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

Takhirov A., Çıbık A. B., Eroğlu F. G., Kaya Merdan S.

Journal of Scientific Computing, vol.96, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s10915-023-02277-4
  • Journal Name: Journal of Scientific Computing
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Keywords: Arrow–Hurwicz, Steady-state Navier–Stokes equations, Two-grid
  • Middle East Technical University Affiliated: Yes

Abstract

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.