Simulations of nonlinear advection-diffusion models through various finite element techniques

Tunc H., Sari M.

SCIENTIA IRANICA INTERNATIONAL JOURNAL OF SCIENCE & TECHNOLOGY, cilt.27, sa.6, ss.2853-2870, 2020 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 6
  • Basım Tarihi: 2020
  • Doi Numarası: 10.24200/sci.2019.51513.2228
  • Dergi Adı: SCIENTIA IRANICA INTERNATIONAL JOURNAL OF SCIENCE & TECHNOLOGY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Geobase, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.2853-2870
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

In this study, the Burgers equation is analyzed in both numerically and mathematically by considering various finite element based techniques including Galerkin, Taylor-Galerkin and collocation methods for spatial variation of the equation. The obtained time dependent ordinary differential equation system is approximately solved by α-family of time approximation. All these methods are theoretically explained using cubic B-spline basis and weight functions for a strong form of the model equation. Von Neumann matrix stability analysis is performed for each of these methods and stability criteria are determined in terms of the problem parameters. Some challenging examples of the Burgers equation are numerically solved and compared with the literature and exact solutions. Also, the proposed techniques have been compared with each other in terms of their advantageous and disadvantageous depending on the problem types. The more advantageous method of the three, comparison to other two, has been found out for the special cases of the present problem in detail.