An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows

DEMİR M., Kaya S.

Applied Numerical Mathematics, vol.156, pp.140-157, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 156
  • Publication Date: 2020
  • Doi Number: 10.1016/j.apnum.2020.04.010
  • Journal Name: Applied Numerical Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.140-157
  • Keywords: Subgrid artificial viscosity model, Higher order, Finite element method, Navier-Stokes equations, Linearly extrapolated BDF2, VARIATIONAL MULTISCALE METHOD, TIME-STEPPING SCHEME, STOKES, STABILITY, APPROXIMATION, CONVERGENCE, EQUATIONS, ENERGY, ORDER
  • Middle East Technical University Affiliated: Yes


© 2020 IMACSThis report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, including both energy and helicity balance of the method. We also show that the approximate solutions of the method are unconditionally stable and optimally convergent. Several numerical tests are presented for validating the support of the derived theoretical results.