NUMERICAL ANALYSIS AND TESTING OF A FULLY DISCRETE, DECOUPLED PENALTY-PROJECTION ALGORITHM FOR MHD IN ELSASSER VARIABLE

Date

2016-01-01

Author

AKBAŞ, MİNE
Kaya Merdan, Songül
MOHEBUJJAMAN, Muhammed
rebholz, leo

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 consider a fully discrete, efficient algorithm for magnetohydrodynamic (MHD) flow that is based on the Elsasser variable formulation and a timestepping scheme that decouples the MHD system but still provides unconditional stability with respect to the timestep. We prove stability and optimal convergence of the scheme, and also connect the scheme to one based on handling each decoupled system with a penalty-projection method. Numerical experiments are given which verify all predicted convergence rates of our analysis on some analytical test problems, show the results of the scheme on a set of channel flow problems match well the results found when the computation is done with MHD in primitive variable, and finally show the scheme performs well on a channel flow over a step.

Subject Keywords

Magnetohydrodynamics, Elsasser variables, Penalty-projection method, Finite element method

URI

https://hdl.handle.net/11511/54622

Journal

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions AYDIN, AYHAN; Karasözen, Bülent (2009-01-01) Systems of coupled non-linear Schrodinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton sol...
Numerical Solution of Multi-scale Electromagnetic Boundary Value Problems by Utilizing Transformation-Based Metamaterials Ozgun, Ozlem; Kuzuoğlu, Mustafa (2011-06-23) We present numerical solution techniques for efficiently handling multi-scale electromagnetic boundary value problems having fine geometrical details or features, by utilizing spatial coordinate transformations. The principle idea is to modify the computational domain of the finite methods (such as the finite element or finite difference methods) by suitably placing anisotropic metamaterial structures whose material parameters are obtained by coordinate transformations, and hence, to devise easier and effic...
Software metamaterials: Transformation media based multi-scale techniques for computational electromagnetics Ozgun, Ozlem; Kuzuoğlu, Mustafa (2013-03-01) This paper presents computational models employing special transformation-based media-which we call software metamaterials-for the purpose of enhancing the ability of numerical modeling methods for solving multi-scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both. The multi-scale problems, in general, suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the pro...
Numerical Modelling and Experimental Analysis of Vibratory and Acoustics Behaviours of a Special Design Squirrel-Cage Three-Phase Asynchronous Machine Ionescu, R. M.; Negoita, A.; N'Diaye, A.; Torregrossa, D.; Djerdir, A.; Miraoui, A.; Scutaru, Gh. (2011-09-10) The paper presents a comparison between the obtained results from testing a special design 5 kW squirrel-cage three-phase asynchronous machine and the numerical model of the same machine, simulated under the FLUX2D Finite Element Software. The aim is to validate the numerical model in the loaded and unloaded cases. The resulting model will be used for further research into the vibratory behaviour and noise of the motor. In this paper, an experimental approach is used to show the influence of load on motor v...
Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations Akinci, Gokay; YILMAZ, ASIM EGEMEN; Kuzuoğlu, Mustafa (2014-12-01) Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage sche...

Citation Formats

M. AKBAŞ, S. Kaya Merdan, M. MOHEBUJJAMAN, and l. rebholz, “NUMERICAL ANALYSIS AND TESTING OF A FULLY DISCRETE, DECOUPLED PENALTY-PROJECTION ALGORITHM FOR MHD IN ELSASSER VARIABLE,” INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, pp. 90–113, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54622.