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We present a complete numerical analysis for a general discretization of a coupled flow–mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix–fracture interfaces, as well as nonlinear poromechanical coupling. Fractures are described as planar surfaces, yielding the so-called mixed- or hybrid-dimensional models. Small displacements and a linear elastic behavior are considered for the matrix. The model accounts for discontinuous fluid pressures at matrix–fracture interfaces in order to cover a wide range of normal fracture conductivities. The numerical analysis is carried out in the Gradient Discretization framework (see J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin [ The gradient discretisation method , Springer, Cham, 2018]), encompassing a large family of conforming and nonconforming discretizations. The convergence result also yields, as a by-product, the existence of a weak solution to the continuous model. A numerical experiment in 2D is presented to support the obtained result, employing a Hybrid Finite Volume scheme for the flow and second-order finite elements (\mathbb {P}_2) for the mechanical displacement coupled with face-wise constant (\mathbb P_0) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions. [ABSTRACT FROM AUTHOR]

Bernoulli's equation is a famous, elegant fluid mechanics relation that, in its most popular version, relates pressure, velocity, and elevation changes along each streamline in a steady barotropic inviscid flow. Despite its simplicity and restrictive assumptions, this equation is a powerful and effective analysis tool in a variety of real-flow situations. However, the Bernoulli equation is unfortunately not Galilean-invariant, i.e., it does not satisfy the desirable property of remaining unchanged under a Galilean transformation between two inertial reference frames reciprocally moving with constant velocity. In a previous paper, the author presented a Galilean-invariant formulation of the Bernoulli equation, in which a new term is introduced in the definition of the Bernoulli constant. In the present technical note, this Galilean-invariant form of the Bernoulli relation is extended to (1) unsteady flow, (2) compressible flow, and (3) a noninertial frame of reference accelerating with constant rectilinear acceleration. Similar extensions are consolidated for the classic Bernoulli equation and treated in fundamental fluid mechanics textbooks. The use of the updated Galilean-invariant Bernoulli equation in these less-restrictive contexts is illustrated with typical engineering application examples. The results demonstrate that the extended version of the Bernoulli principle can also be applied along the same flow lines in a reference frame moving with constant velocity relative to another reference frame in which the conventional Bernoulli equation is valid, provided that the Bernoulli constant includes a suitable additional term. [ABSTRACT FROM AUTHOR]

A two-dimensional body that moves suddenly in a viscous fluid can instantly generate vortices at its sharp edges. Recent work using inviscid flow theory, based on the Birkhoff–Rott equation and the Kutta condition, predicts that the 'starting vortices' generated by the sharp and straight edges of a body – i.e. the vortices formed immediately after motion begins – can be one of three distinct self-similar types. We explore the existence of these starting vortices for a flat plate and two symmetric Joukowski aerofoils immersed in a viscous fluid, using high-fidelity direct numerical simulations (DNS) of the Navier–Stokes equations. A lattice Green's function method is employed and simulations are performed for chord Reynolds numbers ranging from 5040 to 45 255. Vortices generated at the leading and trailing edges of the flat plate show agreement with the derived inviscid theory, for which a detailed assessment is reported. Agreement is also observed for the two symmetric Joukowski aerofoils, demonstrating the utility of the inviscid theory for arbitrary bodies. While this inviscid theory predicts an abrupt transition between the starting-vortex types, DNS shows a smooth transition. This behaviour occurs for all Reynolds numbers and is related to finite-time effects – there is a maximal time for which the (self-similar) starting vortices exist. We confirm the inviscid prediction that the leading-edge starting vortex of a flat plate can be suppressed dynamically. This has implications for the performance of low-speed aircraft such as model aeroplanes, micro air vehicles and unmanned air vehicles. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or difference in density between the two layers, and the flow is inviscid. Unlike in previous studies, we consider solutions which are localised perturbations rather than periodic or quasi-periodic perturbations of a background shear flow. We rigorously construct a curve of exact solutions and give the leading order terms in an asymptotic expansion. We also give a thorough qualitative description of the fluid particle paths, which can include stagnation points, critical layers, and streamlines which meet the boundary. [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]

We study the motion of tiny heavy inertial particles advected by a two-dimensional inviscid fluid flow, composed of N identical point vortices regularly placed on a ring and rotating as a solid body, therefore forming a vortex crystal. In the limit of weak particle inertia, we show asymptotically that, in the reference frame of the crystal, inertial particles have N asymptotically stable equilibrium positions located outside the crystal, in agreement with numerical observations by Ravichandran et al. ["Clustering of heavy particles in vortical flows: A selective review," Sādhanā 42, 597–605 (2017)]. In addition to these "satellite" attracting points, we observe that for N ≥ 3 , the center of the ring, though degenerate, is a stable equilibrium position for inertial particles. This creates a kind of cage formed by vortices, where inclusions slowly drift toward the center under the effect of the surrounding vortices. The central attracting point is observed to persist even at larger Stokes numbers, in contrast with the satellite attracting points that vanish when the Stokes number is above some critical value. [ABSTRACT FROM AUTHOR]

Separation membranes based on graphene oxide (GO) have attracted much attention due to their good separation properties. But its instability in water and rejection of divalent salt ions is a problem that needs to be solved urgently. In this study, molybdenum disulfide (MoS2) is intercalated into graphene oxide by adding polyethyleneimine (PEI) solution drop by drop for cross-linking, and then GO/MoS2/PEI composite membrane is prepared by vacuum filtration. As MoS2 hydrophobicity increases frictionless water flow channels to improve water flux, PEI cross-linking improves membrane stability and rejection of divalent salt ions. The modified composite membrane has a high rejection of 94.8 % for Mg2+, and water flux is increased by 30 % relative to GO/PEI membrane. In addition, the rejection of the composite membrane to different salt solutions is investigated by MgCl2, MgSO4, NaCl and Na2SO4 solutions, and the results obtained are, in order, R(MgCl2) > R (MgSO4) > R(NaCl) > R(Na2SO4). This modified composite membrane has great potential for salt ion removal. [ABSTRACT FROM AUTHOR]

