A monolithic approach for the incompressible magnetohydrodynamics equations

Kayhan Ata; Mehmet Sahin

A monolithic approach for the incompressible magnetohydrodynamics equations

Kayhan Ata, Mehmet Sahin

Department of Astronautical Engineering

Istanbul Technical University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

A numerical algorithm has been developed to solve the incompressible magneto-hydrodynamics (MHD) equations in a fully coupled form. The numerical approach is based on the side centered finite volume approximation where the velocity and magnetic filed vector components are defined at the center of edges/faces, meanwhile the pressure term is defined at the element centroid. In order to enforce a divergence free magnetic field, a magnetic pressure is introduced to the induction equation. The resulting large-scale algebraic linear equations are solved using a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains. The parallel implementation of the present fully coupled unstructured MHD solver is based on the PETSc library for improving the efficiency of the parallel algorithm. The numerical algorithm is validated for 2D lid-driven cavity flows and backward step problems for both conducting and insulating walls.

Original language	English
Title of host publication	Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017
Editors	Manolis Papadrakakis, Eugenio Onate, Bernhard A. Schrefler
Publisher	International Center for Numerical Methods in Engineering
Pages	491-501
Number of pages	11
ISBN (Electronic)	9788494690921
Publication status	Published - 2017
Event	7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017 - Rhodes Islad, Greece Duration: 12 Jun 2017 → 14 Jun 2017

Publication series

Name	Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017
Volume	2017-January

Conference

Conference	7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017
Country/Territory	Greece
City	Rhodes Islad
Period	12/06/17 → 14/06/17

Bibliographical note

Publisher Copyright:
© 2017 International Center for Numerical Methods in Engineering. All rights reserved.

Keywords

Backward facing step
Incompressible magnetohydrodynamics
Lid-driven cavity
Monolithic
Semi-staggered finite volume method

Cite this

Ata, K., & Sahin, M. (2017). A monolithic approach for the incompressible magnetohydrodynamics equations. In M. Papadrakakis, E. Onate, & B. A. Schrefler (Eds.), Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017 (pp. 491-501). (Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017; Vol. 2017-January). International Center for Numerical Methods in Engineering.

Ata, Kayhan ; Sahin, Mehmet. / A monolithic approach for the incompressible magnetohydrodynamics equations. Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017. editor / Manolis Papadrakakis ; Eugenio Onate ; Bernhard A. Schrefler. International Center for Numerical Methods in Engineering, 2017. pp. 491-501 (Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017).

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title = "A monolithic approach for the incompressible magnetohydrodynamics equations",

abstract = "A numerical algorithm has been developed to solve the incompressible magneto-hydrodynamics (MHD) equations in a fully coupled form. The numerical approach is based on the side centered finite volume approximation where the velocity and magnetic filed vector components are defined at the center of edges/faces, meanwhile the pressure term is defined at the element centroid. In order to enforce a divergence free magnetic field, a magnetic pressure is introduced to the induction equation. The resulting large-scale algebraic linear equations are solved using a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains. The parallel implementation of the present fully coupled unstructured MHD solver is based on the PETSc library for improving the efficiency of the parallel algorithm. The numerical algorithm is validated for 2D lid-driven cavity flows and backward step problems for both conducting and insulating walls.",

keywords = "Backward facing step, Incompressible magnetohydrodynamics, Lid-driven cavity, Monolithic, Semi-staggered finite volume method",

author = "Kayhan Ata and Mehmet Sahin",

note = "Publisher Copyright: {\textcopyright} 2017 International Center for Numerical Methods in Engineering. All rights reserved.; 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017 ; Conference date: 12-06-2017 Through 14-06-2017",

year = "2017",

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series = "Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017",

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Ata, K & Sahin, M 2017, A monolithic approach for the incompressible magnetohydrodynamics equations. in M Papadrakakis, E Onate & BA Schrefler (eds), Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017. Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017, vol. 2017-January, International Center for Numerical Methods in Engineering, pp. 491-501, 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017, Rhodes Islad, Greece, 12/06/17.

A monolithic approach for the incompressible magnetohydrodynamics equations. / Ata, Kayhan; Sahin, Mehmet.
Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017. ed. / Manolis Papadrakakis; Eugenio Onate; Bernhard A. Schrefler. International Center for Numerical Methods in Engineering, 2017. p. 491-501 (Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017; Vol. 2017-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Sahin, Mehmet

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N2 - A numerical algorithm has been developed to solve the incompressible magneto-hydrodynamics (MHD) equations in a fully coupled form. The numerical approach is based on the side centered finite volume approximation where the velocity and magnetic filed vector components are defined at the center of edges/faces, meanwhile the pressure term is defined at the element centroid. In order to enforce a divergence free magnetic field, a magnetic pressure is introduced to the induction equation. The resulting large-scale algebraic linear equations are solved using a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains. The parallel implementation of the present fully coupled unstructured MHD solver is based on the PETSc library for improving the efficiency of the parallel algorithm. The numerical algorithm is validated for 2D lid-driven cavity flows and backward step problems for both conducting and insulating walls.

AB - A numerical algorithm has been developed to solve the incompressible magneto-hydrodynamics (MHD) equations in a fully coupled form. The numerical approach is based on the side centered finite volume approximation where the velocity and magnetic filed vector components are defined at the center of edges/faces, meanwhile the pressure term is defined at the element centroid. In order to enforce a divergence free magnetic field, a magnetic pressure is introduced to the induction equation. The resulting large-scale algebraic linear equations are solved using a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains. The parallel implementation of the present fully coupled unstructured MHD solver is based on the PETSc library for improving the efficiency of the parallel algorithm. The numerical algorithm is validated for 2D lid-driven cavity flows and backward step problems for both conducting and insulating walls.

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Ata K, Sahin M. A monolithic approach for the incompressible magnetohydrodynamics equations. In Papadrakakis M, Onate E, Schrefler BA, editors, Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017. International Center for Numerical Methods in Engineering. 2017. p. 491-501. (Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2017).

A monolithic approach for the incompressible magnetohydrodynamics equations

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Bibliographical note

Keywords

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