Multicomponent lattice Boltzmann equation method with a discontinuous hydrodynamic interface

Kinematics of chromodynamic multicomponent lattice Boltzmann simulation with a large density contrast

The utility of an enhanced chromodynamic, color gradient or phase-field multicomponent lattice Boltzmann (MCLB) equation for immiscible fluids with a density difference was demonstrated by Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] and Ba et al. [Phys. Rev. E 94, 023310 (2016)2470-004510.1103/PhysRevE.94.023310], who advanced earlier work by Liu et al. [Phys. Rev. E 85, 046309 (2012)PLEEE81539-375510.1103/PhysRevE.85.046309] by removing certain error terms in the momentum equations. But while these models' collision scheme has been carefully enhanced by degrees, there is, currently, no quantitative consideration in the macroscopic dynamics of the segregation scheme which is common to all. Here, by analysis of the kinetic-scale segregation rule (previously neglected when considering the continuum behavior) we derive, bound, and test the emergent kinematics of the continuum fluids' interface for this class of MCLB, concurrently demonstrating the circular relationship with-and competition between-the models' dynamics and kinematics. The analytical and numerical results we present in Sec. V confirm that, at the kinetic scale, for a range of density contrast, color is a material invariant. That is, within numerical error, the emergent interface structure is isotropic (i.e., without orientation dependence) and Galilean-invariant (i.e., without dependence on direction of motion). Numerical data further suggest that reported restrictions on the achievable density contrast in rapid flow, using chromodynamic MCLB, originate in the effect on the model's kinematics of the terms deriving from our term F_{1i} in the evolution equation, which correct its dynamics for large density differences. Taken with Ba's applications and validations, this result significantly enhances the theoretical foundation of this MCLB variant, bringing it somewhat belatedly further into line with the schemes of Inamuro et al. [J. Comput. Phys. 198, 628 (2004)JCTPAH0021-999110.1016/j.jcp.2004.01.019] and the free-energy scheme [see, e.g., Phys. Rev. E. 76, 045702(R) (2007)10.1103/PhysRevE.76.045702, and references therein] which, in contradistinction to the present scheme and perhaps wisely, postulate appropriate kinematics a priori.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.