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Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes–Einstein and Stokes–Einstein–Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes–Einstein and Stokes–Einstein–Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level. [ABSTRACT FROM AUTHOR]

The Lattice Boltzmann Method (LBM) is an approach for modeling mesoscopic fluid flow and heat transfer, based on modeling distributions of particles moving and colliding on a lattice. Using a perturbative formulation of the Boltzmann equation, it scales to the macroscopic Navier–Stokes equation. We simulate natural thermal convection via LBM in a 2D rectangular box being heated from below and cooled from above, and use the results as training, testing, and generalization datasets to build a deep learning model. GoogLeNet, a convolutional neural network, is used to classify the simulation results based on two parameters: Rayleigh (R a) and Prandtl (P r) numbers, from a single snapshot of either the entire modeling field of resolution 1024 × 1024 , or a 224 × 224 crop. For each fixed P r in a range from 1 to 128, increasing by a factor of 2, we estimate R a with an accuracy varying from 40% to 90%, depending on the chosen augmentation strategy. For each fixed R a in the range from 10 5 to 10 9 , increasing of a factor 10 , the method predicts P r with a systematically lower accuracy ranging from 30% to 80%. This approach has great potential for industrial applications like being able to control the industrial flow or scientific research on geophysical ones including the transport of heat in the earth's interiors, ocean, and atmosphere. [ABSTRACT FROM AUTHOR]

We study the zero dissipation limit problem for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids. We prove that if the solution of the inviscid Euler system is piecewise smooth with a 1-shock and a 3-shock issuing from the same point, there exists a family of smooth solutions to the compressible Navier-Stokes equations which converges to the inviscid solution away from the shock discontinuities at a rate of ε η , ∀ η ∈ (0 , 1 2) as the viscosity ε tends to zero, provided that the heat-conducting coefficient κ = O (ε). Different from the result in [19] , which only holds on [ 0 , T − h ] for ∀ h > 0 , here we can prove it holds on the whole time interval [ 0 , T ] for the existence of the inviscid solution. [ABSTRACT FROM AUTHOR]

We are concerned with the long time existence of smooth solutions to full compressible Navier-Stokes equations in 3D bounded domains with Dirichlet boundary conditions on the velocity and temperature. The smallness restriction on the initial data or time interval is unnecessary. Under the condition that the limiting system admits a reasonably smooth solution on a given time interval, we verify that the compressible system admits the smooth solution on the same interval as well, provided that the Mach number is sufficiently small. Moreover, as the Mach number goes to zero, the solution of the compressible system converges uniformly to that of the incompressible one. We utilize some geometric techniques to overcome difficulties introduced by non-slip boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem of a two-phase flow system consisting of the compressible isothermal Euler equations and the incompressible Navier-Stokes equations coupled through the drag force, which can be formally derived from the Vlasov-Fokker-Planck/incompressible Navier-Stokes equations. When the initial data is a small perturbation around an equilibrium state, we prove the global well-posedness of the classical solutions to this system and show the solutions tends to the equilibrium state as time goes to infinity. In order to resolve the main difficulty arising from the pressure term of the incompressible Navier-Stokes equations, we properly use the Hodge decomposition, spectral analysis, and energy method to obtain the L 2 time decay rates of the solution when the initial perturbation belongs to L 1 space. Furthermore, we show that the above time decay rates are optimal. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena, with the non-slip boundary condition on an impermeable wall. Due to the difficulty from the disappearance of the velocity on the impermeable boundary, quite few results for compressible Navier-Stokes equations and no result for the radiative Euler equations are available at this moment. So the asymptotic stability of the rarefaction wave proven in this paper is the first rigorous result on the global stability of solutions of the radiative Euler equations with the non-slip boundary condition. It also contributes to our systematical study on the asymptotic behaviors of the rarefaction wave with the radiative effect and different boundary conditions such as the inflow/outflow problem and the impermeable boundary problem in our series papers including [5,6]. [ABSTRACT FROM AUTHOR]

This study investigates the spheroidization of titanium Ti-6Al-4V powder particles using numerical models developed in Abaqus and OpenFOAM. Spherical particles are crucial in powder-based additive manufacturing due to their superior flowability, packing density, and mechanical properties, enhancing printing precision and the quality of final products. While conventional techniques such as gas atomization and plasma spheroidization have been extensively researched, the potential of laser spheroidization remains underexplored. To address this gap, detailed numerical analyses of laser spheroidization were conducted, modeling heat transfer from the laser to powder particles using a transient uncoupled heat transfer method with latent heat considerations, while particle deformation was simulated with a phase-fraction-based interface-capturing approach integrated with Navier-Stokes equations. The results, validated against analytical models, indicate that particles within the 20–80 μm range experience optimal spheroidization within a 0.005-second residence time under laser heating, with particles smaller than 30 μm reaching evaporation temperatures of 5,000°C, while larger particles reshape without evaporating under a typical heat flux of 94 MW/m2 (1.8 kW laser power). This study demonstrates that laser spheroidization of Ti-6Al-4V powder can potentially increase powder yield by 10%, offering higher power density and shorter melting times compared to plasma spheroidization, thus presenting a more efficient alternative for achieving spherical particles of specific sizes. [ABSTRACT FROM AUTHOR]

