Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime

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Ceylan T., Okutmuştur B.

TURKISH JOURNAL OF MATHEMATICS, cilt.41, ss.1027-1041, 2017 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1602-38
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1027-1041
  • Anahtar Kelimeler: Relativistic Burgers equation, spacetime, Schwarzschild-de Sitter metric, Schwarzschild-de Sitter background, finite volume method, Godunov scheme, SCHEMES
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive there lativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constantis also taken into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments.

The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds haverecently been derived and analyzed numerically via nite volume approximation based on the concerned models. In thiswork, we derive the relativistic Burgers equation on a Schwarzschild{(anti-)de Sitter spacetime and introduce a second-order Godunov-type nite volume scheme for the approximation of discontinuous solutions to the model of interest. Theeffect of the cosmological constant is also taken into account both theoretically and numerically. The efficiency of themethod for solutions containing shock and rarefaction waves are presented by several numerical experiments.