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The occurrence of fluid flow near a wellhead is the major concern of the petroleum industry, as pressure drop, loss of formation, and other variables of interest are mostly affected in this region. The fluid flows from the hydrocarbon reservoir to the wellbore can be characterized as laminar to turbulent; thus, it is important to model this phenomenon with the integrated wellbore-reservoir model. Using 3D Navier–Stokes equations, an integrated wellbore-reservoir model is created in this study, and it incorporates the formation damage zone. For the porous-porous and porous-fluid interfaces, the General Grid Interface (GGI) approach is applied in conjunction with the conservative mass flux interface model. Model equations are solved using a velocity-pressure coupling solver that is pressure-based. For reliable and quick results, the system of equations is solved using an algebraic multigrid approach. The pressure diffusivity equation's analytical solution under steady-state flow circumstances is used to validate the model. The integrated wellbore-reservoir model is applied to different reservoir scenarios, for example, different production rates, formation zones, and reservoir formation conditions. The results indicate that the present Computational Fluid Dynamics (CFD) model can be extended to simulate the real field scale model. integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with efficient computational techniques can lead the field of petroleum industries to advance current knowledge. [ABSTRACT FROM AUTHOR]

Natural rock fractures often exhibit non-matching characteristics at certain scales, leading to uneven aperture distributions that significantly affect fluid flow. This study investigates the impact of the mismatch between the upper and lower surfaces on the flow through three-dimensional rough fractures. By applying fractal theory, a rough upper surface of the fracture is generated, and different degrees of mismatch are introduced by adding random noise to this surface. This approach enables the construction of a variety of three-dimensional rough fracture flow models. Numerical simulations, which involve directly solving the Navier-Stokes equations, are used to simulate flow through a rough single fracture, assessing the effects of various degrees of mismatch between the surfaces. The study also examines how the inclusion of the matrix alters flow characteristics. The results demonstrate that the Forchheimer equation accurately describes the nonlinear flow behavior in fractures with different degrees of mismatch. The increased mismatch intensifies the uneven distribution of fracture apertures, causing the flow velocity to shift from uniform to discrete and the streamlines to become increasingly curved. The overall tortuosity of the flow path increases and the formation of 'concave' and 'convex' areas leads to vortex zones, promoting nonlinear seepage. The correlation between both viscous and inertial permeability with the degree of mismatch is negative, whereas the impact of matrix permeability on the flow capacity of the fracture shows a positive correlation with a mismatch. [ABSTRACT FROM AUTHOR]

This study aims to evaluate the impacts of roof ridges and semi-cylindrical tiles on the wind loading on traditional single-eave hip roofs. To the best of the authors' knowledge, the semi-cylindrical tiles have been considered in the simulation of ancient Chinese architecture for the first time. Several roof models with various ridges and semi-cylindrical tiles are simulated by solving the Reynolds-averaged Navier-Stokes equations (RANS) using the computational fluid dynamics (CFD) technique. The results reveal that the addition of roof ridges and semi-cylindrical tiles has a considerable structural protection effect, which can significantly reduce the suctions, as well as the turbulence fluctuation, on both the windward and leeward sides: the average of negative mean wind pressure coefficients is reduced by 33% on the leeward surface, and approximately 48% on the windward surface one. When the number of protruding ridges and semi-cylindrical tiles increases (decreasing the diameter of them by 40%), the average of area mean wind pressure coefficient for all the wind directions decreases by about 30% on the windward side and about 50% on the leeward side. The average of maximum spatial wind pressure coefficient decreases by about 25% on the windward side and about 40% on the leeward side. [ABSTRACT FROM AUTHOR]

We derived an explicit form of the Jacobian for discrete approximations of a nonlinear initial boundary value problems (IBVPs) in matrix-vector form. The Jacobian is used in Newton’s method to solve the corresponding nonlinear system of equations. The technique was exemplified on the incompressible Navier-Stokes equations discretized using summation-by-parts (SBP) difference operators and weakly imposed boundary conditions using the simultaneous approximation term (SAT) technique. The convergence rate of the iterations is verified by using the method of manufactured solutions. The methodology in this paper can be used on any numerical discretization of IBVPs in matrix-vector form, and it is particularly straightforward for approximations in SBP-SAT form. [ABSTRACT FROM AUTHOR]

This paper studies regularity properties of the weak solutions to the 3D Navier–Stokes equations with damping in the whole space and bounded domains. We find the space restriction on the initial velocity to guarantee the local existence of strong solutions. Based on it, we complete the existence results for the global strong solutions in the whole space and improve the restriction on the damping exponent for the existence of the global strong solutions in the bounded domains. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with L 2 decay of weak solutions of several well-known incompressible fluid models, such as the n-dimensional ( n ≥ 2 ) Navier–Stokes equations with fractional hyperviscosity, the three-dimensional convective Brinkman–Forchheimer equations and the generalized SQG equation. A new approach, different from the classical Fourier splitting method develpoed by Schonbek (Commun Partial Differ Equ 11:733–763, 1986) and the spectral representation technique by Kajikiya and Miyakawa (Math Z 192:135-148,1986), is presented. By using the new approach, we can recover and improve some known decay results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the stability of a stationary solution of free boundary problems of the incompressible Navier–Stokes equations in a three-dimensional bounded domain with surface tension. More precisely, this article proves that if the initial angular momentum is sufficiently small and if the initial configuration is sufficiently close to equilibrium, then there exists a global classical solution that converges exponentially fast to a uniform rigid rotation of the liquid as t → ∞ with respect to a certain axis. The proof of the unique existence of a stationary solution is also given. [ABSTRACT FROM AUTHOR]