We study the stability and convergence properties of a semi-implicit time stepping scheme for the incompressible Navier–Stokes equations with variable density and viscosity. The density is assumed to be approximated in a way that conserves the minimum-maximum principle. The scheme uses a fractional time-stepping method and the momentum, which is equal to the product of the density and velocity, as a primary unknown. The semi-implicit algorithm for the coupled momentum-pressure is shown to be conditionally stable and the velocity is shown to converge in L 2 norm with order one in time. Numerical illustrations confirm that the algorithm is stable and convergent under classic CFL condition even for sharp density profiles. [ABSTRACT FROM AUTHOR]

We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is driven by a uniform flow at spatial infinity, with constant dimensionless velocity λ. We show that if λ is below a critical value, λ c (say), there is a unique and stable time-independent configuration, where the body is in equilibrium and the flow is steady. We also prove that, if λ < λ c , no oscillatory flow may occur. Successively, we investigate possible loss of uniqueness by providing necessary and sufficient conditions for the occurrence of a steady bifurcation at some λ s ≥ λ c. [ABSTRACT FROM AUTHOR]

At present paper, we study the pathwise behavior of the solutions of 2D non-autonomous stochastic Navier-Stokes equation driven by a linear non-degenerate noise. When the stochastic external force is an H − 1 / 2 -valued Q -Wiener process and the deterministic non-autonomous external force is normal function in L l o c 2 (R ; V ′) , we establish the existence of uniform random attractor for the equation in H. We also obtain the regularity of uniform random attractor for the equation driven by the H -valued Q -Wiener process with the deterministic non-autonomous external force being normal in L l o c 2 (R ; H). Finally, we investigate the existence of uniform random attractor for the equation driven by an H -valued cylindrical Wiener process in H and V , respectively. [ABSTRACT FROM AUTHOR]

This paper aims to investigate appropriate mathematical models devoted to the optimization of some cleaning processes related to pharmaceutical contaminant removal. In our recent works, we found the rehabilitation of the existing cleaning plants as a viable solution for the removal of this type of micropollutants from waters by introducing efficient techniques such as adsorption on granulated active carbon filters and micro-, nano-, or ultrafiltration. To have these processes under better control and to assure the transfer from small- to large-scale treatment stations, specific mathematical models are necessary. Starting from Navier–Stokes equations and imposing proper boundary conditions, some mathematical physics problems are obtained for which adequate solving methods via variational methods and surjectivity results are proposed. The importance of these solution characterizations consists in their continuation in adequate numerical methods and the possibility to visualize the result by using a CFD program. [ABSTRACT FROM AUTHOR]

In this study, two improved parallel finite element algorithms based on two-grid strategies are developed to approximate the stationary Navier–Stokes equations. Algorithms are devised to improve the existing local and parallel finite element methods to arrive at L 2 optimal velocity approximation by considering one further coarse grid correction. Rigorously numerical analysis is established, and numerical experiments are reported to support the theoretical findings. [ABSTRACT FROM AUTHOR]

For use with the lattice Boltzmann method, the macroscopic boundary conditions need to be transformed into their mesoscopic counterparts. Commonly used mesoscopic boundary conditions use the equilibrium density function, which introduces undesirable artifacts into the numerical solution, especially near interfaces with other types of boundary conditions. In this work, several variants of the mesoscopic boundary conditions are summarized and numerically investigated by means of benchmark problems for the incompressible Navier-Stokes equations with known analytical solutions. To improve the numerical approximation of the velocity and pressure fields, moment-based boundary conditions are extended for the D3Q27 velocity model. Furthermore, the interpolated boundary conditions are improved. These newly developed boundary conditions are shown to produce results with a substantially smaller numerical error. [ABSTRACT FROM AUTHOR]

We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a velocity correction projection method for the Micropolar Navier-Stokes Equations. The velocity correction method are adopted to approximate the time derivative term, stability analysis and error estimation of the first-order semi-discrete scheme are proved. At the same time, the optimal error estimate using the technique of dual norm are obtained. In this way, the divergence free of the velocity u can be conserved. Finally, the numerical results show the method has an optimal convergence order. The numerical results are consistent with our theoretical analysis, and our method is effective. [ABSTRACT FROM AUTHOR]

