A new method preserving the positive definiteness of a second order tensor variable in flow simulations with application to viscoelastic turbulence

Housiadas, Kostas D.; Luo, Wei; Beris, Antony N.

doi:10.1016/j.compfluid.2009.08.006

Cited by 12 publications

(7 citation statements)

References 37 publications

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“…In recent calculations by Oliveira (2017), with normalized residuals of about 10 −4 , the number of outer iterations rose to about 10 or higher, with the possibility of divergence within a time step. Some of the authors mentioned in the next subsection employ fractional-step methods together with iteration, e.g., Richter et al (2010), Housiadas et al (2010), D'Avino et al (2012 (for some of the schemes proposed, namely the Gear implicit and the Crank-Nicolson), and Castillo & Codina (2015) (who refer to the need for 9-13 outer iterations for a lid-driven cavity flow problem).…”

Section: Iterative Methods When the Time Derivatives In The Semidiscretized Equations 20 And 22mentioning

confidence: 99%

“…The gains in computational efficiency make fractional-step semi-implicit methods highly attractive for unsteady viscoelastic simulations provided numerical stability is not too compromised (Fiétier & Deville 2003, van Os & Phillips 2004. Such methods are particularly suitable for orthogonal Cartesian meshes and are often applied to simulate some turbulent flows [e.g., DNS or LES (large eddy simulation) in a rectangular domain with periodic boundary conditions, using time steps much smaller than those imposed by the CFL (Courant-Friedrichs-Lewy) condition (Vaithianathan & Collins 2003, Dubief et al 2005, Housiadas et al 2010, Richter et al 2010, presumably due to stability considerations and the need to resolve the small-flow timescales]. In this situation, the final equations are rather simple (although the physics is of course complex) and fractional step methods become very efficient.…”

Section: Fractional-step Methodsmentioning

confidence: 99%

“…Another technique to bound tr A < L 2 , suggested by Vaithianathan & Collins (2003), was later retaken by Housiadas et al (2010): While A is bound by the above limit, a modified tensor A = f (A)A is unbounded. By transforming the governing equations from A toÂ, transforming again to solve for logÂ (natural logarithm), and limiting the maximum attainable value of logÂ so that its Frobenius norm becomes smaller than a specified limit ( logÂ F ≤ M), Housiadas et al (2010) developed a code for turbulence of dilute polymer solutions that was shown to be more robust than their previous unbounded code (in terms of avoiding overflows whenÂ or logÂ is too large).…”

Section: Boundedness Of Tr Amentioning

confidence: 99%

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Numerical Methods for Viscoelastic Fluid Flows

Alves

Oliveira

Pinho

2021

Annu. Rev. Fluid Mech.

154

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Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow instabilities and major modifications to the fluid dynamics. Recent developments in the numerical methods for the simulation of viscoelastic fluid flows, described by continuum-level differential constitutive equations, are surveyed, with a particular emphasis on the finite-volume method. This method is briefly described, and the main benchmark flows currently used in computational rheology to assess the performance of numerical methods are presented. Outstanding issues in numerical methods and novel and challenging applications of viscoelastic fluids, some of which require further developments in numerical methods, are discussed. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 53 is January 6, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Section: Iterative Methods When the Time Derivatives In The Semidiscretized Equations 20 And 22mentioning

confidence: 99%

Section: Fractional-step Methodsmentioning

confidence: 99%

Section: Boundedness Of Tr Amentioning

confidence: 99%

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Numerical Methods for Viscoelastic Fluid Flows

Alves

Oliveira

Pinho

2021

Annu. Rev. Fluid Mech.

154

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“…In addition, it ensures positive definiteness of the conformation tensor and the hyperbolic-like nature of the constitutive equation. Hence, if SM with sufficiently high-order approximating function and is coupled with available schemes that ensure positive definiteness of the conformation tensor (Housiadas, Wang & Beris 2010), reliable results can be obtained. To this end, the HM technique used in this study can be viewed as an equivalent technique to traditional SM with a sufficiently high value.…”

Section: Problem Formulation and Computational Detailsmentioning

confidence: 99%

Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow

et al. 2021

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The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ( $Re$ ) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

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“…The availability of high-performance computers has allowed direct numerical simulation (DNS) of polymer drag reduction flows from the mid-nineties, starting with the pioneering computations of Sureshkumar et al [2] who were the first to simulate drag reduction with a viscoelastic model. Following this, a great deal of DNS studies have improved our knowledge of 'viscoelastic' turbulence: Dimitropoulos et al [3][4][5][6], De Angelis et al [7], Min et al [8], Dubief et al [9], Housiadas and Beris [10,11], and Housiadas et al [12], among others, gathered a substantial amount of plane channel flow data for various drag reduction regimes.…”

Section: Introductionmentioning

confidence: 96%