Immiscible fluid displacement in porous media occurs in several natural and industrial processes. For example, during petroleum extraction from porous rock reservoirs, water is used to displace oil. In this paper, we investigate the primary drainage and imbibition in a heterogeneous porous medium using an improved numerical model based on the multicomponent pseudopotential lattice Boltzmann method. We apply recent developments from the literature and develop new pressure boundary conditions. We show that the proposed model is able to simulate realistic viscosity ratios, and it allows independent tuning of surface tension from viscosity. Moreover, the model suppresses a nonphysical behavior of previous schemes, in which trapped fluid volumes significantly change with time. Furthermore, we show that the developed model correctly captures the underlying physical phenomena of fluid displacements. We simulate oil–water flows and verify that the measured values of irreducible water and residual oil saturations are realistic. Finally, we vary the wetting conditions of the porous medium to represent different wettability states. For the different scenarios, we show that the simulations are in good agreement with the experimental results.

We generalize a recently developed improved multicomponent pseudopotential lattice Boltzmann method in three dimensions and analyze its applicability to simulate flows through realistic porous media. The model is validated and characterized via benchmarks, and we investigate its performance by simulating the displacement of immiscible fluids in three-dimensional geometries. Two samples are considered, namely, a pack of spheres obtained numerically and a Bentheimer sandstone rock sample obtained experimentally. We show that with this model, it is possible to simulate realistic viscosity ratios, to tune surface tension independently, and, most importantly, to preserve the volume of trapped fluid. We also evaluate the computational performance of the model on the graphical processing unit and mention the implemented optimizations to increase the computational speed and reduce the memory requirements.

An accurate implementation of wetting and pressure drop is crucial to correctly reproduce fluid displacement processes in porous media. Although several strategies have been proposed in the literature, a systematic comparison of them is needed to determine the most suitable for practical applications. Here, we carried out numerical simulations to investigate the performance of two widely used wettability schemes in the lattice Boltzmann color gradient model, namely, the geometrical wetting scheme by Leclaire et al. [Phys. Rev. E 95(3), 033306 (2017)](scheme-I) and the modified direction of the color gradient scheme by Akai et al. [Adv. Water Resour. 116, 56–66 (2018)] (scheme-II). We showed that scheme-II was more accurate in simulating static contact angles of a fluid droplet on a solid surface. However, scheme-I was more accurate in simulating a dynamic case of a binary fluid flow in a horizontal capillary tube described by the Washburn equation. Moreover, we investigated the performance of two popular pressure gradient implementation types. Type-I used the so-called Zou–He pressure boundary conditions at the inlet and the outlet of the domain, while type-II used an external body force as a pressure gradient. We showed that the type-I implementation was slightly more accurate in simulating a neutrally wetting fluid in a horizontal capillary tube described by the Washburn equation. We also investigated the differences between the two types of pressure gradient implementation in simulating two fluid displacement processes in a Bentheimer sandstone rock sample: the primary drainage and the imbibition displacement processes.

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Simulations of nematohydrodynamics on graphics processing units (GPUs) are typically performed using double precision, which ensures accuracy but significantly increases computational cost. However, consumer-grade GPUs are optimized for single-precision calculations, making double-precision simulations inefficient on widely available hardware. In this work, we demonstrate that single-precision simulations can achieve the same accuracy as double-precision methods while delivering a 27-fold increase in the computational speed. To achieve this, we introduce two key improvements: (i) the shifted distribution function in the lattice Boltzmann method, which mitigates precision loss at low velocities, and (ii) the use of larger time steps in the finite-difference solver, which reduces numerical errors and improves the overall accuracy. We find that, unlike in double precision, accuracy in single-precision simulations follows a non-monotonic trend with respect to the finite-difference time step, revealing an optimal regime for precise computations. To illustrate the effectiveness of our approach, we simulate the dynamics of single and multiple skyrmionic tubes in Poiseuille flow. Our results confirm that optimized single-precision simulations enable fast and accurate modeling of complex nematohydrodynamic systems, making large-scale simulations feasible on standard gaming GPUs.

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.