An efficient finite volume method for electric field–space charge coupled problems

Wu, Jian; Traoré, Philippe; Louste, Christophe

doi:10.1016/j.elstat.2012.12.004

Cited by 38 publications

(21 citation statements)

References 36 publications

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“…As discussed in Atten & Moreau (1972), it is not possible to prove rigorously that this principle applies in the free-walls case. However, the numerical simulations conducted by Traoré & Pérez (2012) and Wu et al (2013a) show that the growth of small perturbation proceeds in a monotonic way, without oscillations. This behaviour is observed for weak, moderate and strong injection, i.e.…”

Section: Linear Stability Analysismentioning

confidence: 93%

“…Consequently, strong gradients of charge density may appear and the problem is very sensitive to the effects of numerical diffusion. Several numerical techniques have been used to tackle this difficulty: particle-in-cell (Castellanos, Atten & Pérez 1987;Chicón, Castellanos & Martín 1997;Vázquez, Georghiou & Castellanos 2006), flux-corrected transport (FCT) schemes (Pérez & Castellanos 1989;Vázquez et al 2006;Vázquez, Georghiou & Castellanos 2008), total variation diminishing (TVD) schemes (Traoré & Pérez 2012;Wu, Traoré & Louste 2013a) and, more recently, discontinuous Galerkin finite element (Vázquez & Castellanos 2013).…”

Section: Introductionmentioning

confidence: 99%

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Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Pérez

Vázquez

et al. 2014

J. Fluid Mech.

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We investigate the linear stability threshold of a dielectric liquid subjected to unipolar injection in a two-dimensional rectangular enclosure with rigid boundaries. A finite element formulation transforms the set of linear partial differential equations that governs the system into a set of algebraic equations. The resulting system poses an eigenvalue problem. We calculate the linear stability threshold, as well as the velocity field and charge density distribution, as a function of the aspect ratio of the domain. The stability parameter as a function of the aspect ratio describes paths of symmetry-breaking bifurcation. The symmetry properties of the different linear modes determine whether these paths cross each other or not. The resulting structure has important consequences in the nonlinear behaviour of the system after the bifurcation points.

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Section: Linear Stability Analysismentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Pérez

Vázquez

et al. 2014

J. Fluid Mech.

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“…Both the SMART algorithm and FUD scheme were converted into the upwind based unified formulation [31] for easy implementation. For more details about the application of TVD scheme in solving the charge density equation, please refer to [17], [32].…”

Section: Methodsmentioning

confidence: 99%

“…In numerical studies, the core difficulty lies in the algorithm for the conservation equation of charge density. Some 'special' schemes, such as the particle in cell (PIC) [11]- [13], flux corrected transport (FCT) [12], [14] and total variation diminishing (TVD) [15]- [17] have been used to compute the charge density distribution. However, most numerical studies focused on the finite amplitude regime, which means the driving parameter is close to the linear stability criterion.…”

Section: Introductionmentioning

confidence: 99%

Effect of the mobility parameter on the oscillatory electro-convection of dielectric liquids subject to strong unipolar charge injection

Traoré

Louste

et al. 2013

2013 IEEE Industry Applications Society Annual Meeting

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Two-dimensional numerical calculations were carried out for the isothermal electro-convection in a dielectric liquid induced by the unipolar charge injection. In the dimensionless form, the system is mainly governed by the injection strength number (C), the electric Rayleigh number (1) and a mobility number (M). A strong injection case with C = 10 was considered. Along with the increase of the driving parameter T, oscillatory electro-convection occurs. Critical values of T corresponding to the onset of such oscillatory convection were shown to be highly dependent on M, and were accurately determined. Some precautions including the algorithm for the charge density equation were taken to reduce the numerical diffusion and to ensure the reliability of our findings.

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“…Recent det ailed comput at ional invest igat ions have been conduct ed [17,18,19] t hat have also focused on analysing t he format ion of t he roll st ruct ures which has included spat ial dist ribut ions of charge and velocity magnit ude as well as t emporal variat ions in t hese quant it ies [1,20].…”

Section: Introductionmentioning

confidence: 99%

Characteristics of electrohydrodynamic roll structures in laminar planar Couette flow

Kourmatzis¹,

Shrimpton²

2015

J. Phys. D: Appl. Phys.

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A bst r act .T he behaviour of an incompressible dielect ric liquid subject ed t o a laminar planar Couet t e ow wit h unipolar charge inject ion is invest igat ed numerically in two dimensions. T he comput at ions show new morphological charact erist ics of roll st ruct ures t hat arise in t his forced elect ro-convect ion problem. T he charge and velocity magnit ude dist ribut ions between t he two parallel elect rodes are discussed as a funct ion of t he t op wall velocity and t he EHD Rayleigh number, T for t he case of st rong charge inject ion. A wide enough paramet ric space is invest igat ed such t hat t he observed EHD roll st ruct ures progress t hrough t hree regimes. T hese regimes are de ned by t he presence of a single or double-roll free convect ive st ruct ure as observed elsewhere [1], a sheared or st ret ched roll st ruct ure, and nally by a regime where t he perpendicular velocity gradient is su cient t o prevent t he generat ion of a roll. T hese t hree regimes have been delineat ed as a funct ion of t he wall t o ionic drift velocity U W = E , and t he T number. In t he st ret ched regime, an increase in U W = E can reduce charge and moment um uct uat ions whilst in parallel de-st rat ify charge in t he region between t he two elect rodes. T he st ret ched roll regime is also charact erised by a subst ant ial in uence of U W = E on t he st eady development t ime, however in t he t radit ional non-st ret ched roll st ruct ure regime, no in uence of U W = E on t he development t ime is not ed.

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An efficient finite volume method for electric field–space charge coupled problems

Cited by 38 publications

References 36 publications

Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Effect of the mobility parameter on the oscillatory electro-convection of dielectric liquids subject to strong unipolar charge injection

Characteristics of electrohydrodynamic roll structures in laminar planar Couette flow

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