For decades, superfluid helium has attracted the interest of the scientific community as an extremely pure realisation of a quantum liquid, only accessible at temperatures close to absolute zero. Previously, helium films have only been observed directly using X-rays. However, this method is limited to temperatures above 1 K due to the high levels of energy deposition, and it also suffers from an inability to distinguish between helium isotopes. Here we show that a 3He layer on top of a phase separated mixture film at 170 mK gradually dissolves into the 4He with increasing temperature. We also observe an anomaly in film behaviour near 300 mK and unexpected restoration of the layered structure at 1.5 K which is consistent with a re-entrant phase transition leading to the suppression of superfluidity in the film near 300 mK. Our successful application of neutron scattering to study helium films at ultra-low temperatures opens up new possibilities for future research. Superfluidity, a liquid exhibiting frictionless flow, is so far limited to observations in low-temperature 3He and 4He, where the underlying mechanisms governing the quantum state are complex and different for each isotope, making for a fascinating but challenging phenomenon to study experimentally. The authors use isotope-sensitive neutron reflectometry to investigate mixed 3He/4He superfluid He films on a Si surface, and resolve the structural features and phase transitions that occur with changing temperature. [ABSTRACT FROM AUTHOR]

Three-dimensional (3-D) wing moving steadily over free water surface with the effects of finite depth has been investigated numerically using an iterative boundary element method (IBEM), which was developed for cavitating 3-D hydrofoils advancing under a free surface. The IBEM has been modified and extended for this purpose. The water is incompressible, inviscid and the flow is irrotational. All variables and equations are made dimensionless. In this way the convergence of the numerical scheme is achieved very quickly and consistently. The IBEM is based on Green's theorem. The wing part of problem (including its wake), the free surface problem and the bottom surface problem are solved separately with the effects on each other. The 3-D wing surface, the bottom surface and free surface are modeled with constant strength source and doublet panels. The kinematic boundary condition is applied both on the wing surface and on the bottom surface. On the other hand, the linearized kinematic and dynamic combined condition is applied on the free water surface. The method is first applied to a rectangular wing with a high aspect ratio to compare the pressure distribution on mid-section strip with that of two-dimensional method. Later, the IBEM is applied to a tapered swept-back wing and the effects of finite depth on wing performance have been examined. It is noted that the reduced water depth causes an increase in Kelvin wedge angle, wave height and wave length compared to the infinite depth case. It is also found that a decrease in the depth of bottom surface causes an increase in the loading on the wing. [ABSTRACT FROM AUTHOR]

The paper aims to perform numerical simulations of flapping flight using Discrete Vortex Method (DVM) scheme. The scheme is suitable for moderately low Reynolds number (< ∼ 1 0 5) and computationally less expensive as the flow domain doesn't need to be discretized at each time step. Flapping of a one-dimensional (1D) flexible filament in a two-dimensional (2D) inviscid flow is simulated. The effect of bending by varying the wing shape along the spanwise length on aerodynamic performance was studied. It is observed that compared to rigid wings, bending wings are found to be better in generating lift. The effect of various bending wing configurations (F 1 , F 2 , F 3 and F 4) and different methods of imposing the bending (W 1 , W 2 and W 3) is studied. It was demonstrated that applying wing bending only during the downstroke phase (W 2) is more effective than imposing bending throughout the flapping cycle (W 1). Moreover, an effort is made to replicate the bending configuration observed in manta ray fish (W 3) to investigate its impact on flow domain characteristics, lift, and thrust forces. Furthermore, the inclusion of a winglet is found to significantly enhance lift generation. In addition to the study of bending effects on aerodynamic performance, the study also seeks to emulate a unique aspect of bat flight kinematics, specifically the dynamic variation in wing span length during flapping. In a comparative analysis of two span length variation strategies, it is discerned that exclusively varying span length during the upstroke phase is the optimal approach for achieving increased lift generation. The study highlights the crucial role of wing bending and span length modulation in achieving elevated lift forces while simultaneously reducing drag. These findings are seen as holding significant promise for the design and optimization of Micro Air Vehicles (MAVs) utilizing flapping-based lift generation mechanisms, contributing substantially to the identification of optimal parameters for enhancing MAVs' aerodynamic performance and operational efficiency. [ABSTRACT FROM AUTHOR]

A frequency-domain finite element method and boundary element method (FEM-BEM) coupled numerical method is presented to investigate the dynamic responses of a fluid-filled lined tunnel buried in the ground. The fluid is modeled as an inviscid and compressible liquid, the lining is mimicked as an elastic hollow cylinder, and the ground is modeled as an elastic medium. Initially, based on the Laplace transform and Galerkin method, dynamic governing equations of fluid and those of lining are solved. Meanwhile, dynamic governing equations of ground are solved using methods of Laplace transform, and Helmholtz decomposition together with a reciprocal theorem. In the following stage, fluid, lining, and ground are coupled and solved successfully according to conditions of deformation compatibility and force balance on their interfaces. The solutions in the time domain are obtained with the aid of the inverse Laplace transform. Comparisons with previous studies have validated the proposed numerical method. The dynamic water pressure inside the tunnel and the dynamic radial displacement of the lining under the water hammer are obtained. It is concluded that ignoring the effect of ground may overestimate the magnitude of lining radial displacements and inaccurately evaluate the axial distribution of the displacement. When the stiffness ratio of ground to lining exceeds a certain critical level, the displacement dramatically reduces. [ABSTRACT FROM AUTHOR]

