a series of numerical examples to demonstrate the promise of the proposed algorithm.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-023-10101-8