Volume 33, Issue 1
On Preconditioning of Incompressible Non-Newtonian Flow Problems

Xin He, Maya Neytcheva & Cornelis Vuik

J. Comp. Math., 33 (2015), pp. 33-58.

Published online: 2015-02

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  • Abstract

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the nite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically ecient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian ows, the viscosity is not constant and its variation is an important factor that eects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.

  • Keywords

non-Newtonian ows Navier-Stokes equations Two-by-two block systems Krylov subspace methods Preconditioners

  • AMS Subject Headings

65F10 65F08 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

X.He-1@tudelft.nl (Xin He)

maya.neytcheva@it.uu.se (Maya Neytcheva)

c.vuik@tudelft.nl (Cornelis Vuik)

  • BibTex
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@Article{JCM-33-33, author = {He , Xin and Neytcheva , Maya and Vuik , Cornelis }, title = {On Preconditioning of Incompressible Non-Newtonian Flow Problems}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {1}, pages = {33--58}, abstract = {

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the nite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically ecient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian ows, the viscosity is not constant and its variation is an important factor that eects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1407-m4486}, url = {http://global-sci.org/intro/article_detail/jcm/9826.html} }
TY - JOUR T1 - On Preconditioning of Incompressible Non-Newtonian Flow Problems AU - He , Xin AU - Neytcheva , Maya AU - Vuik , Cornelis JO - Journal of Computational Mathematics VL - 1 SP - 33 EP - 58 PY - 2015 DA - 2015/02 SN - 33 DO - http://doi.org/10.4208/jcm.1407-m4486 UR - https://global-sci.org/intro/article_detail/jcm/9826.html KW - non-Newtonian ows KW - Navier-Stokes equations KW - Two-by-two block systems KW - Krylov subspace methods KW - Preconditioners AB -

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the nite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically ecient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian ows, the viscosity is not constant and its variation is an important factor that eects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.

Xin He , Maya Neytcheva & Cornelis Vuik . (2020). On Preconditioning of Incompressible Non-Newtonian Flow Problems. Journal of Computational Mathematics. 33 (1). 33-58. doi:10.4208/jcm.1407-m4486
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