In this paper, we study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total energy is suitably small. Our result generalizes the Cauchy problems of compressible Navier-Stokes equations with Coulomb force [S. Liu, X. Xu and J. Zhang, Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier-Stokes-Poisson equations subject to large oscillations and non-flat doping profile, J. Differ. Equ. 269 (2020) 8468-8508] and compressible MHD equations [H. Li, X. Xu and J. Zhang, Global classical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum, SIAM J. Math. Anal. 45 (2013) 1356-1387] to the case of bounded domains although tackling many surface integrals caused by the slip boundary condition are complex. The main ingredient of this paper is to overcome the strong nonlinearity caused by Coulomb force, magnetic field, and rotation effect of micro-particles by applying piecewise-estimate method and delicate analysis based on the effective viscous fluxes involving velocity and micro-rotational velocity. [ABSTRACT FROM AUTHOR]

When a flying vehicle approaches a water or land surface, it induces changes in the fluid flow field pattern known as the "ground effect." This research analyzes the ground effect phenomenon, exploring its impact on aerodynamic coefficients and flow patterns around the NACA0012 airfoil in an incompressible subsonic regime under static and dynamic conditions with pitch movements. Numerical simulations and experimental testing in an incompressible subsonic wind tunnel were deployed. The flow field solution is derived from the Navier-Stokes equations, incorporating the Transition SST turbulence model. Initially, the impact of the ground effect phenomenon was investigated at varying distances from the surface in the static state. Subsequently, the airfoil underwent a sinusoidal pitching oscillation at each distance with a specified frequency and amplitude. This allowed for examining its aerodynamic characteristics over time. The static analysis results reveal alterations in the curve's behavior and pressure distribution on the airfoil surface at close distances to the surface. This is attributed to the ground effect phenomenon, which reduces lift force to a certain height and then increases. Dynamic analysis further demonstrates changes in lift coefficient oscillation amplitude. It also exhibits a minimum and maximum lift point phase difference as the airfoil approaches the surface. [ABSTRACT FROM AUTHOR]

This study aims to optimize the influence of the inlet inclination angle on the Indoor Air Quality (IAQ), heat, and temperature distribution in mixed convection within a two-dimensional square cavity filled with an air-CO2 mixture. The air-CO2 mixture enters the cavity through two inlet openings positioned at the top wall, which is set at the ambient temperature (TC). Three values of the Reynolds numbers, ranging from 1000 to 2000, are considered, while the Prandtl number is kept constant (Pr = 0.71). The temperature distribution and streamlines are shown for Rayleigh number (Ra) equal to 104, three inlet inclination angles ϕ (0, π/6 and π/4) and three CO2 concentrations values (1500, 2500, 3500 ppm) applied at both hot vertical walls (maintained at a constant temperature TH). A finite volume method is used under the assumption of two-dimensional laminar flow to solve the Navier-Stokes and energy equations. The results indicate that inlet inclination angle has an impact on the indoor air quality (IAQ), which, in turn, affects the heat transfer distribution and thermal comfort within the cavity. [ABSTRACT FROM AUTHOR]

The quality of crushing, power consumption, and discharging performance of a straw crusher are greatly influenced by the characteristics of its internal flow field. To enhance the straw crusher's flow field properties and improve the efficiency with which crushed material is discharged, first, the main structural parameters influencing the air flow in the crusher are discussed. Then, the coupled gas-solid flow field in the straw crusher is numerically calculated through solution of the Navier-Stokes equations and application of the discrete element method (DEM). Finally, the discharge performance index of the crusher is examined through detailed analysis of the crushed material dynamics. Additionally, a multi-island genetic algorithm is used to optimize the structure and operational factors that have significant effects on the discharge performance. With optimization, the accumulation rate of crushed materials in the bottom region of the straw crusher decreases by 20.08%, and the mass flow rate at the discharge outlet increases by 11.63%. [ABSTRACT FROM AUTHOR]