Recently researchers often normalize the radiation force on spheres in standing waves in inviscid fluids using an acoustic contrast factor (typically denoted by Φ) that is independent of kR where k is the wave number and R is the sphere radius. An alternative normalization uses a function Ys that depends on kR. Here, standard results for Φ are extended as a power series in kR using prior Ys results. Also, new terms are found for fluid spheres and applied to the kR dependence of Φ for strongly responsive and weakly responsive examples. Partial-wave phase shifts are used in the derivation. [ABSTRACT FROM AUTHOR]

We consider circular Rayleigh problem which is incompressible, inviscid axial flows to axisymmetric disturbances. For this problem, we derived unbounded parabolic instability region which intersects with Batchelor and Gill semicircle instability region under certain condition. This has been illustrated with examples. Furthermore, we obtained supremum bound for the growth rate of an unstable mode, amplification factor. [ABSTRACT FROM AUTHOR]

The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves. [ABSTRACT FROM AUTHOR]

We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain Ω. We show the convergence of the weak solution to the compressible Navier-Stokes system to the strong solution to the compressible Euler system when the viscosity and the damping coefficients tend to zero. [ABSTRACT FROM AUTHOR]

We derive asymptotic estimates for the projection of the vorticity onto principal directions of material stretching in 3D flows. In flows with pointwise bounded vorticity, these estimates predict vorticity alignment with Lyapunov vectors along trajectories with positive Lyapunov exponents. Specifically, we find that in inviscid flows with conservative body forces, the vorticity exactly aligns with the intersection of the planes orthogonal to the dominant forward and backward Lyapunov vectors along trajectories with positive Lyapunov exponent. Furthermore, we derive asymptotic estimates for the vorticity alignment with the intermediate eigenvector of the rate-of-strain tensor for viscous flows under general forcing. We illustrate these results on explicit solutions of Euler's equation and on direct numerical simulations of homogeneous isotropic turbulence. [ABSTRACT FROM AUTHOR]

Pipe flows are commonly found in nature and industry as an effective mean of transporting fluids. They are primarily characterized by their resistance law, which relates the mean flow rate to the driving pressure gradient. Since Poiseuille and Hagen, various flow regimes and fluid rheologies have been investigated, but the behavior of shear-thickening suspensions, which jam above a critical shear stress, remains poorly understood despite important applications (e.g., concrete or food processing). In this study, we build on recent advances in the physics of shear-thickening suspensions to address their flow through pipes and establish their resistance law. We find that for discontinuously shear-thickening suspensions (large particule volume fractions), the flow rate saturates at high driving stress. Local pressure and velocity measurements reveal that this saturation stems from the emergence of a frictional soliton: a unique, localized, superdissipative, and backpropagating flow structure coexisting with the laminar frictionless flow phase observed at low driving stress. We characterize the remarkably steep effective rheology of the frictional soliton and show that it sets the resistance law at the whole pipe scale. These findings offer an unusual perspective on low-Reynolds suspension flows through pipes, intriguingly reminiscent of the transition to turbulence for simple fluids. They also provide a predictive law for the transport of such suspensions in pipe systems, with implications for a wide range of applications. [ABSTRACT FROM AUTHOR]

Immersed boundary (IB) methods have been successfully implemented for different applications. This paper focuses on the immersed boundary implementation for two different governing equations, namely the diffusion equation and Euler equations, using a bi-linear interpolation for the implementation of the boundary condition. The concept of implicit interpolation is introduced which eradicates the problems faced with the explicit interpolation in which it is required to move away from the boundary in the fluid domain in order to complete the interpolation stencil. [ABSTRACT FROM AUTHOR]

When two fluid drops touch, they coalesce due to surface tension. At early times, there is only a relatively small fluid bridge joining the drops. An asymptotic solution is presented for an inertial regime of early-time coalescence, in which inertial forces balance surface tension at leading order. It is demonstrated that viscosity nevertheless has a leading-order effect. Radial momentum is created at the tightly curved edge of the fluid bridge by the net force $2\gamma$ (per unit length) due to surface tension. This momentum is left behind the radially expanding bridge edge in a thin viscous wake. The divergent volume flux in the wake entrains fluid from above and below the bridge, and drives an inviscid irrotational flow in the drops on the scale of the bridge radius. This flow widens the gap between the drops ahead of the bridge, and the larger gap width results in a lower rate of coalescence. Including viscosity in this way improves the agreement between theory and the available experimental and numerical data. [ABSTRACT FROM AUTHOR]

The separation and turbulent transition of the flow in a compressor blade channel are investigated through direct numerical simulations (DNS) at a Reynolds number of 1.367 × 105. Based on the original DNS data, both time-averaged statistics and instantaneous vortex structures of the flow field are extensively analyzed. The vortices are visualized and studied by the Liutex method, and the streaming dynamic mode decomposition (SDMD), a low-storage variant of conventional DMD, is applied to the large datasets obtained on both pressure and suction sides. The physical quantity analyzed with SDMD is the Liutex magnitude R. The DNS results indicate that flow separation occurs on both sides of the blade. On the pressure surface, the separation is weak and the flow remains in a natural transition dominated by viscous Tollmien–Schlichting instabilities. In contrast, owing to the presence of a large laminar separation bubble, the flow experiences a separation transition governed by inviscid Kelvin–Helmholtz instabilities on the suction surface. The SDMD results suggest that a broad range of vortex frequencies exist in the transition flow, and the scale of the spatial structures is negatively correlated with the frequency of the mode. On the pressure surface, the extracted SDMD modes are primarily related to Kelvin–Helmholtz rolls, whereas on the suction side, influenced by the separated boundary layer, the modal structures exhibit greater diversity. [ABSTRACT FROM AUTHOR]