This paper presents a Fluid-Structure Interaction (FSI) numerical study of a deformable two-dimensional floating rectangular tank partially filled with water and subjected to a regular wave effect. It is based on the coupling of a two-phase flow solver from the OpenFOAM code, based on the Finite Volume Method (FVM), and an elastic solid solver from the FEniCS code, based on the Finite Element Method (FEM). The two solvers are coupled using the preCICE library for the Fluid-Structure Interaction (FSI) problem. The Arbitrary Lagrangian-Eulerian (ALE) formulation is adopted for the two-phase Navier-Stokes equations in a moving fluid domain. An implicit coupling scheme is used to solve the FSI problem. The effect of swell excitation is considered by introducing a source term into the equations governing the fluid and the solid. The obtained results show that for the studied case, the tank walls' flexibility increases the sloshing amplitude and the fluctuations at the air-liquid interface, and causes a phase shift in the free surface response compared to the rigid case. The Fast Fourier Transform (FFT) applied to the time responses of the free surface and the tank wall highlights that the obtained results give a good agreement with the analytical solution. [ABSTRACT FROM AUTHOR]

Waves are mainly generated by wind via the transfer of wind energy to the water through friction. When the wind subsides, the waves transition into swells and eventually dissipate. Friction plays a crucial role in the generation and dissipation of waves. Numerous wave theories have been developed based on the assumption of inviscid flow, but these theories are inadequate in explaining the transformation of waves into swells. This study addressed these limitations by analytically deriving general solutions to the Navier–Stokes equations. By expressing the velocity field as the product of a solution to the Helmholtz equation and a time-dependent univariate function, the Navier–Stokes equations are decomposed into an ordinary differential equation and the Euler equations, which are solved using tensor calculus. This paper provides solutions for viscous flow with shear currents when applied to the water wave problem. These solutions were validated through their application to the vorticity equation. The decay modulus of water waves was compared with experimental data, showing a significant degree of concordance. In contrast to other wave theories, this study clarified the process through which waves evolve into swells.

Abstract We consider the problem of water–air two-phase flow, which occurs during water aeration by air injection. We present and analyze a new model incorporating a nonlocal boundary condition, integrating the effect of the air phase through a source term applied to the water phase. This term is described using a kinetic approach based on the Vlasov equation. A numerical study is conducted, and numerical experiments are presented to demonstrate the effectiveness of the presented model

Abstract Pedestrian two-stage crossings are common at large, busy signalized intersections with long crosswalks and high traffic volumes. This design aims to address pedestrian operation and safety by allowing navigation in two stages, negotiating each traffic direction separately. Understanding crosswalk behavior, especially during bidirectional interactions, is essential. This paper presents a two-stage pedestrian crossing model based on Physics-Informed Neural Networks (PINNs), incorporating fluid dynamics equations to determine characteristics such as speed, density, acceleration, and Reynolds number during crossings. The study shows that PINNs outperform traditional deep learning methods in calculating and predicting pedestrian fluid properties, achieving a mean squared error as low as 10–8. The model effectively captures dynamic pedestrian flow characteristics and provides insights into pedestrian behavior impacts. The results are significant for designing pedestrian facilities to ensure comfort and optimizing signal timing to enhance mobility and safety. Additionally, these findings can aid autonomous vehicles in better understanding pedestrian intentions in intelligent transportation systems.

In this article, a numerical study was carried out to study the dynamic adaptive grid method, based on the concept of the equidistribution method. The article explores a method for adapting the computational grid to solving two-dimensional Navier-Stokes differential equations, which describe the physical processes of gas dynamics specifically for the problem of a two-dimensional channel with an expansion coefficient (H/h) = 2. Different flow characteristics were calculated at different Reynolds numbers Re = from 100 to 1000, to get the actual thread behavior. Calculations are performed for laminar flow mode. The results of the longitudinal velocity profiles in different sections of the channel and the length of the primary and secondary vortices are obtained with a change in the Reynolds number after the ledge. For the numerical solution of this problem, a second-order accuracy McCormack scheme was used. To confirm the adequacy and reliability of the numerical results, a careful comparison was made with the experimental data of Armaly V.F. et al., taken from the literature. It is also shown that as a result of using this method of adaptive grids, it is possible to improve the numerical accuracy obtained for a given number of node points. It is shown that the existing method of multiple 2D adaptive meshes makes it easier to concentrate meshes in the required areas. This method should prove useful for many Navier-Stokes flow calculations.

