On the numerical solution of a convection–diffusion equation for particle orientation dynamics on geodesic grids

Zharovsky, Evgeniy; Moosaie, Amin; Duc, Anne Le; Manhart, Michael; Simeon, Bernd

doi:10.1016/j.apnum.2012.06.004

Cited by 14 publications

(11 citation statements)

References 21 publications

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“…Such grids have become popular in meteorology [8,9,10,11], and the FVM has proved its reliablity in various convection-dominated applications [12]. We were able to show that the approach with geodesic grids yields high quality solutions for particle orientation dynamics [13]. However, due to the localized phenomena the results obtained so far suggest further developments towards a fully adaptive algorithm in space and time.…”

Section: Introductionmentioning

confidence: 92%

“…This initial discretization can then be refined to obtain a mesh with the desired resolution. In a recent work, we employed uniform refinement [13] as shown in Fig. 2, but since the solution features highly localized phenomena (Fig.…”

Section: Geodesic Gridsmentioning

confidence: 98%

“…The icosahedron is symmetric to its center of mass, which in our case is the origin. This allows us to employ an initial triangulation consisting of ten instead of twenty triangles, and also with respect to the refined grids we have savings of 50 % by exploiting this symmetry, see [13].…”

Section: Geodesic Gridsmentioning

confidence: 99%

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A space-time adaptive approach to orientation dynamics in particle laden flows

Zharovsky

Simeon

2010

Procedia Computer Science

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1949 Toms discovered that a minute amount of polymer fibers suspended into a Newtonian solvent can increase the flow-rate of the fluid and thus reduce the turbulent drag. Today, the mechanism behind this effect is still not completely understood. We aim at studying this phenomenon numerically by directly solving the governing FokkerPlanck equation (FoP) for particle orientation statistics. From a numerical analysis point of view, this is a convectiondominated convection-diffusion equation in orientation space where the convection term depends on the fluid flow. Since the orientation space is naturally given by the surface of the unit sphere, we tackle the problem by combining a geodesic grid discretization with the Finite Volume Method (FVM). Due to an isolated moving peak in the solution of the FoP, we employ a space-time adaptive approach and discuss the performance of the adaptive algorithm with respect to different refinement strategies for an analytical test problem (simple shear flow) and for input data from the direct numerical simulation of a turbulent channel flow. Furthermore, the results are compared to previous approaches based on uniform grids. It turns out that the space-time adaptive algorithm is indeed advantageous for certain flow fields but so far not as robust as approaches with fixed grids.

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Section: Introductionmentioning

confidence: 92%

Section: Geodesic Gridsmentioning

confidence: 98%

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A space-time adaptive approach to orientation dynamics in particle laden flows

Zharovsky

Simeon

2010

Procedia Computer Science

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“…However, the CPU-time of this solver was relatively high for weakly Brownian and non-Brownian fibers. Zharovsky et al [20] also developed a direct Fokker-Planck solver based on the finite volume method.…”

Section: Accepted M M a N U mentioning

confidence: 99%

On the structure of vorticity and near-wall partial enstrophy in fibrous drag-reduced turbulent channel flow

Moosaie

Manhart

2015

Journal of Non-Newtonian Fluid Mechanics

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“…Thus, one way of obtaining the fibers orientation distribution is to solve the corresponding Fokker-Planck equation. This can be done either directly [12][13][14] or by means of a stochastic simulation [15,16]. Both approaches yield the "exact" result in a sense that they do not need any further modeling.…”

Section: Introductionmentioning

confidence: 98%

A priori analysis of a closure model using the reconstruction of the orientation distribution function in flow of fiber suspensions

2011

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A closure model for flow-induced fiber orientation is proposed that is based on a reconstruction of the orientation distribution function (ODF). An a priori analysis by using Monte-Carlo simulation was performed. The main results are as follows. For strong rotary Brownian motion (low Péclet numbers), the model performs well even by using only the second moment to reconstruct the ODF. By considering the fourth moment in the reconstruction procedure, the accuracy of the model is improved and the model is applicable to higher Péclet numbers. At very high Péclet numbers and for non-Brownian fibers, the solution predicted by the proposed model deviates from the reference solution.

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On the numerical solution of a convection–diffusion equation for particle orientation dynamics on geodesic grids

Cited by 14 publications

References 21 publications

A space-time adaptive approach to orientation dynamics in particle laden flows

A space-time adaptive approach to orientation dynamics in particle laden flows

On the structure of vorticity and near-wall partial enstrophy in fibrous drag-reduced turbulent channel flow

A priori analysis of a closure model using the reconstruction of the orientation distribution function in flow of fiber suspensions

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