Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations

© 2022 Elsevier Inc.This paper considers the backward Euler based linear time filtering method for the developed energy-momentum-angular momentum conserving (EMAC) formulation of the time dependent-incompressible Navier-Stokes equations in the case of weakly enforced divergence constraint. The method adds time filtering as a post-processing step to the EMAC formulation to enhance the accuracy and to improve the approximate solutions. We show that in comparison with the Backward-Euler based EMAC formulation without any filter, the proposed method not only leads to a 2-step, unconditionally stable and second order accurate method but also increases numerical accuracy of solutions. Numerical studies verify the theoretical findings and demonstrate preeminence of the proposed method over the unfiltered case.
Journal of Mathematical Analysis and Applications


Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the Navier-Stokes equations
Vargün, Duygu; Kaya Merdan, Songül; Department of Mathematics (2018)
This thesis studies a projection-based variational multiscale (VMS) method based on a linearly extrapolated second order backward difference formula (BDF2) to simulate the incompressible time-dependent Navier-Stokes equations (NSE). The method concerns adding stabilization based on projection acting only on the small scales. To give a basic notion of the projection-based VMS method, a three-scale VMS method is explained. Also, the principles of the projection-based VMS stabilization are provided. By using t...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems
Bozkaya, Canan (2005-03-18)
The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Least-squares finite element solution of Euler equations with adaptive mesh refinement
Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012)
Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
AKBAŞ, MERAL; Kaya, Serap; Kaya Merdan, Songül (2017-07-01)
We prove long-time stability of linearly extrapolated BDF2 (BDF2LE) timestepping methods, together with finite element spatial discretizations, for incompressible Navier-Stokes equations (NSE) and related multiphysics problems. For the NSE, Boussinesq, and magnetohydrodynamics schemes, we prove unconditional long time L-2 stability, provided external forces (and sources) are uniformly bounded in time. We also provide numerical experiments to compare stability of BDF2LE to linearly extrapolated Crank-Nicolso...
Parallel processing of two-dimensional euler equations for compressible flows
Doǧru, K.; Aksel, M.h.; Tuncer, İsmail Hakkı (2008-12-01)
A parallel implementation of a previously developed finite volume algorithm for the solution of two-dimensional, unsteady, compressible Euler equations is given. The conservative form of the Euler equations is discretized with a second order accurate, one-step Lax-Wendroff scheme. Local time stepping is utilized in order to accelerate the convergence. For the parallel implementation of the method, the solution domain is partitioned into a number of subdomains to be distributed to separate processors for par...
Citation Formats
M. Demir, A. Çıbık, and S. Kaya Merdan, “Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations,” Journal of Mathematical Analysis and Applications, vol. 516, no. 2, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85135520674&origin=inward.