An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier--Stokes equations at high Reynolds number

PE Farrell, L Mitchell, F Wechsung - SIAM Journal on Scientific Computing, 2019 - SIAM
In [M. Benzi and MA Olshanskii, SIAM J. Sci. Comput., 28 (2006), pp. 2095--2113] a
preconditioner of augmented Lagrangian type was presented for the two-dimensional …

Modified augmented Lagrangian preconditioners for the incompressible Navier–Stokes equations

M Benzi, MA Olshanskii, Z Wang - International Journal for …, 2011 - Wiley Online Library
We study different variants of the augmented Lagrangian (AL)‐based block‐triangular
preconditioner introduced by the first two authors in [SIAM J. Sci. Comput. 2006; 28: 2095 …

SIMPLE‐type preconditioners for cell‐centered, colocated finite volume discretization of incompressible Reynolds‐averaged Navier–Stokes equations

CM Klaij, C Vuik - … Journal for Numerical Methods in Fluids, 2013 - Wiley Online Library
This paper contains a comparison of four SIMPLE‐type methods used as solver and as
preconditioner for the iterative solution of the (Reynolds‐averaged) Navier–Stokes …

An overlapping Schwarz algorithm for almost incompressible elasticity

CR Dohrmann, OB Widlund - SIAM journal on numerical analysis, 2009 - SIAM
Overlapping Schwarz methods are extended to mixed finite element approximations of
linear elasticity which use discontinuous pressure spaces. The coarse component of the …

Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization

T Heister, G Rapin - … Journal for Numerical Methods in Fluids, 2013 - Wiley Online Library
Efficient preconditioning for Oseen‐type problems is an active research topic. We present a
novel approach leveraging stabilization for inf‐sup stable discretizations. The Grad‐Div …

An efficient and modular grad–div stabilization

JA Fiordilino, W Layton, Y Rong - Computer Methods in Applied Mechanics …, 2018 - Elsevier
This paper presents two modular grad–div algorithms for calculating solutions to the Navier–
Stokes equations (NSE). These algorithms add to an NSE code a minimally intrusive module …

[PDF][PDF] Preconditioners for incompressible Navier-Stokes solvers

A Segal, M Ur Rehman, C Vuik - … : Theory, Methods and …, 2010 - homepage.tudelft.nl
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 …

[HTML][HTML] Robust stabilised finite element solvers for generalised Newtonian fluid flows

R Schussnig, DRQ Pacheco, TP Fries - Journal of Computational Physics, 2021 - Elsevier
Various materials and solid-fluid mixtures of engineering and biomedical interest can be
modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on …

ℋ︁‐LU factorization in preconditioners for augmented Lagrangian and grad‐div stabilized saddle point systems

S Börm, S Le Borne - … journal for numerical methods in fluids, 2012 - Wiley Online Library
The (mixed finite element) discretization of the linearized Navier–Stokes equations leads to
a linear system of equations of saddle point type. The iterative solution of this linear system …

An augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity with piecewise linear equal-order finite elements

J Zhang - Computer Methods in Applied Mechanics and …, 2010 - Elsevier
We study an augmented Lagrangian approach to Bingham fluid flows in a lid-driven square
cavity. The piecewise linear equal-order finite element spaces for both the velocity and the …