International Journal for Numerical Methods in Fluids

Pang, B. Y.; Xiao, Y.; Yang, L. M.

doi: 10.1002/fld.70081pmid: N/A

In this work, a multiscale, zonal‐coupled physics‐informed neural network (PINN) framework, termed BL‐NS‐PINNs, is proposed for accurately predicting steady laminar near‐wall flow fields at high Reynolds numbers without requiring near‐wall data. The framework ensures physical continuity across flow regions by solving the Blasius and Navier–Stokes equations in the inner and outer zones, respectively, while enforcing velocity consistency within the matching region. Numerical experiments demonstrate that BL‐NS‐PINNs significantly outperform conventional PINNs trained with data supervision, accurately capturing near‐wall flow features and sharp gradients in high‐Reynolds‐number laminar boundary layers. The method is further extended to wedge flows with self‐similar solutions, offering both a theoretical foundation and a practical pathway for integrating wall functions into data‐driven boundary‐layer modeling. Overall, BL‐NS‐PINNs effectively overcome the limitations of conventional PINNs in resolving sharp near‐wall velocity gradients and show strong potential for efficient, high‐fidelity modeling of high‐Reynolds‐number flows.

Issakhov, Alibek; Sabyrkulova, Aidana; Abylkassymova, Aizhan

doi: 10.1002/fld.70067pmid: N/A

This study examines the influence of the thermophysical properties of various partition materials on heat transfer processes in a cavity filled with liquid. To achieve this goal, both direct computational fluid dynamics (CFD) and machine learning (ML) methods were applied. Direct CFD simulations were performed to obtain a detailed understanding of the temperature distribution within the cavity for different septum materials. Subsequently, machine learning methods were applied to create regression models capable of predicting changes in the temperature value inside the cavity based on different septum materials. The best results were achieved using third‐degree polynomial regression, achieving a coefficient of determination (R 2) of 0.816. This indicates that the model is well adapted to the data and is able to explain the variability of the target variable. Additionally, random forest regression models were examined, but their results were slightly less accurate compared to polynomial regression. The study demonstrates that integrating machine learning techniques into computational fluid dynamics can significantly improve the analysis and prediction of thermal processes.

Ammosov, Dmitry; Al Kobaisi, Mohammed; Efendiev, Yalchin

doi: 10.1002/fld.70080pmid: N/A

In this paper, we derive multicontinuum poroelasticity models using the multicontinuum homogenization method. Poroelasticity models are widely used in many areas of science and engineering to describe coupled flow and mechanics processes in porous media. However, in many applications, the properties of poroelastic media possess high contrast, presenting serious computational challenges. It is well known that standard homogenization approaches often fail to give an accurate solution due to the lack of macroscopic parameters. Multicontinuum approaches allow us to consider such cases by defining several average states known as continua. In the field of poroelasticity, multiple‐network models arising from the multiple porous media theory are representatives of these approaches. In this work, we extend previous findings by deriving the generalized multicontinuum poroelasticity model. We apply the recently developed multicontinuum homogenization method and provide a rigorous derivation of multicontinuum equations. For this purpose, we formulate coupled constraint cell problems in oversampled regions to consider different averages and gradient effects. Then, we obtain a multicontinuum expansion of the fine‐scale fields and derive the multicontinuum model supposing the smoothness of macroscopic variables. We present the most general version of equations and the simplified ones based on our numerical experiments. Numerical results are presented for different heterogeneous media cases and demonstrate the high accuracy of our proposed multicontinuum models.

Prajapati, Soham; Fakhreddine, Ali; Mahesh, Krishnan

doi: 10.1002/fld.70082pmid: N/A

We develop a three‐dimensional Eulerian framework to simulate fluid‐structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume‐of‐fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF‐based one‐continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface‐capturing (IC) approach, the piecewise linear interface calculation (PLIC) method is used to reconstruct the interface, and the Lagrangian explicit (LE) method is used in the directionally split advection procedure. To model the hyperelastic behavior of the solid, we consider linear and nonlinear Mooney–Rivlin material models, where we use the left Cauchy–Green deformation tensor (B$$ \boldsymbol{B} $$) to account for the solid deformation on an Eulerian grid and the fifth‐order weighted essentially non‐oscillatory (WENO‐Z) finite difference reconstruction method is utilized to treat the advection terms involved in the transport equation of B$$ \boldsymbol{B} $$. Multiple benchmark problems and reversibility tests are considered to verify the accuracy of the approach. Furthermore, to demonstrate the capability of the solver to handle turbulent interactions, we perform direct numerical simulation (DNS) of turbulent channel flow with a deformable compliant bottom wall and a rigid top wall; our observations align well with previous experimental and numerical works. The detailed numerical experiments show that: (i) despite the discontinuity of the interface across the cell boundaries and stress discontinuity across the interface, a VOF/PLIC‐based FSI framework can provide stable and accurate solutions that significantly minimizes numerical artifacts (e.g., flotsam and spurious currents) while maintaining a sharp interface. (ii) The accuracy of a VOF/PLIC‐based FSI approach on coarse grids is comparable to the accuracy of a diffusive IC method‐based FSI approach on much finer grids.

Li, Qing; Wang, Juanyong; Wang, Lei; Zhu, Zijin

doi: 10.1002/fld.70079pmid: N/A

In this work, the droplet impact on a sinusoidally oscillating hydrophobic substrate is numerically simulated using the lattice Boltzmann method. We focus particularly on energy transfer and the maximum droplet spreading diameter (βm$$ {\beta}_m $$) as functions of substrate oscillation parameters, the Weber number, and the wettability of the substrate. Our analysis shows that the maximum spreading diameter scales linearly with the tangential Weber number (Wes$$ W{e}_s $$), calculated from the substrate velocity amplitude. Notably, the spreading dynamics exhibit a nonmonotonic, resonance‐like response, peaking when the spreading time coincides with half the oscillation period. Additionally, decreasing the contact angle strengthens interfacial adhesion to amplify horizontal migration, whereas superhydrophobic surfaces severely attenuate this tangential momentum exchange through inherent slip. Furthermore, the analysis of the normal Weber number (Wen$$ W{e}_n $$) uncovers a “forgetting” mechanism, whereby the droplet ultimately converges to a consistent dynamic response across different Wen$$ W{e}_n $$ as the initial kinetic energy dissipates. The study further elucidates the distinct regulatory effects of amplitude and period: amplitude primarily shifts the overall βm$$ {\beta}_m $$‐Wen$$ W{e}_n $$ scaling relation, while period significantly alters its slope. Based on these insights, we propose a universal scaling law that decomposes the maximum spreading factor into a normal‐inertia‐dominated term and a tangential vibration‐coupling term. A semi‐empirical correlation is subsequently derived, which quantifies the significant spreading enhancement induced by long‐period oscillations and captures the attenuation of this gain at high Wen$$ W{e}_n $$.