An Improved Arrow–Hurwicz Method for the Steady-State Navier–Stokes Equations

Date

2023-06-01

Author

Takhirov, Aziz
Çıbık, Aytekin Bayram
Eroğlu, Fatma Güler
Kaya Merdan, Songül

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This paper presents a novel Arrow–Hurwicz type method for approximating the steady-state Navier Stokes equations using the finite element method. The novel method is inspired from artificial compressibility regularization of unsteady incompressible flows and allows one to circumvent solving saddle-point equations. We derive uniform boundedness and convergence to the exact solution whenever the small data condition for uniqueness of the solution is satisfied. A two-grid version of the scheme is also discussed. Numerical schemes show that the novel scheme significantly accelerates the convergence, without any additional computational cost or decreased accuracy.

URI

https://hdl.handle.net/11511/104635

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Department of Mathematics, Article