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Electromagnetically forced flows in shallow electrolyte layers offer a versatile and nonintrusive method for exploring quasi-two-dimensional fluid dynamics. This review focuses on the experimental and theoretical aspects of such flows driven by Lorentz forces generated by the interaction of injected electric currents and the applied magnetic fields. The method is applicable to both liquid metals and electrolytes, with the latter more commonly used due to their wide availability and ease of handling. Experimental aspects of the method and key components of mathematical flow analysis are discussed. Initially developed for geophysical flow modeling, the method has been instrumental in exploring various other physical phenomena including vortex and wake dynamics, spatiotemporal chaos, and mixing processes. The review also addresses the challenges of achieving true two-dimensionality in laboratory settings and discusses the influence of various parameters, such as layer thickness and forcing intensity, on the flow behavior. Future research directions in the field are highlighted.
Earth is the only known planet with plate tectonics, which involves a mobile upper thermal boundary layer. Other terrestrial planets show a one-plate immobile lithosphere, or stagnant lid, that insulates and isolates their interior. Here, we first review the different types of lids that can develop on rocky and icy bodies. As they formed by accretion, involving high-energy impacts, terrestrial planets likely started hot and molten. We examine the process of lid initiation from a magma ocean stage and develop the equations for lid growth. We survey how lateral perturbations in lid and crust thickness can be amplified during their growth and finally discuss the possible processes at the origin of lid rupture and plate generation.
Lagrangian averaging theories, most notably the generalized Lagrangian mean (GLM) theory of Andrews and McIntyre, have been primarily developed in Euclidean space and Cartesian coordinates. We reinterpret these theories using a geometric, coordinate-free formulation. This gives central roles to the flow map, its decomposition into mean and perturbation maps, and the momentum 1-form dual to the velocity vector. In this interpretation, the Lagrangian mean of any tensorial quantity is obtained by averaging its pull-back to the mean configuration. Crucially, the mean velocity is not a Lagrangian mean in this sense. It can be defined in a variety of ways, leading to alternative Lagrangian mean formulations that include GLM and Soward and Roberts's volume-preserving version. These formulations share key features that the geometric approach uncovers. We derive governing equations both for the mean flow and for wave activities constraining the dynamics of the perturbations. The presentation focuses on the Boussinesq model for inviscid rotating stratified flows and reviews the necessary tools of differential geometry.
This review provides a comprehensive analysis of the literature on vortex-induced vibration (VIV) of flexible circular cylinders in cross-flow. It delves into the details of the underlying physics governing the VIV dynamics of cylinders characterized by low mass damping and high aspect ratio, subject to both uniform and shear flows. It compiles decades of experimental investigations, modeling efforts, and numerical simulations and describes the fundamental findings in the field. Key focal points include but are not limited to amplitude–frequency response behavior, the relationship between the distributed loading acting on the cylinder and the trajectories and the near wake structures around the cylinder, the existence of traveling waves, the identification of power-in/power-out regions, and the modal overlapping and mode competition phenomena.
The environmental setting of the Dead Sea combines several aspects whose interplay creates flow phenomena and transport processes that cannot be observed anywhere else on Earth. As a terminal lake with a rapidly declining surface level, the Dead Sea has a salinity that is close to saturation, so that the buoyancy-driven flows common in lakes are coupled to precipitation and dissolution, and large amounts of salt are being deposited year-round. The Dead Sea is the only hypersaline lake deep enough to form a thermohaline stratification during the summer, which gives rise to descending supersaturated dissolved-salt fingers that precipitate halite particles. In contrast, during the winter the entire supersaturated, well-mixed water column produces halite. The rapid lake level decline of O(1 m/year) exposes vast areas of newly formed beach every year, which exhibit deep incisions from streams. Taken together, these phenomena provide insight into the enigmatic salt giants observed in the Earth's geological record and offer lessons regarding the stability, erosion, and protection of arid coastlines under sea level change.
Raye Jean Montague (1935–2018) was a computer programmer and self-taught engineer who was at the forefront of modernizing naval architecture and naval engineering through the use of computer-aided design. In this biographical review, she is referred to as Montague, the surname she had for much of her professional life. Since she was a working engineer rather than a scholar, she did not create a publication record by which her achievements can be easily tracked, but her name appears in committee memberships, conference and working group proceedings, and other such interstices of computer-aided ship design. This key contributor to computer-aided design and manufacturing and to naval engineering is well worth getting to know.
The problem of the geodynamo is simple to formulate (Why does the Earth possess a magnetic field?), yet it proves surprisingly hard to address. As with most geophysical flows, the fluid flow of molten iron in the Earth's core is strongly influenced by the Coriolis effect. Because the liquid is electrically conducting, it is also strongly influenced by the Lorentz force. The balance is unusual in that, whereas each of these effects considered separately tends to impede the flow, the magnetic field in the Earth's core relaxes the effect of the rapid rotation and allows the development of a large-scale flow in the core that in turn regenerates the field. This review covers some recent developments regarding the interplay between rotation and magnetic fields and how it affects the flow in the Earth's core.
