Two relaxation time lattice Boltzmann method coupled to fast Fourier transform Poisson solver: Application to electroconvective flow

Guan, Yifei; Novosselov, Igor

doi:10.1016/j.jcp.2019.07.029

Cited by 50 publications

(43 citation statements)

References 48 publications

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“…The TRT LBM approach is used to solve the transport equations for fluid flow and charge density, coupled to a fast Poisson solver for electric potential [87,88]. The solver is extended to 3D for the differential equations (Eq.…”

Section: Resultsmentioning

confidence: 99%

“…Without initial perturbation, the system is hydrostatic, and the electrical properties are onedimensional in the z-direction. [87,88], unified SRT LBM [48], and the analytical solution [85,98] To obtain various equilibrium solutions, for example, as shown in FIG. 2, different initialization (initial perturbation) schemes are applied to the hydrostatic base state.…”

Section: System Linearization and Initializationmentioning

confidence: 99%

“…where 3 10  − = is the perturbation magnitude, taken to be the same as in previous 2D analyses [87,88].…”

Section: Fig 1 Hydrostatic Solution Comparison Of the Trt Lbm And Fmentioning

confidence: 99%

“…This unified LBM transforms the elliptic Poisson equation into a parabolic reaction-diffusion equation and introduces artificial coefficients to control the evolution of the electrical potential. A segregated solver was proposed that combines a two-relaxation time (TRT) LBM modeling of the fluid and charge transport, and a Fast Fourier Transform (FFT) Poisson solver for the electrical field [87]. Related to vortex structure transition with the addition of cross-flow, 2D finite-volume simulations of Poiseuille flow have demonstrated that the value of c T is a function of Re and the ion mobility parameter, M [43].…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional electroconvective vortices in cross flow

2020

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The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is onedimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number. 1 0 cc c t Fe Pattern transition after cross-flow applicationThis section studies the transitions of 3D to 2D patterns by applying the cross-flow to already developed square vortex structures, as shown in FIG. 3(a). With weak cross-flow, the systems transitions to oblique 3D vortex structures (oblique transverse and regular longitudinal structures coexist). The increased cross-flow yields a longitudinal rolling pattern, i.e., transverse structures are fully suppressed . FIG. 11 shows the time evolution of maximum * z u in Couette cross-flow. For lower cross-flow velocities (e.g., u * wall=2.40) and, therefore, weak shear stress, the maximum * z u decreases to an equilibrium value, that is somewhat greater than that for the rolling pattern flow (u * wall =2.75). Interestingly, with further increase in u * wall (e.g., u * wall=3.20), the equilibrium value of * z u may decrease below the value of the rolling pattern.And with even further increasing u * wall (e.g., u * wall=3.84), the equilibrium solution develops an oblique 3D structure with maximum uz that is greater than that of the rolling pattern. However, at u * wall = 3.88, a bifurcation occurs, and the steady-state solution has only 2D streamwise

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Section: Resultsmentioning

confidence: 99%

Section: System Linearization and Initializationmentioning

confidence: 99%

“…where 3 10  − = is the perturbation magnitude, taken to be the same as in previous 2D analyses [87,88].…”

Section: Fig 1 Hydrostatic Solution Comparison Of the Trt Lbm And Fmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional electroconvective vortices in cross flow

2020

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“…Let us mention that the force-driven Poiseuille flow modeling follows the same path: whereas a rotated parabolic no-slip and slip solutions are available for any two-point multi-reflection 22,30,40,85 and single-node LSOB, 21,87 they cannot be matched by the moment-based on-grid boundary methods 57,77 with d 0. The recent LI scheme 95 purposes the exact inclined Poiseuille flow modeling but, in reality, its solution is exact only in a straight channel, extending the BB solution 20,22 and MGLI schemes 30,40 to any distance d and to any (stable) K. Yet, this Poiseuille channel problem is a pure-diffusion counterpart of the ADE problem (41). To this end, we complement PPLI with its flow counterpart IPLI in Table XII; the IPLI is exact for the forcedriven Poiseuille flow in a grid-inclined channel and it is parabolicaccurate for any uniform-density Stokes flow, at least.…”

Section: Summary On the Piece-wise Parabolic Solutionsmentioning

confidence: 99%

Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

Ginzburg

Silva

2021

Physics of Fluids

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We introduce two new approaches, called A-LSOB and N-MR, for boundary and interface-conjugate conditions on flat or curved surface shapes in the advection-diffusion lattice Boltzmann method (LBM). The Local Second-Order, single-node A-LSOB enhances the existing Dirichlet and Neumann normal boundary treatments with respect to locality, accuracy, and P eclet parametrization. The normal-multi-reflection (N-MR) improves the directional flux schemes via a local release of their nonphysical tangential constraints. The A-LSOB and N-MR restore all first-and second-order derivatives from the nodal non-equilibrium solution, and they are conditioned to be exact on a piece-wise parabolic profile in a uniform arbitrary-oriented tangential velocity field. Additionally, the most compact and accurate single-node parabolic schemes for diffusion and flow in grid-inclined pipes are introduced. In simulations, the global mass-conservation solvability condition of the steady-state, two-relaxation-time (S-TRT) formulation is adjusted with either (i) a uniform mass-source or (ii) a corrective surface-flux. We conclude that (i) the surface-flux counterbalance is more accurate than the bulk one, (ii) the A-LSOB Dirichlet schemes are more accurate than the directional ones in the high P eclet regime, (iii) the directional Neumann advective-diffusive flux scheme shows the best conservation properties and then the best performance both in the tangential no-slip and interface-perpendicular flow, and (iv) the directional non-equilibrium diffusive flux extrapolation is the least conserving and accurate. The error P eclet dependency, Neumann invariance over an additive constant, and truncation isotropy guide this analysis. Our methodology extends from the d2q9 isotropic S-TRT to 3D anisotropic matrix collisions, Robin boundary condition, and the transient LBM.

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