In this paper, we consider the incompressible 3D Euler and Navier–Stokes equations in a smooth bounded domain. First, we study the 3D Euler equations endowed with slip boundary conditions and we prove the same criteria for energy conservation involving the gradient, already known for the Navier–Stokes equations. Subsequently, we utilize this finding, which is based on a proper approximation of the velocity (and does not require any estimate or additional assumption on the pressure), to explore energy conservation for Beltrami flows. Finally, we explore Beltrami solutions to the Navier–Stokes equations and demonstrate that conditions leading to energy conservation are significantly distinct from those implying regularity. This remains true even when making use of the bootstrap regularity improvement, stemming from the solution being a Beltrami vector field. [ABSTRACT FROM AUTHOR]

This paper is concerned with a simplified model for two-phase fluids with diffuse interface. The model couples the nonhomogeneous incompressible Navier-Stokes equations with the Allen-Cahn equation. The viscosity coefficient is allowed to depend both on the phase variable and on the density. Under some smallness assumptions on initial data, the global existence of unique strong solutions to the 3D Cauchy problem and the initial boundary value problem is established. Meanwhile, we obtain the exponential decay-in-time properties of the solutions. Here, the initial vacuum is allowed and no compatibility conditions are required for the initial data via time weighted techniques. [ABSTRACT FROM AUTHOR]

This paper considers the Keller-Segel model coupled to stochastic Navier-Stokes equations (KS-SNS, for short), which describes the dynamics of oxygen and bacteria densities evolving within a stochastically forced 2D incompressible viscous flow. Our main goal is to investigate the existence and uniqueness of global solutions (strong in the probabilistic sense and weak in the PDE sense) to the KS-SNS system. A novel approximate KS-SNS system with proper regularization and cut-off operators in H s (R 2) is introduced, and the existence of approximate solution is proved by some a priori uniform bounds and a careful analysis on the approximation scheme. Under appropriate assumptions, two types of stochastic entropy-energy inequalities that seem to be new in their forms are derived, which together with the Prohorov theorem and Jakubowski-Skorokhod theorem enables us to show that the sequence of approximate solutions converges to a global martingale weak solution. In addition, when χ (⋅) ≡ const. > 0 , we prove that the solution is pathwise unique, and hence by the Yamada-Wantanabe theorem that the KS-SNS system admits a unique global pathwise weak solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical approximation of incompressible magnetohydrodynamic (MHD) system with variable density. Firstly, we provide first- and second-order time discretization schemes based on the convective form of the Gauge-Uzawa method. Secondly, we prove that the proposed schemes are unconditionally stable. We also provide error estimates through rigorous theoretical analysis. Then, we construct a fully-discrete first-order scheme with finite elements in space and provide its stability result. Finally, we present some numerical experiments to validate the effectiveness of the proposed schemes. Furthermore, we also present the conserved scheme and its numerical results. • Decoupling of velocity and pressure in the Navier-Stokes equations with variable density. • First-order scheme does not need to give an initial value of the pressure. • Both schemes are unconditional energy stability. • Given error estimates for all unknowns. [ABSTRACT FROM AUTHOR]

We define a class of not necessarily linear C 0 -semigroups (P t) t ≥ 0 on C b (E) (more generally, on C κ (E) : = 1 κ C b (E) , for some bounded function κ , which is the pointwise limit of a decreasing sequence of continuous functions) equipped with the mixed topology τ 1 M for a large class of topological (not necessarily Polish) state spaces E. If these semigroups are linear, classical theory of operator semigroups on locally convex spaces as well as the theory of bicontinuous semigroups apply to them. In particular, they are infinitesimally generated by their generator (L , D (L)) and thus reconstructable through an Euler formula from their strong derivative at zero in (C b (E) , τ 1 M). In the linear case, we prove that such (P t) t ≥ 0 can be characterized as integral operators given by measure kernels satisfying certain tightness properties. As a consequence, transition semigroups of Markov processes are C 0 -semigroups on (C b (E) , τ 1 M) , if they leave C b (E) invariant and they are jointly weakly continuous in space and time. Hence, they can be reconstructed from their strong derivative at zero and thus have a fully infinitesimal description. This solves an open problem for Markov processes. We show that our results apply to a large number of Markov processes, e.g., those given as the laws of solutions to SDEs and SPDEs, including the stochastic 2D Navier-Stokes equations and the stochastic fast and slow diffusion porous media equations. Furthermore, we introduce the notion of a Markov core operator (L 0 , D (L 0)) for the above generators (L , D (L)) and prove that uniqueness of the Fokker-Planck-Kolmogorov equations corresponding to (L 0 , D (L 0)) for all Dirac initial conditions implies that (L 0 , D (L 0)) is a Markov core operator for (L , D (L)). As a consequence, we identify the Kolmogorov operators of a large number of SDEs on finite and infinite dimensional state spaces as Markov core operators for the infinitesimal generators of the C 0 -semigroups on (C κ (E) , τ κ M) given by their transition semigroups. Furthermore, if each P t is merely convex, we prove that (P t) t ≥ 0 gives rise to viscosity solutions to the Cauchy problem given by its associated (nonlinear) infinitesimal generator. We also show that value functions of optimal control problems, both, in finite and infinite dimensions are particular instances of convex C 0 -semigroups on (C κ (E) , τ κ M). [ABSTRACT FROM AUTHOR]