Thermoacoustic instability is a flow instability that arises due to a two-way coupling between acoustic waves and unsteady heat release rate. It can cause damaging, large-amplitude oscillations in the combustors of gas turbines, aeroengines, rocket engines, etc., and the transition to decarbonized fuels is likely to introduce new thermoacoustic instability problems. With a focus on practical thermoacoustic instability problems, especially in gas turbine combustors, this review presents the common types of combustor and burner geometry used. It discusses the relevant flow physics underpinning their acoustic and unsteady flame behaviors, including how these differ across combustor and burner types. Computational tools for predicting thermoacoustic instability can be categorized into direct computational approaches, in which a single flow simulation resolves all of the most important length scales and timescales, and coupled/hybrid approaches, which couple separate computational treatments for the acoustic waves and flame, exploiting the large disparity in length scales associated with these. Examples of successful computational prediction of thermoacoustic instability in realistic combustors are given, along with outlooks for future research in this area.
Our understanding of respiratory flow phenomena has been consolidated over decades with the exploration of in vitro and in silico canonical models that underscore the multiscale fluid mechanics spanning the vast airway complex. In recent years, there has been growing recognition of the significant intersubject variability characterizing the human lung morphometry that modulates underlying canonical flows across subjects. Despite outstanding challenges in modeling and validation approaches, exemplified foremost in capturing chronic respiratory diseases, the field is swiftly moving toward hybrid in silico whole-lung simulations that combine various model classes to resolve airflow and aerosol transport spanning the entire respiratory tract over cumulative breathing cycles. In the years to come, the prospect of accessible, community-curated datasets, in conjunction with the use of machine learning tools, could pave the way for in silico population-based studies to uncover unrecognized trends at the population level and deliver new respiratory diagnostic and pulmonary drug delivery endpoints.
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Niccolò Fonio, Pierre Sagaut, Giuseppe Di Molfetta
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Harrison Nobis, Philipp Schlatter, Eddie Wadbro, Martin Berggren, Dan S. Henningson
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Luca Alberti, Emanuele Carnevali, Andrea Crivellini, Gianmaria Noventa
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Maria Kazolea, Ralph Lteif, Martin Parisot
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Chuang-Yao Zhao, Jia-Yu Mao, Jun-Min Jiang, Di Qi, Fang-Fang Zhang, Qing Liu, Wei Xiao, Pu-Hang Jin, Kong Ling
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Sheng-Bo Zhang, Satyvir Singh, Manuel Torrilhon, Huan-Hao Zhang, Zhi-Hua Chen, Chun Zheng
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Jiaji Xu, Yuhang Hou, Shunhao Peng, Yongliang Feng, Xiaojing Zheng
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Mrityunjoy Saha, Saunak Sengupta, Sudipto Mukhopadhyay, Sukhendu Ghosh
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): A. Gesing, D. Platz, U. Schmid
Publication date: 30 August 2025
Source: Computers & Fluids, Volume 299
Author(s): Weixiong Yuan, Tiegang Liu, Kui Cao, Zhiqiang Zeng, Kun Wang
In this article, we derive a non-hydrostatic extension to the SWE to solve bottom-generated waves along with its pressure relation. This relation is built on a linear vertical velocity assumption, leading us to a quadratic pressure profile, where we alternatively write it so that we can solve it by a projection method without ambiguity due to the involved time derivative of an unknown. Comparison with a linear and a simplified quadratic pressure relation demonstrates the accuracy of the new approach.
We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built on the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two additional unknowns to be solved: vertical momentum and non-hydrostatic pressure. We show that a linear vertical velocity assumption turns out to give us a quadratic pressure relation, which is equivalent to Boussinesq-type equations, the Green-Naghdi equations specifically, making it suitable for weakly dispersive cases. However, this extension involves a time derivative of an unknown parameter, rendering the solution by a projection method ambiguous. In this study, we derive an alternative form of the elliptic system of equations to avoid such ambiguity. The new set of equations satisfies the desired solubility property, while also consistently representing the non-flat moving topography wave generation. Validations are performed using several test cases based on the previous experiments and a high-fidelity simulation. First, we show the efficiency of our model in solving a vertical movement, which represents an undersea earthquake-generated tsunami. Following that, we demonstrate the accuracy of the model for landslide-generated waves. Finally, we compare the performance of our novel set of equations with the linear and simplified quadratic pressure profiles.