We develop a computational fluid dynamics (CFD) framework to design a feedback circulation control system to compensate for fluctuations in the fixed-wing aircraft caused by wind gusts. Circulation control actions are realized using dynamic boundary conditions in the CFD simulations. The dynamic flow responses with the circulation control are obtained by solving the unsteady Reynolds-averaged Navier-Stokes equations. The dynamic lift responses at several oscillation frequencies of wind gusts and the plenum chamber pressure, which controls the circulation, are also obtained. A system identification algorithm from control theory establishes the transfer functions corresponding to the frequency responses. Based on the transfer functions and the aerodynamic characteristics of circulation control, a feedback circulation control algorithm is designed. The performance of the feedback control system is verified by the CFD simulation coupled with the controller as time-varying boundary conditions. At each time step, the controller determines the parameters in the boundary condition according to the instantaneous lift calculated in the previous time step. The simulation results show that the circulation control effectively compensates for the lift perturbations caused by vertical directional wind gusts. The proposed unsteady CFD simulation frameworks provide high-fidelity evaluations of feedback control systems, and it will save costly efforts to set up unsteady wind-tunnel experiments. [ABSTRACT FROM AUTHOR]

For the non-stationary Stokes system, it is well-known that one can improve spatial regularity in the interior, but not near the boundary if it is coupled with the no-slip boundary condition. In this note we show that, to the contrary, spatial regularity can be improved near a flat boundary if it is coupled with the Navier boundary condition, with either infinite or finite slip length. The case with finite slip length is more difficult than the case with infinite slip length. [ABSTRACT FROM AUTHOR]

In the note, the Euler scaling is used to study a certain scenario of potential Type Ⅱ blowups of solutions to the Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

We study the Stokes system with the localized boundary data in the half-space. We are concerned with the local regularity of its solution near the boundary away from the support of the given boundary data which are in the product forms of each spatial variable and the temporal variable. We first show that if the boundary data are smooth in time, the corresponding solutions are also smooth in space and time near the boundary, even if the boundary data are only spatially integrable. Secondly, if the normal component of the boundary data is absent, we are able to construct a solution such that the second normal derivatives of its tangential components become singular near the boundary. Perturbation argument enables us to construct solutions of the Navier-Stokes equations with similar singular behaviors near the boundary in the half-space as the case of Stokes system. Lastly, we provide specific types of the localized boundary data to obtain the pointwise bounds of the solutions up to second derivatives. It turns out that such solutions are globally strong, while the second normal derivatives are unbounded near the boundary. These results can be compared to the previous works in which only the normal component is present. In fact, the non-smooth tangential boundary data in time can also cause spatially singular behaviors of the solution near the boundary, although such behaviors are milder than those caused by the normal boundary data of the same type. [ABSTRACT FROM AUTHOR]

The sheet is concerned with the strong solution to the Cauchy problem of the Navier–Stokes equations with damping term α | u | β - 1 u , α > 0 , β ≥ 1 . In this paper, we provide the global existence for bounded solutions with β > 3 . Furthermore, in the case of β = 3 , we consider a modified damping term: α log (e + | u | 2 ) | u | 2 u . This new term allows us to obtain the global existence and uniqueness of the solution in H 1 . [ABSTRACT FROM AUTHOR]

In this paper, we examine the relevant properties of mild solutions to the fractional Navier–Stokes equations with respect to a time derivative of order 0 < α < 1 in a new spatial framework. On the Heisenberg group, these mild solutions are connected to the sublaplacian provided by the left-invariant vector fields. By applying appropriate conditions, we can obtain global and local mild solutions using the classical bilinear fixed point theorem. Furthermore, we have also established the dependence on the initial value of these mild solutions. [ABSTRACT FROM AUTHOR]

We are considering a steady-state turbulent Reynolds-Averaged Navier–Stokes (RANS) one-equation model, that couples the equation for the velocity-pressure mean field with the equation for the turbulent kinetic energy. Eddy viscosities vanish at the boundary, characterized by terms like d (x , Γ) η and d (x , Γ) β , where 0 < η , β < 1 . We determine critical values η c and β c for which the system has a weak solution. This solution is obtained as the limit of viscous regularizations for 0 < η < η c and 0 < β < β c . [ABSTRACT FROM AUTHOR]

The isentropic compressible Cahn–Hilliard–Navier–Stokes equations are a system of fourth-order partial differential equations that model the evolution of some binary fluids under convection. The purpose of this paper is the design of efficient numerical schemes to approximate the solution of initial-boundary value problems with these equations. The efficiency stems from the implicit treatment of the high-order terms in the equations. Our proposal is a second-order linearly implicit-explicit time stepping scheme applied in a method of lines approach, in which the convective terms are treated explicitly and only linear systems have to be solved. Some experiments are performed to assess the validity and efficiency of this proposal. [ABSTRACT FROM AUTHOR]

Keywords: Navier-Stokes equations; resolvent; free surface; solution formula; Lp estimates.GraphBy Yongting Huang and Tao LuoReported by Author; Author [Extracted from the article]

