Numerical simulation of three-dimensional Couette-Taylor flows

Liao, C. B.; Jane, S.J.; Young, D. L.

doi:10.1002/(sici)1097-0363(19990415)29:7<827::aid-fld819>3.0.co;2-y

Cited by 18 publications

(17 citation statements)

References 9 publications

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“…(14). This is followed by solving implicitly for the polymeric stress ( n+1 ) at the (n + 1)th time step, with inclusion of the stress diffusion term, given as…”

Section: Effect Of Artificial Stress Diffusivitymentioning

confidence: 99%

“…The least negative eigenvalue determines the growth/decay rate of the perturbations. Based on several experimental and theoretical studies, a series of flow transitions that occur starting from the base Couette flow to fully turbulent flow are well documented for the Newtonian Taylor-Couette flow for different rotational speed ratios of the cylinders [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions

Thomas¹,

Al-Mubaiyedh²,

Sureshkumar³

et al. 2006

Journal of Non-Newtonian Fluid Mechanics

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“…(14). This is followed by solving implicitly for the polymeric stress ( n+1 ) at the (n + 1)th time step, with inclusion of the stress diffusion term, given as…”

Section: Effect Of Artificial Stress Diffusivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions

Thomas¹,

Al-Mubaiyedh²,

Sureshkumar³

et al. 2006

Journal of Non-Newtonian Fluid Mechanics

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“…We thus have focused on a particular configuration: counterrotating Taylor-Couette flow, for which it is easy to obtain axially symmetric Taylor vortices (although these might relax back to Couette flow after several rotation periods; e.g. Liao et al 1999). The geometry described in Fig.…”

Section: Three Dimensions: Taylor-couette Flowmentioning

confidence: 99%

Multidimensional, compressible viscous flow on a moving Voronoi mesh

Muñoz

Springel

Marcus

et al. 2012

Monthly Notices of the Royal Astronomical Society

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Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.

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“…Since then, a variety of flow transitions have been observed experimentally for a relatively broad range of inner to outer cylinder ratios [2]. There are several flow regions existing in the Taylor Couette flow, which consist of different spatial and temporal patterns [3]. The most interesting phenomenon of Taylor Couette flow is the orderly progress of non-linear flow state observed in the system, as it undergoes the transition to turbulence [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%