Shear rate projection schemes for non-Newtonian fluids

Deteix, Jean; Yakoubi, Driss

doi:10.1016/j.cma.2019.06.006

Cited by 18 publications

(5 citation statements)

References 32 publications

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“…Muhammad et al [24] studied Carreau nanofluid under the influence of slip over a wedge with motile microorganisms and thermal radiation effects. Besides, these many scientists carried to analyze the stagnation point flow and other non-Newtonian fluids with aspect to the following citations, provided a detailed view of flows [25][26][27][28][29][30][31][32][33].…”

Section: Introduction E Low Thermal Conductivity Features Of Various Non-mentioning

confidence: 99%

Thermal Radiation Effects on Unsteady Stagnation Point Nanofluid Flow in View of Convective Boundary Conditions

Rasheed

Islam

Khan

et al. 2021

Mathematical Problems in Engineering

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The present communication particularizes nonlinear convective non-Newtonian stagnation point flow and heat transference effects in stretchable flow of nanofluid. Magnetohydromagnetic steady viscous flow of nanofluid is examined. Heat transfer attributes of nanofluids are addressed via a numerical algorithm. Conductivity and diffusivity characteristics of fluid are depending on temperature and concentration and furthermore, on mass conservation, momentum, energy, and concentration yield partial differential equations (PDEs). The boundary layer flow concept pioneered by Prandtl has been employed to simplify the nonlinear constitutive flow laws which are then changed to ordinary differential equations. A built-in bvp4c algorithm in Mathematica software yields convergent outcomes of nonlinear (ODEs) systems. A comprehensive analysis has been made elucidating the physical significance of various governing parameters effects presented graphically. Additionally, the flow nature was confirmed versus streamlines.

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Section: Introduction E Low Thermal Conductivity Features Of Various Non-mentioning

confidence: 99%

Thermal Radiation Effects on Unsteady Stagnation Point Nanofluid Flow in View of Convective Boundary Conditions

Rasheed

Islam

Khan

et al. 2021

Mathematical Problems in Engineering

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“…Nonetheless, most stabilisation methods are based on perturbed incompressibility equations devised under classical Newtonian assumptions. Probably for that reason, the use of LBB-compatible finite elements is somewhat more frequent in the literature for quasi-Newtonian fluids [6][7][8][9][10][11][12][13][14][15][16]. Although such compatible spaces offer an ideal setting from a theoretical standpoint, they are not always viable options.…”

Section: Introductionmentioning

confidence: 99%

An Equal-Order Finite Element Framework for Incompressible Non-Newtonian Flow Problems

Pacheco¹,

Steinbach²

2021

14th WCCM-ECCOMAS Congress

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Various materials of engineering and biomedical interest can be modelled as generalised Newtonian fluids, i.e., via an apparent viscosity depending locally on the flow field. In spite of the particular features of those models, they are often handled in practice by classical numerical techniques originally conceived for Newtonian fluids. Methods designed specifically for the generalised case are rather scarce in the literature, as well as their use in practical applications. As it turns out, tackling non-Newtonian problems with standard finite element formulations can have undesired consequences such as the induction of spurious pressure boundary layers and the emergence of natural boundary conditions not suitable for realistic flow scenarios. In this context, we introduce a novel framework that deals with those issues while maintaining simplicity and low computational cost. The new stabilised formulation is based on a modified system combining the continuity equation with a Poisson equation for the pressure and consistent pressure boundary conditions. A weak enforcement of the rheological law is employed to enable full consistency even for first-order finite element pairs. Simple numerical examples are provided to demonstrate the potential of our method in yielding accurate solutions for relevant problems.

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“…In view of these challenges, one might prefer projection or split-step schemes decoupling velocity and pressure [13,14], thereby decomposing the system into convection-diffusion, Poisson and simple mass matrix problems. Nonetheless, projection methods suffer from artificial pressure boundary conditions (refer to Guermond et al [15] for an excellent overview), which often call for corrective measures [16,17].…”

Section: Introductionmentioning

confidence: 99%

“…While schemes of similar kind have been applied to challenging incompressible flow problems [19][20][21][22], the extension to the non-Newtonian case is in many aspects challenging. Deteix and Yakoubi [14] proposed the so-called shear rate projection scheme which, despite being accurate and simple, requires LBB-stable velocity-pressure pairs and the solution of an advection-diffusion equation, two Poisson problems and more than ten scalar mass matrix problems per time step.…”

Section: Introductionmentioning

confidence: 99%

Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow

Schussnig

Pacheco

Fries

2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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In various practically relevant incompressible flow problems, such as polymer flow or biomedicalengineering applications, the dependence of fluid viscosity on the local shear rate plays an impor-tant role. Standard techniques using inf-sup stable finite elements lead to saddle-point systemsposing a challenge even for state-of-the-art solvers and preconditioners.For efficiency, projection schemes or time-splitting methods decouple the governing equations forvelocity and pressure, resulting in more, but easier to solve linear systems. Doing so, boundaryconditions and correction terms at intermediate steps have to be carefully considered in order toprohibit spoiling accuracy. In the case of Newtonian incompressible fluids, pressure and velocitycorrection schemes of high-order accuracy have been devised (see, e.g. [1, 2]). However, the exten-sion to generalised Newtonian fluids is a non-trivial task and considered an open question. Deteixet al. [3] successfully adapted the popular rotational correction scheme to consider for shear-ratedependent viscosity, but this resulted in substantial numerical overhead caused by necessarily pro-jecting viscous stress components.In this contribution we address this shortcoming and present a split-step scheme, extending pre-vious work by Liu [4]. The new method is based on an explicit-implicit treatment of pressure,convection and viscous terms combined with a Pressure-Poisson equation equipped with fully con-sistent Neumann and Dirichlet boundary conditions. Through proper reformulation, the use ofstandard continuous finite element spaces is enabled due to low regularity requirements. Addition-ally, equal-order velocity-pressure pairs are applicable as in the original scheme.The stability, accuracy and efficiency of the higher-order splitting scheme is showcased in challeng-ing numerical examples of practical interest.[1] Karniadakis, G. E., Israeli, M. and Orszag, S. A. High-order splitting methods for the incom-pressible Navier-Stokes equations. J. Comput. Phys., (1991).[2] Timmermans, L.J.P., Minev, P.D. and Van de Vosse, F. N. An approximate projection schemefor incompressible flow using spectral elements. Internat. J. Numer. Methods Fluids, Vol.22(7), pp. 673–688, (1996).[3] Deteix, J. and Yakoubi, D. Shear rate projection schemes for non-Newtonian fluids, Comput.Methods Appl. Mech. Engrg., Vol. 354, pp. 620–636, (2019).[4] Liu, J. Open and traction boundary conditions for the incompressible NavierStokesequations.J. Comput. Phys., Vol. 228(19), pp. 7250..7267, (2009).

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Shear rate projection schemes for non-Newtonian fluids

Cited by 18 publications

References 32 publications

Thermal Radiation Effects on Unsteady Stagnation Point Nanofluid Flow in View of Convective Boundary Conditions

Thermal Radiation Effects on Unsteady Stagnation Point Nanofluid Flow in View of Convective Boundary Conditions

An Equal-Order Finite Element Framework for Incompressible Non-Newtonian Flow Problems

Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow

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