In this article, we develop a linear theory to deal with the time periodic problem for the Navier-Stokes equations on unbounded domains with moving boundary. Compared to the case of bounded domains the underlying modified time-dependent Stokes operators are no longer invertible, thus leading to a more sophisticated construction of the evolution operator. Moreover, Sobolev embeddings on L q spaces imply restrictions on q depending on geometric properties of the domain. The theory is focusing on the half space case, the construction and local-in-time estimates of the evolution operator and its adjoint in view of time periodic solutions. [ABSTRACT FROM AUTHOR]

In this paper we study traveling wave solutions to the free boundary incompressible Navier-Stokes system with generalized Navier-slip conditions. The fluid is assumed to occupy a horizontally infinite strip-like domain that is bounded below by a flat rigid surface and above by a moving surface. We assume that the fluid is acted upon by a bulk force and a surface stress that are stationary in a coordinate system moving parallel to the fluid bottom, and a uniform gravitational force that is perpendicular to the flat rigid surface. We construct our solutions via an implicit function argument, and show that as the slip parameter shrinks to zero, the Navier-slip solutions converge to solutions to the no-slip problem obtained previously. [ABSTRACT FROM AUTHOR]

We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space H 1.5 + ϵ and the initial structure velocity is in H 1 + ϵ , where ϵ ∈ (0 , 1 / 20) . [ABSTRACT FROM AUTHOR]

We propose a modification to the nonlinear term of the three-dimensional incompressible Navier–Stokes equations (NSE) in either advective or rotational form which “calms” the system in the sense that the algebraic degree of the nonlinearity is effectively reduced. This system, the calmed Navier–Stokes Equations (calmed NSE), utilizes a “calming function” in the nonlinear term to locally constrain large advective velocities. Notably, this approach avoids the direct smoothing or filtering of derivatives, thus we make no modifications to the boundary conditions. Under suitable conditions on the calming function, we are able to prove global well-posedness of calmed NSE and show the convergence of calmed NSE solutions to NSE solutions on the time interval of existence for the latter. In addition, we prove that the dynamical system generated by the calmed NSE in the rotational form possesses both an energy identity and a global attractor. Moreover, we show that strong solutions to the calmed equations converge to strong solutions of the NSE without assuming their existence, providing a new proof of the existence of strong solutions to the 3D Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

In this study, we have derived a thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. This model accommodates variations in physical properties such as density, viscosity, heat capacity, and thermal conductivity between the two components. The model equations encompass a Cahn-Hilliard equation with the volume fraction as the phase variable, a Navier-Stokes equation, and a heat equation, and meanwhile maintains mass conservation, energy conservation, and entropy increase simultaneously. Given the highly coupled and nonlinear nature of the model equations, we developed a semi-decoupled, mass-preserving, and entropy-stable time-discrete numerical method. We conducted several numerical tests to validate both our model and numerical method. Additionally, we have investigated the merging process of two bubbles under non-isothermal conditions and compared the results with those under isothermal conditions. Our findings reveal that temperature gradients influence bubble morphology and lead to earlier merging. Moreover, we have observed that the merging of bubbles slows down with increasing heat Peclect number Pe T when the initial temperature field increases linearly along the channel, while bubbles merge faster with heat Peclect number Pe T when the initial temperature field decreases linearly along the channel. • A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. • A semi-decoupled, mass-preserving, and entropy-stable numerical method. • Investigated numerically the merging process of two bubbles under isothermal and non-isothermal conditions. [ABSTRACT FROM AUTHOR]

We show the existence of a weak solution for a system of partial differential equations describing the motion of a flexible solid inside a fluid: A nonlinear, viscoelastic, n-dimensional bulk solid governed by a PDE including inertia is interacting with an incompressible fluid governed by the (n-dimensional) Navier-Stokes equation for n ≥ 2. The result is the first allowing for large bulk deformations in the regime of long time existence for fluid-structure interactions. The existence is achieved by introducing a novel variational scheme involving two time-scales that allows us to extend the method of minimizing movements to hyperbolic problems involving nonconvex and degenerate energies. [ABSTRACT FROM AUTHOR]

In this paper, a modified method is used to approximate the solution to the time-fractional n-dimensional Navier–Stokes equation. The modified method is the Variational Iteration Transform Method, which is implemented in the equation whose fractional order derivative is described in the Caputo sense. The proposed method’s findings are presented and examined using figures. It is demonstrated that the proposed method is efficient, dependable, and simple to apply to various science and engineering applications [ABSTRACT FROM AUTHOR]

