A finite element variational multiscale method for the Navier-Stokes equations

Volker, John
Kaya Merdan, Songül
This paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space L-H for the velocity deformation tensor and a turbulent viscosity nu(T). The connection of this method to the standard formulation of a VMS is explained. The conditions on L-H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier - Stokes equations are studied. Numerical tests with the Smagorinsky large eddy simulation model for nu(T) are presented.


A model for the computation of quantum billiards with arbitrary shapes
Erhan, Inci M.; Taşeli, Hasan (Elsevier BV, 2006-10-01)
An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter.
An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows
Demir, Medine (Elsevier BV, 2020-10-01)
This 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, includin...
The boundary element solution of the magnetohydrodynamic flow in an infinite region
Tezer, Münevver; Bozkaya, Canan (Elsevier BV, 2009-03-15)
We consider the magnetohydrodynamic (MHD) flow which is laminar, steady and incompressible, of a viscous and electrically conducting fluid on the half plane (y >= 0). The boundary y = 0 is partly insulated and partly perfectly conducting. An external circuit is connected so that current enters the fluid at discontinuity points through external circuits and moves up on the plane. The flow is driven by the interaction of imposed electric currents and a uniform, transverse magnetic field applied perpendicular ...
Fundamental solution for coupled magnetohydrodynamic flow equations
Bozkaya, Canan; Tezer, Münevver (Elsevier BV, 2007-06-01)
In this paper, a fundamental solution for the coupled convection-diffusion type equations is derived. The boundary element method (BEM) application then, is established with this fundamental solution, for solving the coupled equations of steady magnetohydrodynamic (MHD) duct flow in the presence of an external oblique magnetic field. Thus, it is possible to solve MHD duct flow problems with the most general form of wall conductivities and for large values of Hartmann number. The results for velocity and ind...
A nested iterative scheme for computation of incompressible flows in long domains
Manguoğlu, Murat; Tezduyar, Tayfun E.; Sathe, Sunil (Springer Science and Business Media LLC, 2008-12-01)
We present an effective preconditioning technique for solving the nonsymmetric linear systems encountered in computation of incompressible flows in long domains. The application category we focus on is arterial fluid mechanics. These linear systems are solved using a nested iterative scheme with an outer Richardson scheme and an inner iteration that is handled via a Krylov subspace method. Test computations that demonstrate the robustness of our nested scheme are presented.
Citation Formats
J. Volker and S. Kaya Merdan, “A finite element variational multiscale method for the Navier-Stokes equations,” SIAM JOURNAL ON SCIENTIFIC COMPUTING, pp. 1485–1503, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42552.