, , , and , “ An Efficient Parallel Algorithm for Three-Dimensional Analysis of Subsidence Above Gas Reservoirs,” International Journal for Numerical Methods in Fluids 31, no. 1 (1999): 247–260, https://doi.org/10.1002/(SICI)1097-0363(19990915)31:1<247::AID-FLD966>3.0.CO;2-D.
The above article, published online on 14 September 1999 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the authors; the journal Editor-in-Chief, Alina Bruma; and John Wiley & Sons Ltd. The retraction has been agreed due to the authors' discovery that the proper permissions for use of Table 1 and Figures 4, 5, 6, 7, and 8 were not obtained prior to publication. As it was not possible to obtain retrospective permission, the article must therefore be retracted.
The CIP (constrained interpolation profile)-Soroban method is an excellent adaptive method. This study proposed a modified CIP-Soroban method to handle scenarios involving severe compressible hydrodynamics with large gradients of physical values and strong nonlinearity. We took the implosion process of inertial confinement fusion as an application example (see snapshots in [a, b]), which demonstrated that the method reduced computational costs for achieving the same precision results compared to the conventional uniform grid CIP method (as shown in [c, d]).
The CIP-Soroban method is an excellent adaptive meshless method capable of solving advection problems with 3rd-order accuracy by combining the Constrained Interpolation Profile/Cubic Interpolated Pseudo-particle (CIP) method. This study proposes a modified version of the CIP-Soroban method specifically designed to address severe compressible hydrodynamic scenarios. The proposed method includes a material distinguishing approach, incorporates a modified form of monitoring functions for grid generation, utilizes a staggered grid arrangement, incorporates the Maximum and minimum Bounds method, solves non-advection terms using a finite difference method, and employs an adjusted procedure for stably solving the governing equations. We applied the modified CIP-Soroban method to simulate the implosion process in inertial confinement fusion (ICF), which is commonly modeled by compressible fluid and has the problems of large gradients of physical values and strong nonlinearity for stable and accurate numerical analysis. Implosion simulations were performed using a series of grids with increasing resolutions, ranging from coarse to fine grid settings, as one of the application examples. The results indicated that compared to the conventional uniform grid CIP method, the modified CIP-Soroban method reduced computational costs (calculation time, memory occupancy, and grid number) for obtaining the same precision results.
In nature, many complex multi-physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU-accelerated, mixed-precision configuration for the FDiRW solver to maximize efficiency through GPU multi-threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU-accelerated mixed-precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU-accelerated mixed-precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium-sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.
Reinforcement learning (RL) is a computational method where an agent learns to complete tasks by interacting with an unknown dynamic environment. An RL agent comprises a policy and a learning algorithm. The policy, typically a function approximator like a neural network, maps observations from the environment to actions. The Actor Network decides which actions to take grounded in the present observations, while the Critic Network assesses these actions by assessing their rewards or penalties. The learning algorithm updates the policy using the feedback from the Critic Network to optimize cumulative rewards.
This work investigates the optimization of airfoil shapes using various reinforcement learning (RL) algorithms, including Deep Deterministic Policy Gradient (DDPG), Twin Delayed Deep Deterministic Policy Gradient (TD3), and Trust Region Policy Optimization (TRPO). The primary objective is to enhance the aerodynamic performance of airfoils by maximizing lift forces across different angles of attack (AoA). The study compares the optimized airfoils against the standard NACA 2412 airfoil. The DDPG-optimized airfoil demonstrated superior performance at lower and moderate AoAs, while the TRPO-optimized airfoil excelled at higher AoAs. In contrast, the TD3-optimized airfoil consistently underperformed. The results indicate that RL algorithms, particularly DDPG and TRPO, can effectively improve airfoil designs, offering substantial benefits in lift generation. This paper underscores the potential of RL techniques in aerodynamic shape optimization, presenting significant implications for aerospace and related industries.
In order to examine the behavior of micropolar nanofluids with radiative and activation energy influences, this work numerically replicates the Cattaneo–Christov heat flux in magnetohydrodynamics. The main conclusions show that while higher Darcy–Forchheimer values improve microrotation profiles, increasing thermophoresis, thermal sources, radiation, and Brownian motion components improve thermal distributions. While more radiation enhances thermal transmission, higher temperature differences and Schmidt numbers increase mass transport rates, and activation energy has an inverse effect on concentration fluctuations and thermal transmission rates.
The present inquiry examines the necessity for enhanced thermal transfer approaches across multiple industrial domains, such as energy generation and processing of materials, through an investigation of the intricate dynamics of micropolar nanofluids. The main objective is to numerically simulate the Cattaneo–Christov heat flux in magnetohydrodynamics (MHD) to investigate the radiative behavior of Darcy–Forchheimer micropolar nanofluids, including the effects of activation energy. The study presumes steady-state conditions and employs particular constitutive equations to characterize the behavior of the nanofluid. The governing equations, which incorporate binary chemical interactions, radiation, and a thermal source, are reformulated with similarity variables into a system of nonlinear ordinary differential equations (ODEs). The BVP4C MATLAB software is utilized for obtaining numerical solutions. The study indicates that an increase in thermophoresis, thermal source, radiation, and Brownian motion factors improves thermal distributions in micropolar nanofluid flow. Moreover, increased radiation parameters result in a rise in the thermal transmission rate, while enhancing activation energy factors leads to a decrease. The findings are essential for enhancing temperature control in systems and for the development of efficient thermal appliances.