In this paper, we consider a three-dimensional nonlinear system consisting of the incompressible Navier-Stokes equations governing fluid motion coupled with the incompressible Maxwell's equations governing the magnetic field. This system is subject to a no-slip boundary condition for the (average) velocity and the perfectly conducting wall condition for the magnetic field. We prove some regularity properties of solutions of this system through an approximation procedure based on Galerkin approximation scheme. As a consequence, we are able to derive some suitable uniform estimates which allow us to show smoothness of the global attractor. Finally, we discuss the relationship between global attractors, invariant measures, time-average measures, and statistical solutions of the three-dimensional system of globally modified magnetohydrodynamics equations in the case of temporally independent forcing terms. [ABSTRACT FROM AUTHOR]

Deriving from the motion of a three-dimensional compressible viscous heat-conducting fluid in an infinite layer bounded above by a free surface, the paper is concerned with the asymptotic behavior of solutions to the linearized compressible Navier-Stokes equations in a strip domain. With the help of the explicit solution formula for the corresponding resolvent problem we have achieved, the time-decay estimates of solutions to this problem in $ L^p $ spaces, $ 2\le p<\infty $, are well established. Moreover, since we are interested in the linearized dynamic boundary condition of the surface wave problem, some exponential decay properties of the solutions are revealed. Our result is crucial and indispensable for developing the $ L^p $ theory for the free boundary problem of the full compressible Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

AbstractWhen a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and forecasting the fluid dynamics under these conditions is one of the most challenging scientific problems in fluid dynamics. It is therefore of high interest to formulate models able to capture the nonlinear spatio-temporal velocity structure as well as produce forecasts in a computationally efficient manner. Traditional statistical approaches are limited in their ability to produce timely forecasts of complex, nonlinear spatio-temporal structures which are at the same time able to incorporate the underlying flow physics. In this work, we propose a model to accurately forecast boundary layer velocities with a deep double reservoir computing network which is capable of capturing the complex, nonlinear dynamics of the boundary layer while at the same time incorporating physical constraints via a penalty obtained by a Partial Differential Equation (PDE). Simulation studies on a one-dimensional viscous fluid demonstrate how the proposed model is able to produce accurate forecasts while simultaneously accounting for energy loss. The application focuses on boundary layer data in a water tunnel with a PDE penalty derived from an appropriate simplification of the Navier-Stokes equations, showing improved forecasting by the proposed approach in terms of mass conservation and variability of velocity fluctuation against non-physics-informed methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following 2D incompressible chemotaxis‐Navier–Stokes equations with the fractional diffusion ∂tn+u·∇n−Δn=−∇·(n∇c)+n(1−n)(n−a),∂tc+u·∇c−Δc=−cn,∂tu+u·∇u+∧2αu+∇P=−n∇ϕ,$$ \left\{\begin{array}{l}{\partial}_tn&#x0002B;u\cdotp \nabla n-\Delta n&#x0003D;-\nabla \cdotp \left(n\nabla c\right)&#x0002B;n\left(1-n\right)\left(n-a\right),\\ {}{\partial}_tc&#x0002B;u\cdotp \nabla c-\Delta c&#x0003D;- cn,\\ {}{\partial}_tu&#x0002B;u\cdotp \nabla u&#x0002B;{\wedge}&#x0005E;{2\alpha }u&#x0002B;\nabla P&#x0003D;-n\nabla \phi, \end{array}\right. $$ where ∧:=(−Δ)12$$ \wedge :&#x0003D; {\left(-\Delta \right)}&#x0005E;{\frac{1}{2}} $$ and α∈[12,1]$$ \alpha \in \left[\frac{1}{2},1\right] $$. The gravitational potential ϕ$$ \phi $$ is generally supposed to be sufficiently smooth given functions. By establishing the new priori estimates, we get the global well‐posedness for the above system with large initial data. [ABSTRACT FROM AUTHOR]

Cavitation may occur in water-jet pump during operation of water-jet propulsion vessel, and once cavitation occurs, the tip clearance pulsating pressure of the impeller may be intensified, resulting in increased vibration of the water-jet propulsion unit. In this paper, the cavitation pulsating pressure characteristics at different positions in the pump are studied by experiment and numerical simulation, and the pulsating pressure characteristics in tip clearance are mainly researched. Based on Star-CCM+ commercial software, unsteady Reynolds-averaged Navier-Stokes equations(RANS) numerical simulation is carried out, and the feasibility of the numerical simulation method is verified by uncertainty analysis. The results show that the cavitation pulsating pressure near the leading edge of the impeller in the tip clearance is the largest. The variation of the tip clearance pulsating pressure with the intensification of cavitation is studied by numerical simulation, and its mechanism is revealed. A dimensionless coefficient of net positive suction head (CNPSH) is proposed, and the study shows that the cavitation pulsation pressure coefficients of pumps of different scales are equal when the working conditions are similar and the CNPSH are equal, which indicates that the cavitation pulsating pressure performance of full scale pump can be predicted by model scale. It is of great significance to evaluate the vibration performance of the full scale water-jet propulsion. [ABSTRACT FROM AUTHOR]

