Year: 2010
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 3 : pp. 245–275
Abstract
In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block preconditioners form an excellent approach for the solution, however, if the grids are not to fine preconditioning, a Saddle point ILU matrix (SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2010.33.1
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 3 : pp. 245–275
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Navier-Stokes equations finite element method block preconditioners SIMPLE-type schemes iterative methods incompressible fluids.
-
Personalized Computational Hemodynamics
Bibliography
2020
https://doi.org/10.1016/B978-0-12-815653-7.16001-4 [Citations: 0] -
An assessment of some solvers for saddle point problems emerging from the incompressible Navier–Stokes equations
Ahmed, Naveed | Bartsch, Clemens | John, Volker | Wilbrandt, UlrichComputer Methods in Applied Mechanics and Engineering, Vol. 331 (2018), Iss. P.492
https://doi.org/10.1016/j.cma.2017.12.004 [Citations: 10] -
A new numerical method for solution of boiling flow using combination of SIMPLE and Jacobian-free Newton-Krylov algorithms
Hajizadeh, A. | Kazeminejad, H. | Talebi, S.Progress in Nuclear Energy, Vol. 95 (2017), Iss. P.48
https://doi.org/10.1016/j.pnucene.2016.11.005 [Citations: 11] -
A comparison of block preconditioners for isogeometric analysis discretizations of the incompressible Navier–Stokes equations
Horníková, Hana | Vuik, Cornelis | Egermaier, JiříInternational Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 6 P.1788
https://doi.org/10.1002/fld.4952 [Citations: 4] -
Scheduled relaxation Jacobi method as preconditioner of Krylov subspace techniques for large-scale Poisson problems
Maity, Ankita | Singh, Krishna MohanNumerical Heat Transfer, Part B: Fundamentals, Vol. 77 (2020), Iss. 2 P.152
https://doi.org/10.1080/10407790.2019.1690875 [Citations: 1] -
Mathematical model to analyze the flow and heat transfer problem in U-shaped geothermal exchangers
Egidi, Nadaniela | Giacomini, Josephin | Maponi, PierluigiApplied Mathematical Modelling, Vol. 61 (2018), Iss. P.83
https://doi.org/10.1016/j.apm.2018.03.024 [Citations: 20] -
ILU Preconditioners for Nonsymmetric Saddle-Point Matrices with Application to the Incompressible Navier--Stokes Equations
Konshin, Igor N. | Olshanskii, Maxim A. | Vassilevski, Yuri V.SIAM Journal on Scientific Computing, Vol. 37 (2015), Iss. 5 P.A2171
https://doi.org/10.1137/15M1012311 [Citations: 19] -
Block-preconditioners for the incompressible Navier–Stokes equations discretized by a finite volume method
He, Xin | Vuik, Cornelis | Klaij, ChristiaanJournal of Numerical Mathematics, Vol. 25 (2017), Iss. 2
https://doi.org/10.1515/jnma-2015-0120 [Citations: 4] -
Isogeometric Analysis and Applications 2018
Preconditioning for Linear Systems Arising from IgA Discretized Incompressible Navier–Stokes Equations
Horníková, Hana | Vuik, Cornelis2021
https://doi.org/10.1007/978-3-030-49836-8_5 [Citations: 0] -
Recycling augmented Lagrangian preconditioner in an incompressible fluid solver
Olshanskii, Maxim A. | Zhiliakov, AlexanderNumerical Linear Algebra with Applications, Vol. 29 (2022), Iss. 2
https://doi.org/10.1002/nla.2415 [Citations: 2] -
Combining the Augmented Lagrangian Preconditioner with the Simple Schur Complement Approximation
He, Xin | Vuik, Cornelis | Klaij, Christiaan M.SIAM Journal on Scientific Computing, Vol. 40 (2018), Iss. 3 P.A1362
https://doi.org/10.1137/17M1144775 [Citations: 6] -
Computational Science – ICCS 2020
A Block Preconditioner for Scalable Large Scale Finite Element Incompressible Flow Simulations
Goik, Damian | Banaś, Krzysztof2020
https://doi.org/10.1007/978-3-030-50420-5_15 [Citations: 0] -
Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape
Santo, Niccolò Dal | Manzoni, AndreaAdvances in Computational Mathematics, Vol. 45 (2019), Iss. 5-6 P.2463
https://doi.org/10.1007/s10444-019-09722-9 [Citations: 13] -
Inexact matrix exponential preconditioner for implicitly restarted Arnoldi method in fluid dynamics stability problems for parallel heterogeneous architecture
Evstigneev, Nikolay M.
Journal of Physics: Conference Series, Vol. 1141 (2018), Iss. P.012121
https://doi.org/10.1088/1742-6596/1141/1/012121 [Citations: 2] -
Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations
He, X. | Vuik, C.Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 2 P.239
https://doi.org/10.4208/nmtma.2016.m1422 [Citations: 3] -
Efficient and robust Schur complement approximations in the augmented Lagrangian preconditioner for the incompressible laminar flows
He, Xin | Vuik, CornelisJournal of Computational Physics, Vol. 408 (2020), Iss. P.109286
https://doi.org/10.1016/j.jcp.2020.109286 [Citations: 2] -
On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows
Singh, K. M. | Avital, E. J. | Williams, J. J. R. | Ji, C. | Bai, X. | Munjiza, A.International Journal for Numerical Methods in Fluids, Vol. 83 (2017), Iss. 5 P.446
https://doi.org/10.1002/fld.4277 [Citations: 18]