In this work, a novel coupled finite-volume method (FVM) and a smoothed-particle-hydrodynamics (SPH) method were developed for the simulation of interactions between inviscid shock waves and structures. In this approach, which considers the particles of a meshless method immersed in an FVM grid, the FVM grid cells are classified into either pure or mixed FVM cells, the latter of which contain SPH particles. A finite-element-method shape function is applied to map the variables from the SPH particles to the FVM cells, and the nodal and cell velocities are then obtained. The interaction of the fluid with the structure is computed using moving reflection boundary conditions at cell interfaces with SPH particles. The interactions of the structure with the fluid are computed from the pressure differences around the SPH particles. The processes for computing the coupled FVM–SPH method are described in detail herein. The validity of the presented coupled FVM–SPH method was verified using a theoretical model of a piston, and the numerical results were found to agree well with the theoretical approximations, indicating the accuracy of the proposed coupled method. The results of the method were then compared with the results of an experiment involving a blast-driven steel plate. Good agreement between the experimental and numerical results was obtained, and the maximum difference was 3.44%, demonstrating the effectiveness of the proposed coupled FVM–SPH method when applied to the interaction of a shock wave with a structure. [ABSTRACT FROM AUTHOR]

In most previous studies on the dynamic responses of floating offshore wind turbines, regular wave conditions are assumed in the analysis with the inviscid flow theory. The focused waves, however, have not been considered even though they may have larger wave heights and more concentrated energies, in general, to cause more significant responses in a floating platform. In this study, the characteristics of the dynamic responses of a semi-submersible wind turbine platform subjected to focused waves are studied using a sliding mesh technique with the three-dimensional shear stress transport k – ω turbulence model. Effects of wave steepness, fluid viscosity, and wave nonlinearity on the dynamic responses are investigated. The high-order wave loading in the transverse direction is found significant under high wave steepness conditions. The viscous effects of fluid notably aggravate the pitch and surge dynamics of the floating platform compared to those from under the inviscid flow conditions. Due to the nonlinear characteristics of the focused wave, the floating platform is found to experience a long vibration period and slow drift dynamics in the surge direction after the focused time with significant fluctuation. [ABSTRACT FROM AUTHOR]

This article presents a description of an analytical, stable, and flexible initial background state for both dry and moist baroclinic wave simulation on an aquaplanet in order to test the dynamical core of numerical weather prediction models and study the dynamics and evolution of extratropical cyclones. The initial background state is derived from an analytical zonal wind speed field, or jet structure, and the hydrostatic primitive equations for moist adiabatic and frictionless flow in spherical coordinates. A baroclinic wave can develop if a perturbation is added to the zonal wind speed field. This new baroclinic wave configuration has been implemented in the Open Integrated Forecasting System (OpenIFS) CY43R3, a global numerical weather prediction model developed by the European Centre for Medium-Range Weather Forecasts. In total, seven parameters can be used to control the generation of the initial background state and hence the development of the baroclinic waves in the OpenIFS configuration file: the jet's width, the jet's height, the maximum zonal mean wind speed of the jet, the horizontal mean of the surface virtual temperature, the surface relative humidity, the lapse rate, and the surface roughness. Nine dry and nine moist initial background states have been generated to test their stability without perturbations. The meteorological stability of the initial states is investigated by examining the spatial distributions of the equivalent potential temperature, the absolute vorticity, and the Brunt–Väisälä frequency. Moreover, the root mean square error (RMSE) of the zonal wind speed has been computed to assess their numerical stability. Finally, six dry and six moist initial background state have been used with an unbalanced perturbation to ensure that the baroclinic life cycles that develop are physically realistic. The resulting baroclinic wave is shown to be sensitive to the jet's width. This configuration for baroclinic wave simulations will be used to create a large ensemble of baroclinic life cycles to study how extratropical cyclones may evolve in the future. [ABSTRACT FROM AUTHOR]

The primary tool currently used for a wind turbine preliminary design is the blade element momentum method, which lacks a detailed wake model and relies on an assumption of non-interacting streamtubes. These simplifications limit the designer's ability to tailor the blade shape to minimize the induced power loss of the rotor. Improved prediction of the induced velocity distribution on the blades can be achieved through the use of vortex-based models at a computational cost low enough for use in design processes requiring many iterations. This paper presents the implementation of a potential flow, lifting-surface methodology using elements of distributed vorticity. The use of such elements provides several advantages including higher resolution than filament-based methods, simulation of non-planar blade planforms, and avoids the need for empirical corrections. Because the wake has a strong influence on the flow at the rotor, the accurate prediction of its geometry is highly important for wind turbine analysis. To this end, a force-free relaxed-wake model is presented as well as less numerically intensive fixed-wake and hybrid-wake models. Comparison is made to the blade element momentum method and Goldstein's theoretical solution for the ideal lightly loaded rotor. [ABSTRACT FROM AUTHOR]