In this paper, we derive the dissipation term in the local energy balance law of weak solutions for a surface growth model arising in the molecular-beam-epitaxy process by using the third-order structure functions. This enables us to address Yang's question posed in [52, J. Differential Equations 283, 2021] , consider generalized Onsager conjecture, and present an upper bound of energy dissipation rate of the form O (ν 3 α − 1 α + 1 ) under the condition that the weak solution h ν belongs to L 3 (0 , T ; B 3 , ∞ α + 1 (T)) with α ∈ (0 , 1) in this model. More importantly, the link between Duchon-Robert's remarkable dissipation term and Lions's classical sufficient condition for energy balance law in the 3D Navier-Stokes equations is illustrated. [ABSTRACT FROM AUTHOR]

We consider the incompressible viscous surface wave problem in the setting that the fluid domain is a horizontal infinite layer in 3 D. The fluid dynamics is governed by the gravity-driven incompressible Navier–Stokes equations, and the effect of surface tension is ignored on the upper free surface. We prove the optimal time-decay rate of the low-order energy of the solution with minimal derivative count 3, which implies that the Lipschitz norm of the velocity decays at the rate (1 + t) − 1. This together with a time-weighted estimate for the highest order spatial derivatives of the free surface function leads to the boundedness of the high-order energy, which improves the result of Wang [9]. [ABSTRACT FROM AUTHOR]

In this paper, we consider Cauchy problem for the 2D incompressible Keller-Segel-Navier-Stokes equations with the fractional diffusion { ∂ t n + u ⋅ ∇ n − Δ n = − ∇ ⋅ (n ∇ c) − n 3 , ∂ t c + u ⋅ ∇ c − Δ c = − c + n , ∂ t u + u ⋅ ∇ u + ∧ 2 α u + ∇ P = − n ∇ ϕ , where ∧ : = (− Δ) 1 2 and α ∈ [ 1 2 , 1 ] . We get the global well-posedness for the above system with the rough initial data by a new priori estimate of the solutions. [ABSTRACT FROM AUTHOR]

Data-driven approaches offer novel opportunities for improving the performance of turbulent flow simulations, which are critical to wide-ranging applications from wind farms and aerodynamic designs to weather and climate forecasting. However, current methods for these simulations often require large amounts of data and computational resources. While data-driven methods have been extensively applied to the continuum Navier-Stokes equations, limited work has been done to integrate these methods with the highly scalable lattice Boltzmann method. Here, we present a physics-informed neural network framework for improving lattice Boltzmann-based simulations of near-wall turbulent flow. Using a small amount of data and integrating physical constraints, our model accurately predicts flow behaviour at a wide range of friction Reynolds numbers up to 1.0 × 106. In contradistinction with other models that use direct numerical simulation datasets, this approach reduces data requirements by three orders of magnitude and allows for sparse grid configurations. Our work broadens the scope of lattice Boltzmann applications, enabling efficient large-scale simulations of turbulent flow in diverse contexts. The authors provide a data-driven near-wall modelling framework for the lattice Boltzmann method using IDDES data. Their model can predict flows with friction Reynolds numbers up to 1,000,000 and effectively handle sparse near-wall grids. [ABSTRACT FROM AUTHOR]

In this paper, we establish the global existence and uniqueness of solution to 2-D inhomogeneous incompressible Navier-Stokes equations (1.1) with initial data in the critical spaces. Precisely, under the assumption that the initial velocity u 0 in L 2 ∩ B ˙ p , 1 − 1 + 2 p and the initial density ρ 0 in L ∞ and having a positive lower bound, which satisfies 1 − ρ 0 − 1 ∈ B ˙ λ , 2 2 λ ∩ L ∞ , for p ∈ [ 2 , ∞ [ and λ ∈ [ 1 , ∞ [ with 1 2 < 1 p + 1 λ ≤ 1 , the system (1.1) has a global solution. The solution is unique if p = 2. With additional assumptions on the initial density in case p > 2 , we can also prove the uniqueness of such solution. In particular, this result improves the previous work in [Abidi-Gui, ARMA(2021)] where u 0 belongs to B ˙ 2 , 1 0 and ρ 0 − 1 − 1 belongs to B ˙ 2 ε , 1 ε , and we also remove the assumption that the initial density is close enough to a positive constant in [Danchin-Wang, CMP(2023)] yet with additional regularities on the initial density here. [ABSTRACT FROM AUTHOR]

