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Volume 23, Issue 2
Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System

Jessica Bosch, Christian Kahle & Martin Stoll

DOI: 10.4208/cicp.OA-2017-0037

Commun. Comput. Phys., 23 (2018), pp. 603-628.

Published online: 2018-02

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  • Abstract

Recently, Garcke et al. [H. Garcke, M. Hinze, C. Kahle, Appl. Numer. Math. 99 (2016), 151–171)] developed a consistent discretization scheme for a thermodynamically consistent diffuse interface model for incompressible two-phase flows with different densities [H. Abels, H. Garcke, G. Grün, Math. Models Methods Appl. Sci. 22(3) (2012)]. At the heart of this method lies the solution of large and sparse linear systems that arise in a semismooth Newton method. 

In this work we propose the use of preconditioned Krylov subspace solvers using effective Schur complement approximations. Numerical results illustrate the efficiency of our approach. In particular, our preconditioner is shown to be robust with respect to parameter changes.

  • Keywords

Navier-Stokes, Cahn-Hilliard, two-phase flow, preconditioning, Schur complement approximation, saddle-point problems.

  • AMS Subject Headings

65F08, 65F10, 65N22, 65F50, 93C20, 74S05, 35K55, 82C26, 35Q30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-603, author = {Jessica Bosch, Christian Kahle and Martin Stoll}, title = {Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {2}, pages = {603--628}, abstract = {

Recently, Garcke et al. [H. Garcke, M. Hinze, C. Kahle, Appl. Numer. Math. 99 (2016), 151–171)] developed a consistent discretization scheme for a thermodynamically consistent diffuse interface model for incompressible two-phase flows with different densities [H. Abels, H. Garcke, G. Grün, Math. Models Methods Appl. Sci. 22(3) (2012)]. At the heart of this method lies the solution of large and sparse linear systems that arise in a semismooth Newton method. 

In this work we propose the use of preconditioned Krylov subspace solvers using effective Schur complement approximations. Numerical results illustrate the efficiency of our approach. In particular, our preconditioner is shown to be robust with respect to parameter changes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0037}, url = {http://global-sci.org/intro/article_detail/cicp/10540.html} }
TY - JOUR T1 - Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System AU - Jessica Bosch, Christian Kahle & Martin Stoll JO - Communications in Computational Physics VL - 2 SP - 603 EP - 628 PY - 2018 DA - 2018/02 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0037 UR - https://global-sci.org/intro/article_detail/cicp/10540.html KW - Navier-Stokes, Cahn-Hilliard, two-phase flow, preconditioning, Schur complement approximation, saddle-point problems. AB -

Recently, Garcke et al. [H. Garcke, M. Hinze, C. Kahle, Appl. Numer. Math. 99 (2016), 151–171)] developed a consistent discretization scheme for a thermodynamically consistent diffuse interface model for incompressible two-phase flows with different densities [H. Abels, H. Garcke, G. Grün, Math. Models Methods Appl. Sci. 22(3) (2012)]. At the heart of this method lies the solution of large and sparse linear systems that arise in a semismooth Newton method. 

In this work we propose the use of preconditioned Krylov subspace solvers using effective Schur complement approximations. Numerical results illustrate the efficiency of our approach. In particular, our preconditioner is shown to be robust with respect to parameter changes.

Jessica Bosch, Christian Kahle and Martin Stoll. (2018). Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System. Communications in Computational Physics. 23 (2). 603-628. doi:10.4208/cicp.OA-2017-0037
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