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

Jessica Bosch, Christian Kahle & Martin Stoll

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

Published online: 2018-02

Preview Full PDF 7 1229
Export citation
  • 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. Gr ¨un, 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

  • Email address
  • References
  • Hide All
    View All

@Article{CiCP-23-603, author = {}, 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. Gr ¨un, 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} }
Copy to clipboard
The citation has been copied to your clipboard