This paper derives well-posedness and asymptotic results that provide qualitative information about the behavior, mechanism and strategies used by living organisms to navigate their biological networks. Chemical driven swimming is a captivating phenomenon that is observed in various living organisms like bacteria and protozoa but the problem in weighted networks is more complex, since the equations of parabolic-parabolic Keller-Segel model coupled with incompressible Navier-Stokes equations must be reformulated in a discrete setting. The starting point is to transpose the coupled system from the Euclidean case to the connected networks with certain network-theoretic simplified approaches, which yields fruitful key results. These results not only enable the construction of global solutions but also serve as a foundation for determining information about the stability and large time behavior of the system. Then, decay rates are well established to predict important features, such as how quickly weak solutions at a given point decrease over time due to dissipative processes. Additionally, the L 1 - convergence of cell densities towards the self-similar Gaussian solution of the heat equation is well proved by time dependent scaling, which shows that the solution maintains its shape and only scales in time and space as time evolves. Finally, this paper includes many numerical tests through a recent robust numerical scheme to illustrate the theoretical results and to develop computational control and prediction of living organisms' trajectories around central nodes in networked flows. [ABSTRACT FROM AUTHOR]

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The article "Two-dimensional turbulence on the ellipsoid" in the Journal of Fluid Mechanics explores the behavior of two-dimensional turbulence on ellipsoids, emphasizing the impact of domain geometry on energy transfer. The study demonstrates that energy transfer is influenced by angular momentum conservation, with spheres restricting energy flow into certain modes, while spheroids and triaxial ellipsoids allow energy to flow into any mode. The research employs numerical experiments to validate these findings and underscores the significance of angular momentum conservation in comprehending turbulence dynamics. Additionally, the study delves into the use of stereographic coordinates to analyze fluid flow dynamics on ellipsoids, highlighting the role of geometry in shaping turbulence. [Extracted from the article]

The article "Spreading of a viscous drop after impact onto a spherical target" in the Journal of Fluid Mechanics explores the dynamics of liquid droplets colliding with solid spherical particles. It investigates both non-axisymmetric and axisymmetric impacts, analyzing parameters such as drop shape, residual film thickness, and spreading angle. The study introduces a new method for measuring liquid viscosity during drop impacts, with potential applications in industrial processes. The research sheds light on optimizing processes involving drop collisions and offers valuable insights for various industries. [Extracted from the article]

The article "Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)" in the Journal of Fluid Mechanics presents a novel method, SPIDER, that combines physical assumptions, weak formulation of differential equations, and sparse regression to extract governing equations of fluid dynamics from turbulent channel flow data. The study successfully identifies key equations such as the Navier-Stokes equation and pressure-Poisson equation from numerical data, even in the presence of high noise levels. This approach offers a systematic and robust method for generating libraries and inferring equations, with potential applications beyond fluid dynamics to other high-dimensional systems. [Extracted from the article]

The article "Dynamics of turbulent energy and dissipation in channel flow" delves into the intricate relationship between turbulent kinetic energy (TKE), turbulence dissipation rate (TDR), and turbulence production rate (TPR) in fully developed turbulent channel flow. The research uncovers time lags between these variables, with correlations that vary based on Reynolds number. The findings emphasize the complex nature of energy transfer and dissipation within different regions of the channel, showcasing correlations that involve both time and wall-distance lags. This study offers valuable insights into the self-sustaining process of turbulent flows, with implications for understanding turbulence dynamics across various contexts. [Extracted from the article]

The article in the Journal of Fluid Mechanics explores dynamic stall onset and vortex shedding in low-Reynolds-number flows, focusing on the leading edge suction parameter (LESP) and boundary enstrophy flux (BEF) as predictive criteria. High-resolution simulations of an airfoil at two Reynolds numbers reveal various unsteady flow phenomena, with BEF effectively identifying stall onset and vortex shedding events. The study underscores the significance of these criteria in comprehending low-Reynolds-number unsteady flows and their implications for flow control. The research, supported by NSF and US Air Force grants, sheds light on the dynamics of vortex shedding on airfoils at low Reynolds numbers. [Extracted from the article]

For the solution of fractional-order two-dimensional Navier-Stokes equations (FOTDNSEs), the current work proposes a novel variant of the Laplace Adomian decomposition approach with the Atangana-Baleanu fractional operator in the Caputo sense (ABCFO). In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the exact solution. Only two components are required for the new approximation analytical technique. When compared to other strategies, the current method is very simple, requires less calculation, and is extremely accurate. [ABSTRACT FROM AUTHOR]

