An Explicitly Decoupled Variational Multiscale Method for Incompressible, Non-Isothermal Flows

Date

2015-01-01

Author

Belenli, Mine A.
Kaya Merdan, Songül
Rebholz, Leo G.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

223
views

0
downloads

We propose, analyze and test a fully decoupled, but still unconditionally stable and optimally accurate, variational multiscale stabilization (VMS) for incompressible, non-isothermal fluid flows. The VMS stabilization is implemented as a post-processing step, and thus can be used with existing codes. A full numerical analysis of the method is given that proves unconditional stability with respect to the timestep size, and that the method converges optimally in both time and space. Numerical tests are provided that confirm the theoretical results, and test the method on a benchmark problem for Marsigli flow.

Subject Keywords

Applied Mathematics, Numerical Analysis, Computational Mathematics

URI

https://hdl.handle.net/11511/36771

Journal

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS

DOI

https://doi.org/10.1515/cmam-2014-0026

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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...
A finite element variational multiscale method for the Navier-Stokes equations Volker, John; Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) 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 ...
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.
A unified approach for the formulation of interaction problems by the boundary element method Mengi, Y; Argeso, H (Wiley, 2006-04-30) A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid-solid and soil-structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods....
A tearing-based hybrid parallel sparse linear system solver NAUMOV, Maxim; Manguoğlu, Murat; SAMEH, Ahmed (Elsevier BV, 2010-09-15) We propose a hybrid sparse system solver for handling linear systems using algebraic domain decomposition-based techniques. The solver consists of several stages. The first stage uses a reordering scheme that brings as many of the largest matrix elements as possible closest to the main diagonal. This is followed by partitioning the coefficient matrix into a set of overlapped diagonal blocks that contain most of the largest elements of the coefficient matrix. The only constraint here is to minimize the size ...

Citation Formats

M. A. Belenli, S. Kaya Merdan, and L. G. Rebholz, “An Explicitly Decoupled Variational Multiscale Method for Incompressible, Non-Isothermal Flows,” COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, pp. 1–20, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36771.