Close Search Advanced
Journals
Resources
About Us
Open Access

On Preconditioning of Incompressible Non-Newtonian Flow Problems

On Preconditioning of Incompressible Non-Newtonian Flow Problems
Preview
Add to basket

Year:    2015

Author:    Xin He, Maya Neytcheva, Cornelis Vuik

Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 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 finite 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 efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that affects 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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1407-m4486

Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 33–58

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    non-Newtonian flows Navier-Stokes equations Two-by-two block systems Krylov subspace methods Preconditioners.

Author Details

Xin He

Maya Neytcheva

Cornelis Vuik

  1. Robust stabilised finite element solvers for generalised Newtonian fluid flows

    Schussnig, Richard | Pacheco, Douglas R.Q. | Fries, Thomas-Peter

    Journal of Computational Physics, Vol. 442 (2021), Iss. P.110436

    https://doi.org/10.1016/j.jcp.2021.110436 [Citations: 10]

  2. An interior proximal point algorithm for nonlinear complementarity problems

    Bnouhachem, Abdellah | Noor, Muhammad Aslam

    Nonlinear Analysis: Hybrid Systems, Vol. 4 (2010), Iss. 3 P.371

    https://doi.org/10.1016/j.nahs.2009.09.010 [Citations: 4]

  3. An self-adaptive LQP method for constrained variational inequalities

    Fu, Xiao-Ling | Bnouhachem, Abdellah

    Applied Mathematics and Computation, Vol. 189 (2007), Iss. 2 P.1586

    https://doi.org/10.1016/j.amc.2006.12.032 [Citations: 2]

  4. Hyperreduced-order modeling of thermally coupled flows

    Espinoza-Contreras, Nicolás | Bayona-Roa, Camilo | Castillo, Ernesto | Gándara, Tomás | Moraga, Nelson O.

    Applied Mathematical Modelling, Vol. 125 (2024), Iss. P.59

    https://doi.org/10.1016/j.apm.2023.08.028 [Citations: 0]

  5. Local and parallel finite element methods based on two-grid discretizations for a non-stationary coupled Stokes-Darcy model

    Li, Qingtao | Du, Guangzhi

    Computers & Mathematics with Applications, Vol. 113 (2022), Iss. P.254

    https://doi.org/10.1016/j.camwa.2022.03.029 [Citations: 6]

  6. A modulus-based nonmonotone line search method for nonlinear complementarity problems

    Zhang, Xu | Peng, Zheng

    Applied Mathematics and Computation, Vol. 387 (2020), Iss. P.125175

    https://doi.org/10.1016/j.amc.2020.125175 [Citations: 4]

  7. An Augmented Lagrangian Preconditioner for Implicitly Constituted Non-Newtonian Incompressible Flow

    Farrell, P. E. | Gazca-Orozco, P. A.

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 6 P.B1329

    https://doi.org/10.1137/20M1336618 [Citations: 10]

  8. A two‐level finite element method for the stationary Navier‐Stokes equations based on a stabilized local projection

    Zhang, Yan | He, Yinnian

    Numerical Methods for Partial Differential Equations, Vol. 27 (2011), Iss. 2 P.460

    https://doi.org/10.1002/num.20533 [Citations: 16]

  9. A priori error estimates of a three-step two-level finite element Galerkin method for a 2D-Boussinesq system of equations

    Bajpai, Saumya | Swain, Debendra Kumar

    Computers & Mathematics with Applications, Vol. 146 (2023), Iss. P.137

    https://doi.org/10.1016/j.camwa.2023.06.025 [Citations: 1]

  10. A self-adaptive descent LQP alternating direction method for the structured variational inequalities

    Bnouhachem, Abdellah

    Numerical Algorithms, Vol. 86 (2021), Iss. 1 P.303

    https://doi.org/10.1007/s11075-020-00890-0 [Citations: 0]

  11. Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations

    Li, Qingtao | Du, Guangzhi

    Numerical Algorithms, Vol. 88 (2021), Iss. 4 P.1915

    https://doi.org/10.1007/s11075-021-01100-1 [Citations: 11]

  12. A multilevel finite element method in space‐time for the Navier‐Stokes problem

    He, Yinnian | Liu, Kam‐Moon

    Numerical Methods for Partial Differential Equations, Vol. 21 (2005), Iss. 6 P.1052

    https://doi.org/10.1002/num.20077 [Citations: 67]

  13. A parallel Oseen-linearized algorithm for the stationary Navier–Stokes equations

    Shang, Yueqiang | He, Yinnian

    Computer Methods in Applied Mechanics and Engineering, Vol. 209-212 (2012), Iss. P.172

    https://doi.org/10.1016/j.cma.2011.11.003 [Citations: 30]

  14. Two‐level Newton iterative method for the 2D/3D steady Navier‐Stokes equations

    He, Yinnian | Zhang, Yan | Shang, Yueqiang | Xu, Hui

    Numerical Methods for Partial Differential Equations, Vol. 28 (2012), Iss. 5 P.1620

    https://doi.org/10.1002/num.20695 [Citations: 37]

  15. A new logarithmic-quadratic proximal method for nonlinear complementarity problems

    Bnouhachem, Abdellah | Noor, Muhammad Aslam | Khalfaoui, Mohamed | Zhaohan, Sheng

    Applied Mathematics and Computation, Vol. 215 (2009), Iss. 2 P.695

    https://doi.org/10.1016/j.amc.2009.05.042 [Citations: 3]

  16. Stability and convergence of two‐grid Crank‐Nicolson extrapolation scheme for the time‐dependent natural convection equations

    Liang, Hongxia | Zhang, Tong

    Mathematical Methods in the Applied Sciences, Vol. 42 (2019), Iss. 18 P.6165

    https://doi.org/10.1002/mma.5713 [Citations: 3]

  17. Two‐level discretization of the Navier‐Stokes equations with r‐Laplacian subgridscale viscosity

    Borggaard, Jeff | Iliescu, Traian | Roop, John Paul

    Numerical Methods for Partial Differential Equations, Vol. 28 (2012), Iss. 3 P.1056

    https://doi.org/10.1002/num.20673 [Citations: 14]

  18. Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data

    Liang, Hongxia | Zhang, Tong

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 8 P.2221

    https://doi.org/10.1016/j.camwa.2018.12.002 [Citations: 3]

  19. An LQP-based descent method for structured monotone variational inequalities

    Li, Min | Zhong, Weijun

    Journal of Computational and Applied Mathematics, Vol. 235 (2011), Iss. 5 P.1523

    https://doi.org/10.1016/j.cam.2010.08.039 [Citations: 0]