This paper presents two downsampling algorithms for vortex particle methods (VPMs) that reduce the number of computational elements representing the vorticity field. The two methods demonstrate significant reductions in particle count and computation time in benchmark cases at a cost of diffusive errors. Gentle compression steps are reported to maintain accuracy comparable to reference cases. The study recommends testing periodic compression steps on more complex flow cases to evaluate the long-term impact on performance and accuracy.
Computational efficiency of vortex particle methods (VPMs) is hindered by the particle count increasing in simulation time. To reduce the number of computational elements, two algorithms are presented that downsample the discretized vorticity field representation in two-dimensional variable-core-size VPMs. The two methods are based on existing schemes of particle merging and regridding, and are adapted to follow a compression parameter set a priori. The effectiveness of the schemes is demonstrated on two benchmark cases of external flow: A stationary Lamb-Oseen vortex and an advecting vortex dipole. In both cases, compression is associated with a drastic reduction in particle count and computation time at a cost of diffusive errors in the vorticity field. Crucially, for gentle compression steps applied at appropriate intervals, the immediate errors in the vorticity field are comparable to reference cases despite great improvements in computational time. To examine the long-term impact of compression on accuracy and performance, it is recommended that repeated compressive steps be tested on more complex cases of bluff-body wakes, with a focus on the impact of downsampling on surface forces.
Numerical solution for the barotropic vorticity equation in complex geometry using the meshless point collocation method. The spatial domain is represented by a set of nodes. The collocation method numerically solves the strong form governing equations.
We present a novel meshless Lagrangian method for numerically solving the barotropic vorticity equation on a rotating sphere, an essential model in geophysical fluid dynamics. Our approach combines a particle-based discretization with a Discretization Corrected Particle Strength Exchange (DCPSE) operator, offering a consistent and accurate approximation of differential operators on unstructured node distributions. The method is implemented in a fully Lagrangian framework, inherently conserving circulation and enabling straightforward adaptation to complex geometries. We validate the proposed scheme against standard test cases for global circulation and Rossby-Haurwitz waves. The results demonstrate excellent agreement with reference solutions obtained from high-resolution spectral and finite difference models. In particular, our method captures the essential dynamics of the vorticity field with high fidelity and low numerical diffusion, while exhibiting convergence and stability properties suitable for long-term integrations. This study highlights the potential of meshless Lagrangian techniques in large-scale geophysical simulations. These techniques provide an alternative to traditional grid-based approaches and facilitate the natural handling of adaptive and irregular node distributions.
Control volume free element method is proposed to solve incompressible Navier-Stokes equations for the first time. The proposed scheme employs a fully coupled pressure based method to avoid pressure oscillations. Test cases indicate that the proposed method is efficient and robust.
In this work, the control volume free element method (CVFrEM) is proposed for turbulent forced and natural convection problems. In the proposed method, the control volume at each collocation node is generated locally within the free element formed for the node, based on which the governing equations are discretized using the Green-Gauss formula. In contrast to conventional segregated SIMPLE-like algorithms, the newly proposed method achieves fully coupled velocity and pressure, thereby significantly improving convergence characteristics. The computational framework has been validated through the turbulent natural and forced convection problems involving conjugate heat transfer. Comprehensive verification has been carried out by systematically comparing numerical results with benchmark solutions from the literature and experimental measurements. Numerical experiments on several test cases demonstrate the computational efficiency of the proposed method and its numerical robustness.
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Bowen Li, Bin Shi
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Ran Bi, Jingrun Chen, Weibing Deng
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Benoit J. Allard, Lucian Ivan, James G. McDonald
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Shi Jin, Nana Liu, Yue Yu
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Jiangce Chen, Wenzhuo Xu, Zeda Xu, Noelia Grande Gutiérrez, Sneha Prabha Narra, Christopher McComb
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Elena Beretta, Maolin Deng, Alberto Gandolfi, Bangti Jin
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Amareshwara Sainadh Chamarthi
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Yuanhong Chen, Zhen Gao, Jan S. Hesthaven, Yifan Lin, Xiang Sun
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Qian Zhang, Dmitry Krotov, George Em Karniadakis
Publication date: 1 October 2025
Source: Journal of Computational Physics, Volume 538
Author(s): Shunhao Peng, Yongliang Feng, Xiaojing Zheng
