Two deep learning (DL) models addressing the super-resolution (SR) reconstruction of turbulent flows from low-resolution coarse flow field data are developed. One is the static convolutional neural network (SCNN), and the other is the novel multiple temporal paths convolutional neural network (MTPC). The SCNN model takes instantaneous snapshots as an input, while the MTPC model takes a time series of velocity fields as an input, and it includes spatial and temporal information simultaneously. Three temporal paths are designed in the MTPC to fully capture features in different time ranges. A weight path is added to generate pixel-level weight maps of each temporal path. These models were first applied to forced isotropic turbulence. The corresponding high-resolution flow fields were reconstructed with high accuracy. The MTPC seems to be able to reproduce many important features as well, such as kinetic energy spectra and the joint probability density function of the second and third invariants of the velocity gradient tensor. As a further evaluation, the SR reconstruction of anisotropic channel flow with the DL models was performed. The SCNN and MTPC remarkably improve the spatial resolution in various wall regions and potentially grasp all the anisotropic turbulent properties. It is also shown that the MTPC supplements more under-resolved details than the SCNN. The success is attributed to the fact that the MTPC can extract extra temporal information from consecutive fluid fields. The present work may contribute to the development of the subgrid-scale model in computational fluid dynamics and enrich the application of SR technology in fluid mechanics.

We propose a method for approximating the adhesion parameters in the Shan and Chen multicomponent, multiphase lattice Boltzmann model that leads to the desired fluid-solid contact angle. The method is a straightforward application of Young’s equation with substitution of the Shan and Chen cohesion parameter and a density factor for the fluid-fluid interfacial tension, and the adhesion parameters for the corresponding fluid-solid interfacial tensions.

In this paper, the viscous coupling effects for immiscible two-phase (gas-liquid) flow in porous media were studied using the Shan–Chen-type single-component multiphase lattice Boltzmann model. Using the model, the two-phase flows in porous media with density ratio as high as 56 could be simulated and the contact angle of the gas-liquid interface at a solid wall is adjustable. To investigate viscous coupling effects, the co- and countercurrent steady-state two-phase flow patterns and relative permeabilities as a function of wetting saturation were obtained for different capillary numbers, wettabilities, and viscosity ratios. The cocurrent relative permeabilities seem usually larger than the countercurrent ones. The opposing drag-force effect and different pore-level saturation distributions in co- and countercurrent flows may contribute to this difference. It is found that for both co- and countercurrent flows, for strongly wet cases and viscosity ratio $M>1$ , $k_{\text{nw}}$ increase with the driving force and the viscosity ratio. However, for neutrally wet cases, the variations of $k_{\text{nw}}$ and $k_w$ are more complex. It is also observed that different initial pore-level saturation distributions may affect final steady-state distribution, and hence the relative permeabilities. Using the cocurrent and countercurrent steady flow experiments to determine the generalized relative permeabilities seems not correct.

The rotation of a neutrally buoyant spheroidal particle in a Couette flow is studied by a multi-relaxation-time (MRT) lattice Boltzmann method. We find several new periodic and steady rotation modes for a prolate spheroid for Reynolds numbers ( $\mathit{Re}$ ) exceeding 305. The simulations cover the regime up to $\mathit{Re}\leq 700$ . The rotational behaviour of the spheroid appears to be not only sensitive to the Reynolds number but also to its initial orientation. We discuss the effects of initial orientation in detail. For $305\lt \mathit{Re}\lt 345$ we find that the prolate spheroid reaches a periodic mode characterized by precession and nutation around an inclined axis which is located close to the middle plane where the velocity is zero. For $345\lt \mathit{Re}\lt 385$ , the prolate spheroid precesses around the vorticity direction with a nutation. For $\mathit{Re}$ close to the critical ${\mathit{Re}}_{c} \approx 345$ , a period-doubling phenomenon is observed. We also identify a motionless mode at higher Reynolds numbers ( $\mathit{Re}\gt 445$ ) for the prolate spheroid. For the oblate spheroid the dynamic equilibrium modes found are log rolling, inclined rolling and different steady states for $\mathit{Re}$ increasing from 0 to 520. The initial-orientation effects are studied by simulations of 57 evenly distributed initial orientations for each $\mathit{Re}$ investigated. Only one mode is found for the prolate spheroid for $\mathit{Re}\lt 120$ and $385\lt \mathit{Re}\lt 445$ . In other $\mathit{Re}$ regimes, more than one mode is possible and the final mode is sensitive to the initial orientation. However, the oblate spheroid dynamics are insensitive to its initial orientation.