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

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

JOURNAL OF SCIENTIFIC COMPUTING, cilt.96, sa.2, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 96 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s10915-023-02277-4
  • Dergi Adı: JOURNAL OF SCIENTIFIC COMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Arrow–Hurwicz, Steady-state Navier–Stokes equations, Two-grid
  • Gazi Üniversitesi Adresli: Evet

Özet

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.