Iterative solvers for quadratic discretizations of the generalized Stokes problem

Guénette, R.; Fortin, A.; Labbe, Jean-Louis; Marcotte, Jean-Philippe

doi:10.1002/fld.581

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Finally, the method will be compared with common Krylov methods such as BiCGStab or TFQMR methods preconditioned by the same block triangular matrix but with SOR or SSOR as the F preconditioner. This approach has been studied by Guénette et al [32].…”

Section: Performance Of the Preconditioner For The Matrix Fmentioning

confidence: 96%

Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations

Maliki

Guénette

2010

Numerical Methods in Fluids

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SUMMARYWe develop an efficient preconditioning techniques for the solution of large linearized stationary and non-stationary incompressible Navier-Stokes equations. These equations are linearized by the Picard and Newton methods, and linear extrapolation schemes in the non-stationary case. The time discretization procedure uses the Gear scheme and the second-order Taylor-Hood element P 2 − P 1 is used for the approximation of the velocity and the pressure. Our purpose is to develop an efficient preconditioner for saddle point systems. Our tools are the addition of stabilization (penalization) term r ∇(div(·)), and the use of triangular block matrix as global preconditioner. This preconditioner involves the solution of two subsystems associated, respectively, with the velocity and the pressure and have to be solved efficiently. Furthermore, we use the P 1 − P 2 hierarchical preconditioner recently proposed by the authors, for the block matrix associated with the velocity and an additive approach for the Schur complement approximation. Finally, several numerical examples illustrating the good performance of the preconditioning techniques are presented.

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Section: Performance Of the Preconditioner For The Matrix Fmentioning

confidence: 96%

Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations

Maliki

Guénette

2010

Numerical Methods in Fluids

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“…But the method has a handicap because it is very difficult to apply the FDM to complex geometries. Therefore, many researchers adopted the finite element method (FEM) in two-dimensional analyses [8][9]. Because the viscoelastic flow simulation requires huge computing power, efforts have been continued to find more economic and efficient methods.…”

Section: Introductionmentioning

confidence: 99%

“…Advanced numerical schemes were developed and the elastic viscous split stress scheme (EVSS) and its modified versions have been widely used together with FVM [8,[14][15].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional numerical simulation of viscoelastic flow through an abrupt contraction geometry

2005

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A numerical scheme for simulating three-dimensional viscoelastic flow was developed. The three-dimensional finite volume method (FVM) based on a non-staggered grid and the semi-implicit method for pressure-linked equations (SIMPLE) were adopted to solve the continuity and momentum equations. As we used a non-staggered grid, the momentum interpolation method (MIM) was employed to avoid checkerboard type pressure fields. Viscoelastic properties of the fluid were described by the Phan-Thien and Tanner (PTT) model, which was treated by the compressive interface capturing scheme for arbitrary meshes (CICSAM). The elastic viscous split stress scheme (EVSS) was used to decouple the velocity and the stress fields. Algebraic equations obtained by the above schemes were handled by an iterative solver and a multi-grid method was applied to accelerate convergence. In order to verify the scheme developed in this study, Newtonian flow in a rectangular duct was studied and the resulting velocity fields were compared with the analytical flow fields. Then viscoelastic flow in 4:1 contraction geometry, one of the most frequently used benchmarking problems, was predicted by applying the fully three-dimensional finite volume method.

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An adaptive remeshing strategy for shear-thinning fluid flow simulations

Fortin

Bertrand

Fortin

et al. 2004

Computers & Chemical Engineering

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Iterative solvers for quadratic discretizations of the generalized Stokes problem

Cited by 4 publications

References 14 publications

Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations

Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations

Three-dimensional numerical simulation of viscoelastic flow through an abrupt contraction geometry

An adaptive remeshing strategy for shear-thinning fluid flow simulations

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