This study presents an innovative implicit–explicit time-stepping algorithm based on a first-order temporal accuracy method, addressing challenges in simulating all-regimes of fluid flows. The algorithm's primary focus is on mitigating stiffness inherent in the density-based "Roe" method, pivotal in finite volume approaches employing unstructured meshes. The objective is to comprehensively evaluate the method's efficiency and robustness, contrasting it with the explicit fourth-order Runge–Kutta method. This evaluation encompasses simulations across a broad spectrum of Mach numbers, including scenarios of incompressible and compressible flow. The scenarios investigated include the Sod Riemann problem to simulate compressible Euler equations, revealing the algorithm's versatility, and the low Mach number Riemann problem to analyze system stiffness in incompressible flow. Additionally, Navier–Stokes equations are employed to study viscous and unsteady flow patterns around stationary cylinders. The study scrutinizes two time-stepping algorithms, emphasizing accuracy, stability, and computational efficiency. The results demonstrate the implicit–explicit Runge–Kutta algorithm's superior accuracy in predicting flow discontinuities in compressible flow. This advantage arises from the semi-implicit nature of the equations, reducing numerical errors. The algorithm significantly enhances accuracy and stability for low Mach number Riemann problems, addressing increasing stiffness as Mach numbers decrease. Notably, the algorithm optimizes computational efficiency for both low Mach number Riemann problems and viscous flows around cylinders, reducing computational costs by 38%–68%. The investigation extends to a two dimensional hypersonic inviscid flow over cylinder and double Mach reflection case, showcasing the method's proficiency in capturing complex and hypersonic flow behavior. Overall, this research advances the understanding of time discretization techniques in computational fluid dynamics, offering an effective approach for handling a wide range of Mach numbers while improving accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The evolution of a separated boundary layer on the rough surface in the vicinity of a leading edge of a model airfoil is documented at varying angles of attack. Particle image velocimetry and hotwire data are analyzed to elucidate the flow feature, depicting the manifestation of the shear layer, its rollup, growth of perturbations, spectral response, and intermittency. For a hydrodynamically smooth surface, a laminar separation bubble often appears near the leading edge, where the shear layer becomes inviscidly unstable. Wall roughness amplifies the near-wall perturbations, resulting in earlier transition and reattachment. This leads to a reduction in bubble length and laminar shear layer length compared to the smooth surface at the corresponding angle of attack. Notably, despite the amplification of selective frequency, the inviscid instability is bypassed on the rough surface for varying angles of attack. Moreover, the linear stability analysis proves inadequate in predicting the most amplified frequency and the growth of disturbances. Furthermore, the universal intermittency curve formulated for the bypass transition is valid for the separation-induced transition, illustrating the significance of viscous effect. [ABSTRACT FROM AUTHOR]

In this present article, the use of a throttling device in the form of movable flap to study scramjet inlet unstart has been investigated numerically. The flap has been employed as an effort to simulate the rise in combustor pressure of the scramjet. Computational analysis for freestream Mach number and freestream pressure of 6.0 and 488 M respectively, have been performed by a two-dimensional compressible CFD in-house Finite volume solver for perfect gas. Convective fluxes have been evaluated using AUSM scheme. Inviscid flow has been assumed for all the simulations. Particular point of interest in these simulations is the application of Immersed Boundary Method along the wall boundaries, enabling the use of structured grid for complex geometries. The results demarcate the starting condition of the inlet based on the flap throttling values. Comparative results in the form of Mach number and pressure contours are presented for different flap positions. The use of Immersed Boundary Method has been successfully displayed by simulating a movable flap. [ABSTRACT FROM AUTHOR]

In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems. [ABSTRACT FROM AUTHOR]

We present here exact solutions to the equations of geophysical fluid dynamics that depict inviscid flows moving in the azimuthal direction on a circular path, around the globe, and which admit a velocity profile below the surface and along it. These features render this model suitable for the description of the Antarctic circumpolar current (ACC). The governing equations we work with–taken to be the Euler equations written in spherical coordinates–also incorporate forcing terms which are generally regarded as means that ensure the general balance of the ACC. Our approach allows for a variable density (depending on the depth and latitude) of discontinuous type which divides the water domain into two layers. Thus, the discontinuity gives rise to an interface. The velocity in both layers and the pressure in the lower layer are determined explicitly, while the pressure in the upper layer depends on the free surface and the interface. Functional analytical techniques render (uniquely) the surface and interface-defining functions in an implicit way. We conclude our discussion by deriving relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations. A regularity result concerning the interface is also derived. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations. However, in the flow around airfoils, the fluid is greatly accelerated near the leading edge, resulting in a local sharper transition, which is difficult to capture by PINNs. Therefore, PINNs are still rarely used to solve the flow around airfoils. In this study, we combine physical-informed neural networks with mesh transformation, using a neural network to learn the flow in the uniform computational space instead of physical space. Mesh transformation avoids the network from capturing the local sharper transition and learning flow with internal boundary (wall boundary). We successfully solve inviscid flow and provide an open-source subsonic flow solver for arbitrary airfoils. Our results show that the solver exhibits higher-order attributes, achieving nearly an order of magnitude error reduction over second-order finite volume method (FVM) on very sparse meshes. Limited by the learning ability and optimization difficulties of the neural network, the accuracy of this solver will not improve significantly with mesh refinement. Nevertheless, it achieves comparable accuracy and efficiency to second-order FVM on fine meshes. Finally, we highlight the significant advantage of the solver in solving parametric problems, as it can efficiently obtain solutions in the continuous parameter space about the angle of attack. [ABSTRACT FROM AUTHOR]

