Two preconditioners for saddle point problems in fluid flows

Niet, Arie C. de; Wubs, Fred W.

doi:10.1002/fld.1401

Cited by 44 publications

(38 citation statements)

References 22 publications

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“…The literature on this class of preconditioners is huge. We refer for more details to the articles [2,3,4,18,23], the surveys [5,8,10,30] and the books [12,28], with numerous references therein. In general, the exact factorization of a two-by-two block matrix is…”

Section: Problem Formulation and Linearizationmentioning

confidence: 99%

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

Vuik

2016

Numer. Math. Theory Methods Appl.

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In this report we explore the performance of the SIMPLER , augmented Lagrangian, 'grad-div' preconditioners and their variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem Reynolds number varies from a low to the limiting number for a laminar flow.Mathematics subject classification: 65F10, 65F08.

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Section: Problem Formulation and Linearizationmentioning

confidence: 99%

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

Vuik

2016

Numer. Math. Theory Methods Appl.

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“…The literature on this class of preconditioners is huge. We refer for more details to the articles [2,3,4,20,25], the surveys [5,8,9,32] and the books [1,12,30], with numerous references therein. In general, the exact factorization of a two-by-two block matrix reads…”

Section: Preconditioning the Variable Viscosity Oseen-type Problemmentioning

confidence: 99%

On Preconditioning of Incompressible Non-Newtonian Flow Problems

He¹

2015

JCM

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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 effects 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.Mathematics subject classification: 65F10 65F08 65N30.

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“…Remark 2.2. Only few results can be found in the literature related to the preconditioning of the pressure Schur complement operator for fluid equations with Coriolis terms, see for instance [7][8][9]. Here we follow the approaches given in [8,9] and [19] to construct a preconditioner for the discrete counterpart of the Schur operator:…”

Section: Modified Pressure Equationmentioning

confidence: 99%

A discrete projection method for incompressible viscous flow with coriolis force

Sokolov

Olshanskii

Turek

2008

Computer Methods in Applied Mechanics and Engineering

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a b s t r a c tThe paper presents a new discrete projection method for the numerical solution of the Navier-Stokes equations with Coriolis force term. On an algebraic level we interpret one time step of the projection method as an incomplete factorization of the linearized Navier-Stokes system and as the iteration of an Uzawa type algorithm with special preconditioning for the pressure block. This enables us to modify the well-known projection method in a way to account for possibly dominating Coriolis terms. We consider a special multigrid method for solving the velocity subproblems and a modified projection (pressure correction) step. Results of numerical tests are presented for a model problem as well as for 3D flow simulations in stirred tank reactors.

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Two preconditioners for saddle point problems in fluid flows

Cited by 44 publications

References 22 publications

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

On Preconditioning of Incompressible Non-Newtonian Flow Problems

A discrete projection method for incompressible viscous flow with coriolis force

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