In our present paper, we have employed the Atangana–Baleanu derivative in the multi-layered Navier–Stokes condition to analyse the nature of the flow. Actually, the stream, the impacts and modifications caused by the operator and the mathematical technique approach are the main subjects of our attention. In this exploratory work, the Laplace transform strategy and the Atangana–Baleanu fractional operator were combined. Due to the Atangana–Baleanu operator’s convergence in many engineering and technological issues, it is employed. We have also carefully evaluated the presence and uniqueness of the outcome. To visualize the variations in the flow, we have presented the graphs of the stream’s velocity components in each direction during the study [ABSTRACT FROM AUTHOR]

The present study examines numerically a three-dimensional (3D) laminar and stationary flow around an idealized metal foam cell shaped as an empty cube with cylindrical edges. The physical configuration adopted consists of an isolated cell placed inside a plane channel crossed by air as a working fluid. The numerical investigation is carried out using the dimensionless Navier-Stokes equations resolved by finite volume method. The flow configurations given for several Reynolds numbers are described entirely using 2D and 3D maps. The plane maps give streamlines at the side and top fiber planes: the vertical side of the cell is normal to the flow. In addition, the critical locations and zones characterizing the flow are also localized: the saddle points, separation nodes, attachment points, foci of the recirculation zones, and the attachment lines. For the Reynolds number in the range 75 ≤ Re ≤ 500, the results show that the topography of the streamlines at the vertical plane in the middle of the lateral fibers of the cell (z = 5.3Dp) is developed into arc-shaped vortex rollers in the gap. In the wake, two saddle points reveal the zones of influence of these spiral structures, formed by two vortices (Bt and Nw) and zones of upwash and downwash. At a high value of Re (Re = 500), the upwash weakens but does not disappear. Two recirculation bubbles are associated with the two saddles, in the gap and the wake of the upper fibers, parallel to the flow. At Re =500, the distribution flow loses its symmetry and displays matter transfer between the two recirculation. The displacement of the saddle point in the wake is 9.65 times that in the gap. No vortex shedding is observed in the wake of cell due to the nullity of the frequency shedding (f = 0).The results indicate also that decreasing the pore diameter favors recirculation inside the cell gap. These recirculation lengths (Lrz, Lry) located respectively in the wake of planes z = 5.3Dp and y = Dp reduce the drag coefficient in equal proportion (51%) in the range 75 ≤ Re ≤ 500. It appears that the wake of the lateral fibers of the z=5.3Dp plane contributes better to the drag coefficient. We consider that the predominance of downwash associated with the instability of saddle point S.2 in the wake when Re increases leads to a decrease in the drag coefficient in the wake. [ABSTRACT FROM AUTHOR]

Adding a certain percentage of hydrogen into the natural gas pipeline network is regarded as an efficient way to store and transport hydrogen. CH4-H2 binary fuel is also considered to be an important means of hydrogen utilization. In this paper, flame acceleration (FA) in stoichiometric CH4/H2/air mixtures with various hydrogen blend ratios (i.e., Hbr = 0%, 20%, 50%, 80%, and 100%) was studied experimentally and numerically. In the experiments, high-speed photography was used to record the FA process. In the numerical simulations, the two-dimensional, fully-compressible, reactive Navier-Stokes equations were solved using a high-order algorithm on a dynamically adapting mesh. The chemical reaction and diffusive transport of the mixtures were described by a calibrated chemical-diffusive model. The numerical predictions agree reasonably with the experimental measurements. The results show that a larger hydrogen blend ratio leads to a faster FA. The difference in FA due to hydrogen blending mainly depends on the property change of the fuel mixtures, the increase of flame surface area and the interactions between flame and pressure waves, corresponding to three different stages. In addition, the heat loss to the channel walls and obstacle surfaces has an impact on the FA process, especially in the mixtures with low hydrogen blend ratios (i.e., Hbr ≤ 20%). This is related to the weakening of interactions between pressure waves and flame under isothermal boundary condition. [ABSTRACT FROM AUTHOR]

By making full use of the Fourier localization technique and the Littlewood-Paley decomposition, we establish refined estimates for the product operates under different frameworks. This together with a decomposition of the curl operator enables us to obtain three regularity criteria of the weak solution for the 3D incompressible Navier-Stokes equations involving the signed curl operators. To our knowledge, this is the first instance of exhibiting regularity criteria in terms of 'partial vorticity'. Our results also improve some known regularity criteria for the Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

In this paper, we establish the global existence and uniqueness of strong solution to the three-dimensional generalized Navier-Stokes equations with nonlinear damping term. [ABSTRACT FROM AUTHOR]

We consider the pointwise in space $ L^p $-type regularity for elliptic and parabolic equations of-order $ m $ in $ \mathbb{R}^{n} $. We provide pointwise Schauder estimates for the general range of $ L^{p} $ exponents, extending previous results from $ p>n/m $ to $ 1

Summary: We propose an implicit discontinuous Galerkin (DG) discretization for incompressible two‐phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L‐stable TR‐BDF2 method is adopted for the time discretization of the Navier‐Stokes equations and of the level set method. Adaptive mesh refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks. A specific analysis on the influence of different choices of the mixture viscosity is also carried out. [ABSTRACT FROM AUTHOR]