A comprehensive analysis of the unsteady flow dynamics past the 30P30N three-element high lift wing is performed by means of large eddy simulations at different angles of attack (α = 5°, 9°, and 23°) and at a Reynolds number of R e c = 750 000 (based on the nested chord). Results are compared with experimental and numerical investigations, showing a quantitatively good agreement and, thus, proving the reliability and accuracy of the present simulations. Within the slat and main coves, large recirculation bubbles are bounded by shear layers, where the onset of turbulence is triggered by Kelvin–Helmholtz instabilities. In the energy spectrum of the velocity fluctuations, the footprint of these instabilities is detected as a broadband peak; its frequency being moved toward lower values as the angle of attack increases. Kelvin–Helmholtz vortices roll-up and break down into small scales that eventually impinge into the slat and main coves lower surfaces. The slat impingement shows to be more prominent, and hence, larger velocity and pressure fluctuations are observed. The impingement strength diminishes with the angle of attack in both coves, while higher fluctuations are originated on the slat and main respective suction sides, leading to larger boundary layers. This is associated with the displacement of the stagnation point with the angle of attack. Another salient feature observed is the laminar-to-turbulent flow transition in the main and flap leading edges although the average location of this transition seems to not be affected by the angle of attack. Tollmien–Schlichting instabilities precede this transition, with the disturbances amplified by the inviscid mode at low angles of attack, while at α = 23 ° , the local Reynolds number on the main suction side is incremented and the viscous mode becomes important. The analysis shows that the turbulent wake formed at the trailing edge of all elements dominates the dynamics downstream. This is especially true at the higher angle of attack, where a large region of velocity deficit above the flap is observed, thus indicating the onset of stall conditions. [ABSTRACT FROM AUTHOR]

The vast majority of reduced‐order models (ROMs) first obtain a low dimensional representation of the problem from high‐dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately, convection‐dominated problems generally have a slowly decaying Kolmogorov n$$ n $$‐width, which makes obtaining an accurate ROM built solely from training data very challenging. The accuracy of a ROM can be improved through enrichment with HDM solutions; however, due to the large computational expense of HDM evaluations for complex problems, they can only be used parsimoniously to obtain relevant computational savings. In this work, we exploit the local spatial coherence often exhibited by these problems to derive an accurate, cost‐efficient approach that repeatedly combines HDM and ROM evaluations without a separate training phase. Our approach obtains solutions at a given time step by either fully solving the HDM or by combining partial HDM and ROM solves. A dynamic sampling procedure identifies regions that require the HDM solution for global accuracy and the reminder of the flow is reconstructed using the ROM. Moreover, solutions combining both HDM and ROM solves use spatial filtering to eliminate potential spurious oscillations that may develop. We test the proposed method on inviscid compressible flow problems and demonstrate speedups up to a factor of five. [ABSTRACT FROM AUTHOR]

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This paper is concerned with the sonic-supersonic structures for the two-dimensional steady compressible inviscid multiphase flow equations. We construct a local classical supersonic solution near a given smooth sonic curve. This problem is originated from the transonic channel multiphase flows, which are one kind of the most important problems in mathematical fluid dynamics. In order to overcome the difficulties caused by the parabolic degeneracy near sonic and the multivariable dependence of pressure, we adopt the mixed variables of the pressure and angle functions and derive the characteristic decompositions of these quantities. In terms of the angle coordinate system, the multiphase flow equations can be transformed into a new degenerate hyperbolic system with an explicit singularity-regularity structure. We verify the convergence of the iterative sequence generated by the new system and then return the solution to the original physical variables. As a by-product, we obtain the existence of sonic-supersonic solutions for the steady full Euler equations with non-polytropic gases. [ABSTRACT FROM AUTHOR]

Surface quasi-geostrophy (SQG) describes the two-dimensional active transport of a temperature field in a strongly stratified and rotating environment. Besides its relevance to geophysics, SQG bears formal resemblance with various flows of interest for turbulence studies, from passive scalar and Burgers to incompressible fluids in two and three dimensions. This analogy is here substantiated by considering the turbulent SQG regime emerging from deterministic and smooth initial data prescribed by the superposition of a few Fourier modes. While still unsettled in the inviscid case, the initial value problem is known to be mathematically well-posed when regularised by a small viscosity. In practice, numerics reveal that in the presence of viscosity, a turbulent regime appears in finite time, which features three of the distinctive anomalies usually observed in three-dimensional developed turbulence: (i) dissipative anomaly, (ii) multifractal scaling, and (iii) super-diffusive separation of fluid particles, both backward and forward in time. These three anomalies point towards three spontaneously broken symmetries in the vanishing viscosity limit: scale invariance, time reversal, and uniqueness of the Lagrangian flow, a fascinating phenomenon that Krzysztof Gawȩdzki dubbed spontaneous stochasticity. In the light of Gawȩdzki's work on the passive scalar problem, we argue that spontaneous stochasticity and irreversibility are intertwined in SQG and provide numerical evidence for this connection. Our numerics, though, reveal that the deterministic SQG setting only features a tempered version of spontaneous stochasticity, characterised in particular by non-universal statistics. [ABSTRACT FROM AUTHOR]

The cross-flow perpendicular to the inviscid main flow in the boundary layer has potential instability, causing the transition from laminar flow to turbulent flow. In order to explore the mechanism of cross-flow in the blade boundary layer on transition, this paper studies the rectangular cascade of a certain compressor stator blade. Large eddy simulation calculations and flow display experiments for six attack angles with end wall cascades were carried out. It is found that the disturbance is dominated by the two-dimensional Kelvin–Helmholtz (K–H) instability. The transition begins at the position where the separation bubble begins to fall off into a two-dimensional K–H vortex and is completed where the K–H vortex breaks. The closer to the blade root, the later the transition occurs and the smaller the total pressure loss. The cross-flow velocity develops alternately between positive and negative, showing severe instability with more than 4 inflection points. The study on variable angles of attack shows that there is a superposition of two mechanisms, namely, separation bubble transition and cross-flow transition, at an angle of attack from −4° to 10°. In summary, although the separation bubble transition is dominated by K–H vortices, the occurrence of cross-flow instability is closely related to the transition position. [ABSTRACT FROM AUTHOR]

