A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

Şahin, Mehmet; Wilson, H.J.

doi:10.1016/j.jnnfm.2007.06.008

Cited by 35 publications

(29 citation statements)

References 32 publications

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“…Sahin, K. Mohseni and S. P. Colin related to 1/r and 1/r 2 terms in the cylindrical coordinates and will result in better conditioned linear systems. The modified governing equations are discretized by extending the dilation-free semistaggered finite volume method (Sahin, 2005;Sahin and Wilson, 2007) to the cylindrical swirl-free coordinates, and readers are referred to our previous publication (Sahin and Mohseni, 2009) for the full details of this discretization. The continuity equation is satisfied exactly within each element and special attention is given to satisfy the geometric conservation law at a discrete level.…”

Section: The Numerical Methodsmentioning

confidence: 99%

The numerical comparison of flow patterns and propulsive performances for the hydromedusaeSarsia tubulosaandAequorea victoria

Şahin

Mohseni

Colin

2009

Journal of Experimental Biology

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SUMMARYThe thrust-generating mechanism of a prolate hydromedusa Sarsia tubulosa and an oblate hydromedusa Aequorea victoria was investigated by solving the incompressible Navier-Stokes equations in the swirl-free cylindrical coordinates. The calculations clearly show the vortex dynamics related to the thrust-generating mechanism, which is very important for understanding the underlying propulsion mechanism. The calculations for the prolate jetting hydromedusa S. tubulosa indicate the formation of a single starting vortex ring for each pulse cycle with a relatively high vortex formation number. However, the calculations for the oblate jet-paddling hydromedusa A. victoria indicate shedding of the opposite-signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction as the vortices move away from the hydromedusa in the wake. In addition to this jet propulsion mechanism, the hydromedusa's bell margin acts like a paddle and the highly flexible bell margin deforms in such a way that the low pressure leeward side of the bell margin has a projected area in the direction of motion. This thrust is particularly important during refilling of the subumbrella cavity where the stopping vortex causes significant pressure drag. The swimming performances based on our numerical simulations, such as swimming velocity, thrust, power requirement and efficiency, were computed and support the idea that jet propulsion is very effective for rapid body movement but is energetically costly and less efficient compared with the jet-paddling propulsion mechanism.

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Section: The Numerical Methodsmentioning

confidence: 99%

The numerical comparison of flow patterns and propulsive performances for the hydromedusaeSarsia tubulosaandAequorea victoria

Şahin

Mohseni

Colin

2009

Journal of Experimental Biology

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“…The steady base flow was found using a semi-staggered finite volume method, similar to earlier work [13] but using Newton's method rather than time-dependent calculation. If the underlying flow is unstable, time-dependent simulations will never find a steady state.…”

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confidence: 86%

Molecular physics of a polymer engineering instability: Experiments and computation

et al. 2008

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Entangled polymer melts exhibit a variety of flow instabilities that limit production rates in industrial applications. We present both experimental and computational findings, using flow of monodisperse linear polystyrenes in a contraction-expansion geometry, which illustrate the formation and development of one such flow instability. This viscoelastic disturbance is first observed at the slit outlet and subsequently produces large-scale fluid motions upstream. A numerical linear stability study using the molecular structure based Rolie-Poly model confirms the instability and identifies important parameters within the model, which gives physical insight into the underlying mechanism. Chain stretch was found to play a critical role in the instability mechanism, which partially explains the effectiveness of introducing a low-molecular weight tail into a polymer blend to increase its processability. There are numerous types of experimentally observed instability in polymer melt flow; a recent review [1] highlights three forms observed in extrusion that occur at increasing rates of flow. The first two are "sharkskin" instabilities, which develop due to free surface effects, and "stick-spurt" or "stick-slip" instabilities, which result from material compression and stick-slip at the wall. While the mechanisms underlying the formation of these first two are relatively well understood [2,3], the third class, termed "volume instability", is less so [4]. This instability in converging flows for extrusion and injection moulding has been known for many years, and an empiricism has been developed. But as yet there is no understanding of the underlying physics of the problem, and the inherent connection between the viscoelastic instability and the molecular polymer dynamics. Understanding the underlying physical process would greatly enhance industry's ability to define efficient processing conditions. This letter outlines recent work in which we created an idealised model flow, related to the engineering flows in that the essential elements are present, but simplified so that the experimental variables are well-controlled and so the whole flow field can be modelled. We have use molecularly well-characterised materials (building on previous work for monodisperse materials under tightly controlled flow conditions [5,6]) so that the connection between viscoelastic properties and molecular structure can be maintained without empirical fitting. Through these careful *

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“…There are different ways to discretize (1.1), examples are a MAC discretization on a staggered grid and collocated finite difference methods [27,30], finite volume [36] or LBB-stable finite elements [13]. In this paper we consider Galerkin finite element discretization methods, although the approach is essentially independent of a specific discretization method.…”

Section: Finite Element Approximationmentioning

confidence: 99%

A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution

Aposporidis

Haber

Olshanskii

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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In this paper we introduce a mixed formulation of the Bingham fluid flow problem. We consider both the original and a regularized version of the problem, where a parameter ε is introduced, forcing the entire domain to be formally a fluid region. In general, common solvers for the regularized problem experience performance degradation when the parameter ε gets smaller. The method studied here introduces an auxiliary tensor variable and shows enhanced numerical properties for small values of ε. Good performance is also observed for the non-regularized case. The well posedness for the regularized problem and the equivalence -at the continuous level -between the original (primitive variables) and the mixed formulation are demonstrated. We analyze properties of linearized problems that are relevant for the convergence of numerical solvers. A finite element method for the mixed formulation is discussed. Numerical results confirm the predicted better performances of the mixed formulation comparing to the primitive variables formulation. A comparison to a non regularized solver based on the augmented Duvaut-Lions-Glowinski formulation of the problem is carried out as well.

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A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

Cited by 35 publications

References 32 publications

The numerical comparison of flow patterns and propulsive performances for the hydromedusaeSarsia tubulosaandAequorea victoria

The numerical comparison of flow patterns and propulsive performances for the hydromedusaeSarsia tubulosaandAequorea victoria

Molecular physics of a polymer engineering instability: Experiments and computation

A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution

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