This work presents a comprehensive framework for the sensitivity analysis of the Navier–Stokes equations, with an emphasis on the stability estimate of the discretized first‐order sensitivity of the Navier–Stokes equations. The first‐order sensitivity of the Navier–Stokes equations is defined using the polynomial chaos method, and a finite element‐volume numerical scheme for the Navier–Stokes equations is suggested. This numerical method is integrated into the open‐source industrial code TrioCFD developed by the CEA. The finite element‐volume discretization is extended to the first‐order sensitivity Navier–Stokes equations, and the most significant and original point is the discretization of the nonlinear term. A stability estimate for continuous and discrete Navier–Stokes equations is established. Finally, numerical tests are presented to evaluate the polynomial chaos method and to compare it to the Monte Carlo and Taylor expansion methods. [ABSTRACT FROM AUTHOR]

In this article, we aim to establish the optimal time decay rates of strong solutions to a two-phase flow model derived from a type of coupled fluid-kinetic equation. It is proved that the strong solutions converge to the given constant states with algebraic time decay rates under some additional assumptions on the initial data.

In 2008, Cai and Jiu showed that the Cauchy problem of the Navier-Stokes equations, with damping α∣u∣β−1u\alpha {| u| }^{\beta -1}u for α>0\alpha \gt 0 and β≥1\beta \ge 1 has global weak solutions in L2(R3){L}^{2}\left({{\mathbb{R}}}^{3}). In this article, we study the uniqueness and the continuity in L2(R3){L}^{2}\left({{\mathbb{R}}}^{3}) of this global weak solution. We also prove the large time decay for this global solution for β≥103\beta \ge \frac{10}{3}.

Abstract The occurrence of fluid flow near a wellhead is the major concern of the petroleum industry, as pressure drop, loss of formation, and other variables of interest are mostly affected in this region. The fluid flows from the hydrocarbon reservoir to the wellbore can be characterized as laminar to turbulent; thus, it is important to model this phenomenon with the integrated wellbore-reservoir model. Using 3D Navier–Stokes equations, an integrated wellbore-reservoir model is created in this study, and it incorporates the formation damage zone. For the porous-porous and porous-fluid interfaces, the General Grid Interface (GGI) approach is applied in conjunction with the conservative mass flux interface model. Model equations are solved using a velocity-pressure coupling solver that is pressure-based. For reliable and quick results, the system of equations is solved using an algebraic multigrid approach. The pressure diffusivity equation’s analytical solution under steady-state flow circumstances is used to validate the model. The integrated wellbore-reservoir model is applied to different reservoir scenarios, for example, different production rates, formation zones, and reservoir formation conditions. The results indicate that the present Computational Fluid Dynamics (CFD) model can be extended to simulate the real field scale model. integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with efficient computational techniques can lead the field of petroleum industries to advance current knowledge.

In this short note, we provide a self-contained proof for the criterion $\nabla u\in L^\frac{5}{2}(0, T; L^2(\mathbb{R}^3))$ to Navier–Stokes equations energy balance, which improves some recent results on this problem.

In this study, the replacement of hydrogen with ammonia in a laboratory Moderate or Intense Low-Oxygen Dilution (MILD) burner is being investigated by incorporating air swirling to study NO x formation in the flow field. A CH 4 /H 2 /NH 3 fuel jet is modeled using the RANS (Reynolds-Averaged Navier-Stokes equations) approach for various fuel mixtures with ammonia content ranging from 0% to 18%, while maintaining a constant methane concentration. The study is conducted under two conditions: axial coflow with hot diluted air and swirled with the swirl numbers of 0.6–1.0. The hot oxidizer consists of 9% O 2 and 6% O 2 at 1300 K. The combustion model is based on the eddy dissipation concept, and a detailed chemical mechanism is used to represent the chemical reactions. Numerical simulations suggest that swirl enhances the reactivity of nitrogen-containing reactions, with the sensitivity to swirl varying based on the inlet ammonia content. The addition of ammonia and air swirling improve the MILD index but reduce the MILD area. Swirling increases the temperature of the reacting field, while ammonia suppresses it. The results indicate the potential of swilr concept for enhanced dilution, improved flexibility in controlling NO x formation, and overcomed the ammonia reativity drwabacks. • Swirl enhances the combustion characteristics of ammonia fuel. • Hydrogen replacing with ammonia has suppressed the MILD combustion region. • The addition of ammonia and air swirling improves the MILD combustion index. • The swirl concept shows potential for controlling ammonia flame NOx formation. [ABSTRACT FROM AUTHOR]