A finite-volume solver is used to compute the cyclonic motion in a vortex chamber assuming steady, incompressible, and inviscid flow conditions. A parametric campaign enables us to characterize the computed swirl number over a wide range of properties. These include the tangential injection speed, number of injectors, injector port diameter, axial injection plane, and outlet fraction. In addition to the traditional swirl number, both geometric and modified swirl numbers are evaluated. In this process, the characteristic values of all three swirl numbers are determined over a wide range of design and inflow parameters. Overall, the geometric and modified swirl numbers are seen to follow similar trends, being different by a constant multiplier, with the former ranging between 0.9 and 410. We also find that increasing the injection speed has no bearing on the swirl numbers. In contrast, adding more injectors leads to a linear decrease in the swirl number, except for the case of a single injector. Although expanding the injector diameter initially results in larger swirl numbers, these begin to diminish after reaching an optimal diameter. Moreover, as the injection plane is displaced toward the headwall, the swirl number is reduced while remaining positive as long as a coherent cyclonic motion is present. As the injection plane is raised above the chamber midsection plane, the traditional swirl number turns negative. Varying the normalized outlet radius β is also found to affect the pressure and velocity distributions, with a central recirculation zone emerging beyond β = 0.707 and leading to vortex breakdown past β = 0.866. [ABSTRACT FROM AUTHOR]

The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V. Arnold, as the geodesic flow of the right-invariant L 2 -metric on the group of volume-preserving diffeomorphisms of the flow domain. In this paper we describe the common origin and symmetry of generalized flows, multiphase fluids (homogenized vortex sheets), and conventional vortex sheets: they all correspond to geodesics on certain groupoids of multiphase diffeomorphisms. Furthermore, we prove that all these problems are Hamiltonian with respect to a Poisson structure on a dual Lie algebroid, generalizing the Hamiltonian property of the Euler equation on a Lie algebra dual. [ABSTRACT FROM AUTHOR]

The flight of a migratory bird-like flapping-wing aircraft is characterized by a low Reynolds number and unsteadiness. The selection of airfoil profiles is critical to designing an efficient flapping-wing aircraft. To choose the suitable airfoil for various wing sections, it is necessary to calculate the aerodynamic forces of the unsteady two-dimensional airfoil with a Reynolds number in the range of 105. While accurate, calculating this by solving the Navier–Stokes equations is impractical for early design stages due to its high consumption of computing resources and time. The computational demands for extending it to 3D aerodynamic calculations are even more prohibitive. In this paper, a relatively simple method is proposed. The two-dimensional unsteady panel method is utilized to derive the inviscid flow field, the unsteady integral boundary layer method is utilized to solve the boundary layer viscous flow, and the eN transition model is adopted to predict the position of the transition. These models are coupled with the semi-inverse interaction method to solve the aerodynamics of the unsteady low-Reynolds-number two-dimensional airfoil. The unsteady aerodynamics of the symmetric and cambered airfoils at different wing sections are calculated respectively by the proposed method. Mechanism analysis of the calculation results is conducted, and a symmetrical airfoil or a slightly cambered airfoil is recommended for the wing tip, a moderately cambered airfoil is suggested for the outer-wing section, and a highly cambered airfoil is suggested for the inner-wing section. [ABSTRACT FROM AUTHOR]

The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/ h p stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/ h p framework. We introduce revised stabilization parameters, τ s u p g , with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ : the first is described with entropy variables, and the other is the Y Z β parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L 1 and L 2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod's shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries. [ABSTRACT FROM AUTHOR]

The problem of periodic oscillations of a dipole, specifically its strength, along the principal axes in a three-dimensional frozen channel is considered. The key points of the problem are taking into account the linear thickness of ice across the channel and ice porosity within Darcy's law. The fluid in the channel is inviscid and incompressible; the flow is potential. It is expected that the oscillations of a small radius dipole well approximate the oscillations of a small radius sphere at a sufficient depth of immersion of the dipole. It was found that during oscillations along the channel and vertical oscillations, waves are generated in the channel, propagating along the channel with a frequency equal to the frequency of dipole oscillations. These waves decay far from the dipole, and the rate of decay depends on the porosity coefficient. [ABSTRACT FROM AUTHOR]

This study introduces a two-dimensional thermoelastic model for a homogeneous isotropic half-space with double porosity underlying an inviscid liquid half-space featuring temperature variations. The model incorporates the three-phase lag (TPL) heat equation and reveals that in the solid half-space, four coupled longitudinal waves intertwine with one uncoupled transverse wave, while one mechanical wave ripples through the liquid half-space. The investigation highlights dispersion, attenuation, and other effects affected by the thermal properties and the presence of voids. Using plane wave solutions and boundary conditions at the interface, a concise expression for the frequency equation of the model has been derived. Furthermore, the magnitudes of the displacements in the solid half-space and liquid half-spaces, the temperature change, and the volume fractional fields at the interface have been precisely determined. In the graphical section, computer-simulated results of various wave profiles for magnesium crystal material have been generated for different heat conduction thermoelastic models. The study's implications span various fields, such as hydrology, engineering, ultrasonics, navigation, and electronics. [ABSTRACT FROM AUTHOR]

