Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Lavery, Nicholas; Taylor, C.

doi:10.1002/(sici)1097-0363(19990730)30:6<609::aid-fld733>3.0.co;2-6

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Remarks On the Computer Program1

Application To the Rans + (K ε) Set1

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2001

2022

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Cited by 6 publications

(2 citation statements)

References 14 publications

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“…The linear set of equations was solved using a conjugate gradient solver (in the thermal and mechanical problems), Lavery and Taylor [19]. The non-linear equation of equilibrium was solved using the Newton Raphson technique.…”

Section: Remarks On the Computer Programmentioning

confidence: 99%

Influence of initial stresses on the cast behaviour during squeeze forming processes

Postek

Lewis

Gethin

et al. 2005

Journal of Materials Processing Technology

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Section: Remarks On the Computer Programmentioning

confidence: 99%

Influence of initial stresses on the cast behaviour during squeeze forming processes

Postek

Lewis

Gethin

et al. 2005

Journal of Materials Processing Technology

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“…The multigrid cycling is embedded in the whole solver, from outside the linearization cycle. Recent works using non linear multigrid techniques for solving these problems using the same kind of smoother are those of (Cornelius et al, 1999) or (Lavery and Taylor, 1999).…”

Section: Application To the Rans + (K ε) Setmentioning

confidence: 99%

The robustness issue on multigrid schemes applied to the Navier–Stokes equations for laminar and turbulent, incompressible and compressible flows

Vázquez

Ravachol

Chalot

et al. 2004

Numerical Methods in Fluids

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The paper's leitmotiv is condensed in one word: robustness. This is a real hindrance for the successful implementation of any multigrid scheme for solving the Navier-Stokes set of equations. In this paper, many hints are given to improve this issue. Instead of looking for the best possible speed-up rate for a particular set of problems, at a given regime and in a given condition, the authors propose some ideas pursuing reasonable speed-up rates in any situation. In (Vázquez et al., 2001) (Vázquez, 1999;Vázquez and Codina, 1998).

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A multigrid approach for steady state laminar viscous flows

Liao

Mashayek

2001

Numerical Methods in Fluids

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SUMMARYIn this paper, we use the laminar viscous flow in a lid-driven cavity as an example to describe and verify a numerical scheme for non-linear partial differential equations. The proposed scheme combines a new analytical method for strongly non-linear problems, namely the homotopy analysis method, with the multigrid techniques. A family of formulas at different orders is given. At the lowest order, the current approach is the same as the traditional multigrid methods. However, our high-order scheme needs a fewer number of iterations and less CPU time than the classical ones.

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Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Cited by 6 publications

References 14 publications

Influence of initial stresses on the cast behaviour during squeeze forming processes

Influence of initial stresses on the cast behaviour during squeeze forming processes

The robustness issue on multigrid schemes applied to the Navier–Stokes equations for laminar and turbulent, incompressible and compressible flows

A multigrid approach for steady state laminar viscous flows

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