In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler–Navier–Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two systems, pressureless Euler system and incompressible Navier–Stoke system, is through the drag force. We construct the global-in-time existence and uniqueness of regular solutions for the pressureless Euler–Navier–Stokes system without using a priori large time behavior estimates. Moreover, we seek for the optimal Sobolev regularity for the solutions. Concerning the temporal decay for solutions, we show that the fluid velocities exhibit the same decay rate as that of the heat equations. In particular, our result provides that the temporal decay rate of difference between two velocities, which is faster than the fluid velocities themselves, is at least the same as the second-order derivatives of fluid velocities. [ABSTRACT FROM AUTHOR]

This paper is concerned with the nonlinear stability of planar Couette flow for the three‐dimensional NS‐NS equations, which are used to model the motion of two‐phase flow. Our result shows that the planar Couette flow is asymptotically stable for the initial perturbations sufficiently small in some Sobolev space if the background velocity and the Reynolds number are sufficiently small. Moreover, it is proved that the solution converges to the stationary state (ρ∗,us,n∗,ws)$$ \left({\rho}_{\ast },{u}_s,{n}_{\ast },{w}_s\right) $$ at an algebraic time decay rate, and we also give the decay rate of the relative velocity. [ABSTRACT FROM AUTHOR]

In this article, a numerical scheme for solving two‐dimensional (2D) time‐dependent incompressible Navier–Stokes equations is presented. The artificial compressibility technique is used to incorporate a time derivative of pressure term to the continuity equation. It is employed for pressure–velocity coupling. The scheme consists of backward difference approximation for time derivatives and central difference approximation for spatial derivatives, implemented on a collocated grid. The discretization of the differential equations yields a system of algebraic equations with a block coefficient matrix. To solve this system efficiently, matrix inversion with sparse matrix computation is employed. The proposed numerical scheme is applied to solve three flow problems (lid‐driven cavity flow, rectangular channel flow, and Taylor–Green vortex problem) to validate the accuracy and applicability of the scheme. The results affirm the scheme's capability to provide precise approximations for solutions to the Navier–Stokes equations. With slight modifications, the scheme can be applied to solve various flow problems with high accuracy, less memory usage, and reduced computational time. [ABSTRACT FROM AUTHOR]

A theory of incompressible turbulent plane jets (TPJs) is proposed by advancing an improved boundary layer approximation over the limiting classical – retaining more terms in the momentum balance equations. A pressure deficit inside the jet (with respect to the ambient) must exist due to transverse turbulence (Miller & Comings, J. Fluid Mech. , vol. 3, 1957, pp. 1–16; Hussain & Clarke, Phys. Fluids , vol. 20, 1977, pp. 1416–1426). Contrary to the universally accepted invariance of the total momentum flux $J_T(x)$ (non-dimensionalized by its inlet value) as a function of the streamwise distance $x$ , we prove that $J_T(x) >1$ – a condition that all TPJs must satisfy; surprisingly, prior theories and most experiments do not satisfy this condition. This motivated us to apply Lie symmetry analysis with translational and dilatational transformations of the modified equations (incorporating $J_T>1$), which yields scaling laws for key jet measures: the mean streamwise and transverse velocities $U(x,y)$ and $V(x,y)$ , the turbulence intensities, the Reynolds shear stress $-\rho \,\overline {u'v'}(x,y)$ , the mean pressure $P(x,y)$ , etc. Experiments satisfying $J_T(x)>1$ validate our predictions for all jet measures, including, among others, the profiles of $U$ , $V$ and $-\rho \,\overline {u'v'}$. We further predict $U \sim x^{-0.24}$ , $V \sim x^{-0.45}$ , $-\rho \,\overline {u'v'}\sim x^{-0.69}$ , the mass flux $Q_m \sim x^{0.55}$ , and $J_T$ increases to approximately 1.5. Contrary to the classical linear jet spread, we find sublinear spread, with the jet half-width growing like $b(x)\sim x^{0.79}$ , indicating a narrower jet. Our predictions differ notably from most results reported in the literature. These contradictions demand revisiting jet studies involving carefully designed facilities and boundary conditions, and highly resolved simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with a kinetic-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier–Stokes equations and the Vlasov– Fokker–Planck equations that model dispersed particles of different sizes. A uniform regularity for random initial data near the global equilibrium is established in some suitable Sobolev spaces by using energy estimates, and we also prove the energy decays exponentially in time by hypocoercivity arguments, which means that the long time behavior of the solution is insensitive to the random perturbation in the initial data. For the generalized polynomial chaos stochastic Galerkin method (gPC-sG) for the model, with initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Stokes number, and the error decays exponentially in time. [ABSTRACT FROM AUTHOR]

This paper considers the discretization of the time-dependent Navier–Stokes equations with the family of inf-sup stabilized Scott–Vogelius pairs recently introduced in [John/Li/Merdon/Rui, Math. Models Methods Appl. Sci., 2024] for the Stokes problem. Therein, the velocity space is obtained by enriching the H 1 -conforming Lagrange element space with some H (div) -conforming Raviart–Thomas functions, such that the divergence constraint is satisfied exactly. In these methods arbitrary shape-regular simplicial grids can be used. In the present paper two alternatives for discretizing the convective terms are considered. One variant leads to a scheme that still only involves volume integrals, and the other variant employs upwinding known from DG schemes. Both variants ensure the conservation of linear momentum and angular momentum in some suitable sense. In addition, a pressure-robust and convection-robust velocity error estimate is derived, i.e., the velocity error bound does not depend on the pressure and the constant in the error bound for the kinetic energy does not blow up for small viscosity. After condensation of the enrichment unknowns and all non-constant pressure unknowns, the method can be reduced to a P k − P 0 -like system for arbitrary velocity polynomial degree k. Numerical studies verify the theoretical findings. [ABSTRACT FROM AUTHOR]

