A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio

Liu, Haihu; Wu, Lei; Ba, Yan; Xi, Guang; Zhang, Yonghao

doi:10.1016/j.jcp.2016.10.007

Cited by 48 publications

(35 citation statements)

References 88 publications

(121 reference statements)

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“…The interface shape needs to be dynamically stable, which requires a balance between interfacial tension, buoyancy, and shear stresses at the scale of each fluid bubble. We solved this problem numerically using a lattice Boltzmann multiphase flow solver based on the color‐gradient method (Leclaire, Parmigiani, Malaspinas, et al, ; Leclaire, Parmigiani, Chopard, & Latt, ; Liu et al, ) that we have used in the past to compute the pore‐scale dynamics of fluid outgassing and migration in magma reservoirs (Parmigiani et al, , ). More details about the numerical method are provided in Appendix A.…”

Section: Physical Modelmentioning

confidence: 99%

A Physical Model for Three‐Phase Compaction in Silicic Magma Reservoirs

Huber

Parmigiani

2018

JGR Solid Earth

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We develop a model for phase separation in magma reservoirs containing a mixture of silicate melt, crystals, and fluids (exsolved volatiles). The interplay between the three phases controls the dynamics of phase separation and consequently the chemical and physical evolution of magma reservoirs. The model we propose is based on the two‐phase damage theory approach of Bercovici et al. (2001, https://doi.org/10.1029/2000JB900430) and Bercovici and Ricard (2003, https://doi.org/10.1046/j.1365-246X.2003.01854.x) because it offers the leverage of considering interface (in the macroscopic limit) between phases that can deform depending on the mechanical work and phase changes taking place locally in the magma. Damage models also offer the advantage that pressure is defined uniquely to each phase and does not need to be equal among phases, which will enable us to consider, in future studies, the large capillary pressure at which fluids are mobilized in mature, crystal‐rich, magma bodies. In this first analysis of three‐phase compaction, we solve the three‐phase compaction equations numerically for a simple 1‐D problem where we focus on the effect of fluids on the efficiency of melt‐crystal separation considering the competition between viscous and buoyancy stresses only. We contrast three sets of simulations to explore the behavior of three‐phase compaction, a melt‐crystal reference compaction scenario (two‐phase compaction), a three‐phase scenario without phase changes, and finally a three‐phase scenario with a parameterized second boiling (crystallization‐induced exsolution). The simulations show a dramatic difference between two‐phase (melt crystals) and three‐phase (melt‐crystals‐exsolved volatiles) compaction‐driven phase separation. We find that the presence of a lighter, significantly less viscous fluid hinders melt‐crystal separation.

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Section: Physical Modelmentioning

confidence: 99%

A Physical Model for Three‐Phase Compaction in Silicic Magma Reservoirs

Huber

Parmigiani

2018

JGR Solid Earth

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“…Since the first axisymmetric lattice Boltzmann (LB) model proposed by Halliday et al, successive models were then developed to truly recover the desired macroscopic equations Furthermore, different attempts were devoted to simplifying the treatments of source terms by either reducing the number of the source terms or avoiding the computations of spatial gradients therein . Moreover, the applicability of the axisymmetric LBM has also been well verified by practical axisymmetric flow tests …”

Section: Introductionmentioning

confidence: 99%

“…5,6,[12][13][14][15][16] Moreover, the applicability of the axisymmetric LBM has also been well verified by practical axisymmetric flow tests. 15,[17][18][19][20][21][22][23] Despite its widespread applications, LBM suffers from some drawbacks, such as its limitation to simple geometry and uniform mesh, constraint to viscous flows, and the intrinsic tie-up between the time interval and the mesh spacing. 24,25 Morover, the implementation of boundary constraints of the second or the third types (ie, the Neumann condition and Robin conditions) for the LB method is still challenging, especially for curved boundaries.…”

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confidence: 99%

An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows

Zhang

Жен

Yang

et al. 2019

Numerical Methods in Fluids

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Summary In this work, an improved axisymmetric lattice Boltzmann flux solver (LBFS) is proposed for simulation of axisymmetric isothermal and thermal flows. This solver globally resolves the axisymmetric Navier‐Stokes (N‐S) equations through the finite volume strategy and locally reconstructs numerical fluxes with solutions to the lattice Boltzmann equation. Compared with previous axisymmetric LBFS, some novel strategies are adopted in this work to simplify the formulations and improve the accuracy. First, the macroscopic equations are reformulated to reduce the number of source terms and remove spatial derivatives involved in the source terms. Second, the local reconstruction of numerical fluxes utilizes relationships given by the Chapman‐Enskog analysis and combines the radial coordinate (r) with the local solution to the standard LB equation. By adopting these two modifications, the present axisymmetric LBFS avoids the fractional‐step formulation and the finite‐difference approximation adopted in the previous solver, which reduces the complexity of implementation. Moreover, an alternative way of predicting intermediate pressure is proposed, which could effectively fix the inaccurate resolution of the pressure field in previous axisymmetric LBFS. Further extensions are made to enrich the applicability of the present solver in thermal axisymmetric flows. Validations on various benchmark tests are carried out for comprehensive evaluation of the robustness and flexibility of the proposed solver.

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“…Wang et al 18 validates a double MRT LB model for axisymmetric convective flow in porous media. Srivastava et al, 19 Liang et al, 20 and Liu et al 21 presented and validated an LBM for axisymmetric multiphase flows. They quantitatively validated the mass conservation and the flow dynamics of an axially symmetric oscillating droplet.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical study of Couette‐Taylor flow with an axial flow using lattice Boltzmann method

Mehrez

Gheith

Aloui

et al. 2019

Numerical Methods in Fluids

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Summary In this study, the numerical models for swirling flows developed by Li et al and Zhou for lattice Boltzmann method (LBM) are chosen. These models were firstly validated using the Couette‐Taylor flow between two concentric cylinders simulations. Numerical results showed the efficiency of the Zhou's model. Numerical simulation results using LBM are in good agreement for the steady and unsteady regimes compared to the literature review. In a second step, the Zhou model was then adopted to our study to determine the Couette‐Taylor instabilities with an axial flow. Two protocols are tested. The first one (direct protocol) starts with an azimuthal flow without any axial flow (Re = 0). Once the regime is established, an axial flow is then superposed to the Couette‐Taylor flow (with a sudden or a progressive manner). The second protocol (inverse protocol) starts with an axial flow at a given Reynolds number (Poiseuille flow). Once the regime is established, an azimuthal flow is the executed (with a sudden or a progressive manner). The effect of various parameters controlling the physical situation is also discussed. The increase of the azimuthal velocity mainly led to the emergence and development of Taylor vortices. Its influence decreases when the axial Reynolds number increases. The relevant result for this study is the change of the critical axial Reynolds number Rec (total disappearance of instabilities) with both protocols and both manners.

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A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio

Cited by 48 publications

References 88 publications

A Physical Model for Three‐Phase Compaction in Silicic Magma Reservoirs

A Physical Model for Three‐Phase Compaction in Silicic Magma Reservoirs

An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows

Theoretical and numerical study of Couette‐Taylor flow with an axial flow using lattice Boltzmann method

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