ON THE LINEARIZATION OF DEFECT-CORRECTION METHOD FOR THE STEADY NAVIER-STOKES EQUATIONS

Title & Authors
ON THE LINEARIZATION OF DEFECT-CORRECTION METHOD FOR THE STEADY NAVIER-STOKES EQUATIONS
Shang, Yueqiang; Kim, Do Wan; Jo, Tae-Chang;

Abstract
Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $\small{m}$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $\small{h}$, the kinematic viscosity $\small{{\nu}}$, the stability factor $\small{{\alpha}}$ and the number of nonlinear iterations $\small{m}$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.
Keywords
Navier-Stokes equations;finite element;defect-correction method;Newton iteration;Picard iteration;
Language
English
Cited by
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