NUMERICAL ANALYSIS AND TESTING OF A FULLY DISCRETE, DECOUPLED PENALTY-PROJECTION ALGORITHM FOR MHD IN ELSASSER VARIABLE

AKBAŞ M., KAYA MERDAN S., MOHEBUJJAMAN M., rebholz l.

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, cilt.13, sa.1, ss.90-113, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2016
  • Dergi Adı: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.90-113
  • Anahtar Kelimeler: Magnetohydrodynamics, Elsasser variables, Penalty-projection method, finite element method, ELEMENT, STABILITY
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We consider a fully discrete, efficient algorithm for magnetohydrodynamic (MHD) flow that is based on the Elsasser variable formulation and a timestepping scheme that decouples the MHD system but still provides unconditional stability with respect to the timestep. We prove stability and optimal convergence of the scheme, and also connect the scheme to one based on handling each decoupled system with a penalty-projection method. Numerical experiments are given which verify all predicted convergence rates of our analysis on some analytical test problems, show the results of the scheme on a set of channel flow problems match well the results found when the computation is done with MHD in primitive variable, and finally show the scheme performs well on a channel flow over a step.