This work is concerned with the global existence of large solutions to the three‐dimensional dissipative fluid‐dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible Navier–Stokes–Poisson–Nernst–Planck equations. Making full use of the algebraic structure of the system, we obtain the global existence of solutions without smallness assumptions imposed on the third component of the initial velocity field and the summation of initial densities of charged species. More precisely, we prove that there exist two positive constants c0,C0$$ {c}_0,{C}_0 $$ such that if the initial data satisfies u0hB˙p,1−1+3p+‖N0−P0‖B˙q,1−2+3qexpC0u03B˙p,1−1+3p2+‖N0+P0‖B˙r,1−2+3r+1expC0u03B˙p,1−1+3p+1≤c0,$$ {\displaystyle \begin{array}{ll}\left({\left\Vert {u}_0^h\right\Vert}_{{\dot{B}}_{p,1}^{-1+\frac{3}{p}}}+{\left\Vert {N}_0-{P}_0\right\Vert}_{{\dot{B}}_{q,1}^{-2+\frac{3}{q}}}\right)& \exp \left\{{C}_0\left({\left\Vert {u}_0^3\right\Vert}_{{\dot{B}}_{p,1}^{-1+\frac{3}{p}}}^2+\left({\left\Vert {N}_0+{P}_0\right\Vert}_{{\dot{B}}_{r,1}^{-2+\frac{3}{r}}}+1\right)\right.\right.\\ {}& \left.\left.\exp \left\{{C}_0{\left\Vert {u}_0^3\right\Vert}_{{\dot{B}}_{p,1}^{-1+\frac{3}{p}}}\right\}+1\right)\right\}\le {c}_0,\end{array}} $$then the incompressible Navier–Stokes–Poisson–Nernst–Planck equations admits a unique global solution. [ABSTRACT FROM AUTHOR]

The development of propulsion devices by using the propulsive mechanisms of aquatic animals such as fish is a challenging task. An attempt has been made to replicate the fishtailed motion that caused thrust in the current investigation. At a low Reynolds number of Re = 1173, the propulsive performance of National Advisory Committee for Aeronautics 0012 flapping foils enduring distinct flapping trajectories (fishtailed and elliptical) is evaluated. A dynamic mesh arbitrary Lagrangian-Eulerian framework is used to understand the desired flapping motion of the foils while solving the flow via incompressible Navier-Stokes equations. Along with the flapping trajectory, the effects of the Strouhal number (St), inter-foils distance (Lx), and phase angle (f) between the foils on the produced thrust are examined. The results demonstrate that using tandem configuration flapping foil with elliptical and fishtailed flapping can significantly increase the induced thrust and propulsive efficiency. [ABSTRACT FROM AUTHOR]

This study investigates the global well-posedness of a coupled Navier–Stokes–Darcy model incorporating the Beavers–Joseph–Saffman–Jones interface boundary condition in two-dimensional Euclidean space. We establish the existence of global strong solutions for the system in both linear and nonlinear cases where porosity depends on pressure. When dealing with the time-dependent porous media, the primary challenge in obtaining closed prior estimates arises from the presence of complex, sharp interfaces. To address this issue, we employ the classical Trace Theorem. Such space-time variable coupled systems are crucial for understanding underground fluid flow. [ABSTRACT FROM AUTHOR]

High-order solvers are accurate but computationally expensive as they require small time steps to advance the solution in time. In this work, we include a corrective forcing to a low-order solution to achieve high accuracy while advancing in time with larger time steps and achieving fast computations. This work is a continuation of our previous research [Manrique de Lara and Ferrer, "Accelerating high order discontinuous Galerkin solvers using neural networks: 1D Burgers' equation," Comput. Fluids 235, 105274 (2022) and F. Manrique de Lara and E. Ferrer, "Accelerating high order discontinuous Galerkin solvers using neural networks: 3D compressible Navier-Stokes equations," J. Comput. Phys. 489, 112253 (2023).], where we compare advanced neural networks: convolutional neural network (CNN) and long short-term memory (LSTM) networks to obtain the corrective forcing that corrects the low-order solution. The CNN exploits local spatial correlations while the LSTM accounts for temporal dependencies in the flow, expanding the validity of the low-order solution. Experimental results on the Taylor–Green vortex problem at Re = 1600, which includes laminar, transitional, and turbulent regimes, demonstrate significant accelerations of these advanced networks over the fully connected network. [ABSTRACT FROM AUTHOR]