Stabilized stress–velocity–pressure finite element formulations of the Navier–Stokes problem for fluids with non-linear viscosity

Castillo, Ernesto; Codina, Ramon

doi:10.1016/j.cma.2014.07.003

Cited by 48 publications

(57 citation statements)

References 38 publications

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“…In the context of a three-field formulation for flow problems, they can be found in [26]. Here we just state the method for the particular case of stationary viscoelastic flows.…”

Section: Residual Based Stabilized Finite Element Methodsmentioning

confidence: 99%

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Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

Castillo

Codina

2014

Computer Methods in Applied Mechanics and Engineering

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“…In the context of a three-field formulation for flow problems, they can be found in [26]. Here we just state the method for the particular case of stationary viscoelastic flows.…”

Section: Residual Based Stabilized Finite Element Methodsmentioning

confidence: 99%

“…with I d the identity on vectors of R d , I d×d the identity on second order tensors and the parameters α i , i = 1, 2, 3, are computed as (see [25,26])…”

Section: Residual Based Stabilized Finite Element Methodsmentioning

confidence: 99%

Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

Castillo

Codina

2014

Computer Methods in Applied Mechanics and Engineering

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“…However, there are restrictions that must be satisfied explicitly in the discrete formulation used. These are the same as for the three-field formulation of the Stokes problem [12,1,13]. A possible remedy to this situation is to use inf-sup stable elements (see [3] for the 2D case and [14] for the 3D case).…”

Section: Galerkin Finite Element Discretizationmentioning

confidence: 99%

Finite element approximation of the viscoelastic flow problem: A non-residual based stabilized formulation

Castillo

Codina

2017

Computers & Fluids

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In this paper, a three-field finite element stabilized formulation for the incompressible viscoelastic fluid flow problem is tested numerically. Starting from a residual based formulation, a non-residual based one is designed, the benefits of which are highlighted in this work. Both formulations allow one to deal with the convective nature of the problem and to use equal interpolation for the problem unknowns σ-up (deviatoric stress, velocity and pressure). Additionally, some results from the numerical analysis of the formulation are stated. Numerical examples are presented to show the robustness of the method, which include the classical 4 : 1 planar contraction problem and the flow over a confined cylinder case, as well as a two-fluid formulation for the planar jet buckling problem.

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“…Nowadays it is used in a wide range of different problems in fluid dynamics ( [30,31,34,[56][57][58]76,81]) and solid mechanics ( [17][18][19][20][21][22]27,28]). Castillo and Codina presented a three fields formulation for visco-elastic [16], power law and Carreau-Yasuda [15] fluids comparing ASGS and OSS. In the present work, the OSS stabilization technique is applied to the Navier-Stokes equations to model regularized Bingham and Herschel-Bulkley flows.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Bingham and Herschel–Bulkley flows with mixed P1/P1 finite elements stabilized with orthogonal subgrid scale

Moreno

Larese

Cervera

2016

Journal of Non-Newtonian Fluid Mechanics

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a b s t r a c tThis paper presents the application of a stabilized mixed pressure/velocity finite element formulation to the solution of viscoplastic non-Newtonian flows. Both Bingham and Herschel-Bulkley models are considered.The detail of the discretization procedure is presented and the Orthogonal Subgrid Scale (OSS) stabilization technique is introduced to allow for the use of equal order interpolations in a consistent way. The matrix form of the problem is given.A series of examples is presented to assess the accuracy of the method by comparison with the results obtained by other authors. The extrusion in a Bingham fluid and the movement of a moving and rotating cylinder are analyzed in detail. The evolution of the streamlines, the yielded and unyielded regions, the drag and lift forces are presented.These benchmark examples show the capacity of the mixed OSS formulation to reproduce the behavior of a Bingham and Herschel-Bulkley flows with the required accuracy.

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Stabilized stress–velocity–pressure finite element formulations of the Navier–Stokes problem for fluids with non-linear viscosity

Cited by 48 publications

References 38 publications

Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

Finite element approximation of the viscoelastic flow problem: A non-residual based stabilized formulation

Modelling of Bingham and Herschel–Bulkley flows with mixed P1/P1 finite elements stabilized with orthogonal subgrid scale

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