SUPG-YZ beta computation of chemically reactive convection-dominated nonlinear models

Cengizci S., UĞUR Ö., Natesan S.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.100, sa.2, ss.283-303, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 100 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1080/00207160.2022.2114794
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.283-303
  • Anahtar Kelimeler: Finite elements, nonlinear reaction kinetics, SUPG stabilization, YZ beta shock-capturing, convection-dominated, 76M10, 76V05, FINITE-ELEMENT APPROXIMATION, DIFFUSION-REACTION EQUATIONS, INVISCID SUPERSONIC FLOWS, DIMINISHING SOLD METHODS, SPURIOUS OSCILLATIONS, MOVING BOUNDARIES, STABILIZATION, FORMULATIONS, DISSIPATION, ADAPTIVITY
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this computational study, we deal with the stabilized finite element solutions of convection-dominated models having nonlinear reaction mechanisms. The existence of advection terms in these models causes the numerical solutions obtained by standard discretization methods to exhibit nonphysical oscillations. The Galerkin finite element method is stabilized using the Streamline-Upwind/Petrov-Galerkin formulation to avoid such spurious oscillations. The stabilized formulation is also complemented with the YZ beta shock-capturing technique to resolve steep gradients and discontinuities accurately. The nonlinear equation systems arising from the spatial discretizations are solved with the Newton-Raphson method supplemented with the ILU-preconditioned GMRES search technique. The proposed methods are tested on a comprehensive set of nonlinear reactive models. Numerical experiments show that the presented methods and techniques eliminate spurious oscillations significantly and resolve strong gradients accurately. All computations are performed in the FEniCS environment.