This article deals with the effects of thermophoresis on thermosolutal mixed convection in a vertical wavy porous cavity. Three distinct flow features are chosen by changing the directions of the moving horizontal borders. A nonuniform temperature, as well as concentration distributions, are introduced to the bottom wall while keeping cold temperature and low concentration for the other walls. The governing equations are modeled to describe thermosolutal phenomena. These equations are solved by reconstructing a recently developed compact scheme. Furthermore, the significance of well-defined parameters influencing the fluid rotation and thermosolutal transfer, namely Richardson number ( 0.01 ≤ Ri ≤ 100 ), Buoyancy ratio (N = 1), number of undulations ( 0 ≤ d ≤ 2 ) of the wavy walls, Lewis number ( 1 ≤ Le ≤ 10 ), thermophoretic coefficient ( 0.0 ≤ K T ≤ 1.0 ), Darcy number ( 0.001 ≤ Da ≤ 0.1 ), and porosity of the porous medium ( 0.1 ≤ ε ≤ 1.0 ) are performed generously. Results are displayed in terms of streamlines, isotherms, iso-concentrations, Nusselt, and Sherwood numbers to evoke the thermosolutal phenomena for various physical parameters. It is observed that thermophoresis is effective in certain circumstances. In addition, heat and mass transfer enhancement is noted with decreasing Richardson number while heat and mass transfer reduction is noted with increasing undulation number of the wavy walls. We have noticed that for the change in Le from 1 to 10, heat transfer is diminished up to 2.91% in Case-1, 3.03% in Case-2, and 2.20% in Case-3 while mass transfer is enhanced by 162.85% in Case-1, 164.05% in Case-2, and 87.03% in Case-3. [ABSTRACT FROM AUTHOR]

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flux approximation. This paper introduces a class of thermodynamically consistent diffuse-interface incompressible fluid mixture models that is fully compatible with the continuum theory of mixtures. The proposed models can be formulated in either constituent or mixture quantities, enabling a direct comparison with the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model with non-matching densities. This comparison reveals the key modelling simplifications employed in the latter. [ABSTRACT FROM AUTHOR]

AbstractErosion wear presents a significant challenge in the operation of hydrodynamic systems, particularly in centrifugal pumps. To address this issue, this study employs the coarse-grained Discrete Element Method (CGDEM) coupled with Computational Fluid Dynamics (CFD) to predict erosion wear areas and elucidate particle behavior dynamics. The simulation considers spherical solid particles (brown corundum) with diameters ranging from 0.3 mm to 1 mm and volume fractions of 15% and 5%. The flow field is calculated using the Navier-Stokes equations and the shear-stress-transport (SST) k-ω model. Particle movement is tracked using Newton’s second law, considering drag and gravitational forces. Results indicate that the highest turbulent kinetic energy (TKE) occurs at a flow rate of Q = 15 m3/h. Moreover, the pressure reduces slightly when the flow rate increases, although flow velocity might increase with volumetric discharge. Additionally, increased particle diameter leads to greater erosion wear, particularly on blade leading edges, the volute tongue area, and the volute casing belly region. As particle mass concentration intensifies, wear rates on the volute wall and inner hub edge also increase. The study’s robustness is demonstrated through alignment between experimental and numerical data. This investigation offers valuable insights into erosion dynamics in centrifugal pumps, crucial for enhancing operational efficiency and mitigating erosion-induced challenges in these critical systems. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness of the steady 1-D shock solutions for the inviscid compressible Euler system in a finite nozzle via asymptotic analysis for physical parameters. The parameters for the heat conductivity and the temperature-depending viscosity are investigated for both barotropic gases and polytropic gases. It finally turns out that the hypotheses on the physical effects have significant influences on the asymptotic behaviors as the parameters vanish. In particular, the positions of the shock front for the limit shock solution (if exists) are different for different hypotheses. Hence, it seems impossible to figure out a criterion selecting the unique shock solution within the framework of the inviscid Euler flows. [ABSTRACT FROM AUTHOR]

Nonmodal development of stationary three-dimensional disturbances in a circular jet is numerically investigated at the Reynolds number Re = 2850. The operating conditions of a laboratory experiment performed earlier in the Institute of Mechanics of Moscow State University are reproduced. A method for calculating optimal disturbances under the conditions of downstream developing main flow is developed. The disturbances associated with different azimuthal numbers are calculated. The shape, character of development, and growth degree of optimal disturbances are determined. [ABSTRACT FROM AUTHOR]