A three-field local projection stabilized formulation for computations of Oldroyd-B viscoelastic fluid flows

Venkatesan, Jagannath; Ganesan, Sashikumaar

doi:10.1016/j.jnnfm.2017.06.007

Cited by 23 publications

(15 citation statements)

References 54 publications

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“…[9][10][11][12][13][14][15] and in the references therein. On the other hand, in the context of non-Newtonian fluids, formal code verification studies based on MMS have started to appear only recently in the literature [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Code Verification of Non-Newtonian Fluid Solvers for Single- and Two-Phase Laminar Flows

Lovato

Toxopeus

Settels

et al. 2021

Journal of Verification, Validation and Uncertainty Quantification

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The presence of complex fluids in nature and industrial applications combined with the rapid growth of computer power over the past decades has led to an increasing number of numerical studies on non-Newtonian flows. In most cases, non-Newtonian models can be implemented in existing Newtonian solvers by relatively simple modification of the viscosity. However, due to scarcity of analytical solutions for non-Newtonian fluid flows and widespread use of regularisation methods, performing Code Verification to ensure that the code is free of mistakes is a challenging task. The Method of Manufactured Solutions (MMS) is a powerful tool to generate analytical solutions for Code Verification. In this article, we present and discuss results of three verification exercises based on MMS: (i) steady single-phase flow; (ii) unsteady two-phase flow with smooth interface; (iii) two-phase flow with free surface. We show that, with the first and second exercise, rigorous verification of non-Newtonian fluid solver is possible both on single and two-phase flows. The third test case revealed that `spurious velocities' typical of free-surface calculations with the Volume-of-Fluid (VoF) model lead to `spurious viscosities' in the non-Newtonian fluid. The procedure is illustrated herein on a second-order finite-volume CFD code using the Herschel-Bulkley fluid model as an example. Nonetheless, the same methodology is applicable to any CFD code and it can be easily extended to all rheological models falling under the class of Generalised Newtonian Fluid (GNF) models.

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Section: Introductionmentioning

confidence: 99%

Code Verification of Non-Newtonian Fluid Solvers for Single- and Two-Phase Laminar Flows

Lovato

Toxopeus

Settels

et al. 2021

Journal of Verification, Validation and Uncertainty Quantification

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“…The initial condition for the velocity and the extra stress were set as

boldu = bold0

and

bold-italicτ = bold0

in the whole domain. We note that these are typical boundary and initial conditions used for this type of channel configuration (Lee, 2012; Rajagopal & Das, 2016; Venkatesan & Ganesan, 2017; Yue et al, 2006).…”

Section: Methodsmentioning

confidence: 99%

Predicting biofilm deformation with a viscoelastic phase‐field model: Modeling and experimental studies

Matouš

Nerenberg

2020

Biotech & Bioengineering

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Biofilms commonly develop in flowing aqueous environments, where the flow causes the biofilm to deform. Because biofilm deformation affects the flow regime, and because biofilms behave as complex heterogeneous viscoelastic materials, few models are able to predict biofilm deformation. In this study, a phase-field (PF) continuum model coupled with the Oldroyd-B constitutive equation was developed and used to simulate biofilm deformation. The accuracy of the model was evaluated using two types of biofilms: a synthetic biofilm, made from alginate mixed with bacterial cells, and a Pseudomonas aeruginosa biofilm. Shear rheometry was used to experimentally determine the mechanical parameters for each biofilm, used as inputs for the model. Biofilm deformation under fluid flow was monitored experimentally using optical coherence tomography. The comparison between the experimental and modeling geometries, for selected horizontal cross sections, after fluid-driven deformation was good. The relative errors ranged from 3.2 to 21.1% for the synthetic biofilm and from 9.1 to 11.1% for the P. aeruginosa biofilm. This is the first demonstration of the effectiveness of a viscoelastic PF biofilm model. This model provides an important tool for predicting biofilm viscoelastic deformation. It also can benefit the design and control of biofilms in engineering systems.

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“…One of the commonly used techniques to overcome or at least minimize the numerical instabilities arising at high Weissenberg numbers is the addition of extra artificial stabilization to the numerical solver. There is a wide body of specialized literature describing and dealing with this issue [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Modeling Challengesmentioning

confidence: 99%

Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow

Pires

Bodnár

2022

Mathematics

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This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with a newly proposed approach using a discrete time derivative of the Laplacian of the extra stress tensor. Both methods are implemented in a finite element code and demonstrated in the solution of a viscoelastic fluid flow in a two-dimensional corrugated channel for a range of Weissenberg numbers. The numerical simulations have shown that this new temporal stress diffusion not only efficiently stabilizes numerical simulations, but also vanishes when the solution reaches a steady state. It is demonstrated that in contrast to the standard tensorial diffusion, the temporal artificial stress diffusion does not affect the final solution.

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A three-field local projection stabilized formulation for computations of Oldroyd-B viscoelastic fluid flows

Cited by 23 publications

References 54 publications

Code Verification of Non-Newtonian Fluid Solvers for Single- and Two-Phase Laminar Flows

Code Verification of Non-Newtonian Fluid Solvers for Single- and Two-Phase Laminar Flows

Predicting biofilm deformation with a viscoelastic phase‐field model: Modeling and experimental studies

Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow

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