The motion of a disk in a Langmuir film bounding a liquid substrate is a classical hydrodynamic problem, dating back to Saffman (J. FluidMech., vol. 73, 1976, p. 593) who focused upon the singular problem of translation at large Boussinesq number, Bq » 1. A semianalytic solution of the dual integral equations governing the flow at arbitrary Bq was devised by Hughes et al. (J. Fluid Mech., vol. 110, 1981, p. 349).When degenerated to the inviscid-film limit Bq → 0, it produces the value 8 for the dimensionless translational drag, which is 50% larger than the classical 16/3-value corresponding to a free surface. While that enhancement has been attributed to surface incompressibility, the mathematical reasoning underlying the anomaly has never been fully elucidated. Here we address the inviscid limit Bq → 0 from the outset, revealing a singular mechanism where half of the drag is contributed by the surface pressure. We proceed beyond that limit, considering a nearly inviscid film. A naïve attempt to calculate the drag correction using the reciprocal theorem fails due to an edge singularity of the leading-order flow. We identify the formation of a boundary layer about the edge of the disk, where the flow is primarily in the azimuthal direction with surface and substrate stresses being asymptotically comparable. Utilising the reciprocal theorem in a fluid domain tailored to the asymptotic topology of the problem produces the drag correction (8 Bq/π)[ln(2/Bq) + γE + 1], γE being the Euler--Mascheroni constant. [ABSTRACT FROM AUTHOR]

For a plane flow of a vibrationally excited dissociating diatomic gas the necessary conditions of the existence of growing (neutral) inviscid perturbations, similar to the Rayleigh criterion of a "generalized" inflection point, are obtained. The corresponding formulas are presented for cases with a certain physical interpretation. In particular, the model of a vibrationally excited one-component gas is considered as the initial stage of thermal dissociation, as well as a widespread model with one dissociation-recombination reaction. The case of a binary molecular-atomic mixture with a vibrationally excited molecular component and a frozen gas-phase dissociation-recombination reaction is considered as an intermediate one. Comparative numerical calculations are carried out, which show, in particular, that under conditions of developed dissociation, the use of the criterion of the generalized inflection point does not take into account the specifics of the process. The wavenumbers and phase velocities of the I and II inviscid modes calculated on its basis may differ significantly from the results obtained with using the new necessary condition. [ABSTRACT FROM AUTHOR]

In R 2 , a symmetric blunt body W b is fixed by smoothing out the tip of a symmetric wedge W 0 with the half-wedge angle θ w ∈ (0 , π 2) . We first show that if a horizontal supersonic flow of uniform state moves toward W 0 with a Mach number M ∞ > 1 being sufficiently large depending on θ w , then the half-wedge angle θ w is less than the detachment angle so that there exist two shock solutions, a weak shock solution and a strong shock solution, with the shocks being straight and attached to the vertex of the wedge W 0 . Such shock solutions are given by a shock polar analysis, and they satisfy entropy conditions. The main goal of this work is to construct a detached shock solution of the steady Euler system for inviscid compressible irrotational flow in R 2 ∖ W b . Especially, we seek a shock solution with the far-field state given as the strong shock solution obtained from the shock polar analysis. Furthermore, we prove that the detached shock forms a convex curve around the blunt body W b if the Mach number of the incoming supersonic flow is sufficiently large, and if the boundary of W b is convex. [ABSTRACT FROM AUTHOR]

The accurate Riemann solutions in fully explicit forms are obtained for the one-dimensional inviscid, compressible, isothermal liquid–gas two-phase flow model of drift-flux type under the action of the unique external force of gravity for a pipeline placed on an inclined plane. It is also shown that the Riemann solution involves either a curved delta shock wave or the vacuum state for the pressureless case. Moreover, the asymptotic limits of Riemann solutions are investigated in detail by letting the pressure drop to zero, in which the formation of curved delta shock wave is obtained from the curved Riemann solution made up of backward shock wave, middle contact discontinuity and forward shock as well as the formation of vacuum state is also achieved from the curved Riemann solution consisting of backward rarefaction wave, middle contact discontinuity and forward rarefaction wave. In addition, some representative numerical results are offered to confirm the formation of delta shock wave and vacuum state. [ABSTRACT FROM AUTHOR]

In this article, we study the inviscid limit of the stochastic incompressible Navier–Stokes equations in three-dimensional space. We prove that a subsequence of weak martingale solutions of the stochastic incompressible Navier–Stokes equations converges strongly to a weak martingale solution of the stochastic incompressible Euler equations in the periodic domain under the well-accepted hypothesis, namely Kolmogorov hypothesis (K41). [ABSTRACT FROM AUTHOR]

The computational cost of iterative design methods has been a challenge in aerodynamics. In this research, the data-driven acceleration of an iterative inverse design method was implemented to reduce its computational cost. Although iterative design methods are robust, a lot of unwanted data is generated during their intermediate stages. Inverse design methods rely on correcting an initial geometry based on a given target parameter distribution. The generated data during the early iterations of the inverse design was incorporated into two deep-learning models to accelerate target geometry attainment. The deep learning models were used to recognize the correlation between the pressure distribution and corresponding geometry as well as the meaningful changes of geometry and pressure distribution toward their targets. The deep learning models were validated in viscous and inviscid compressible flows for various benchmark aerodynamics problems. In conclusion, between 70 to 80% computational cost decrease was observed for online uses of the machine learning module with the inverse design algorithm. This approach suggests incorporating machine learning techniques into design algorithms by exploiting the intermediate data for further improvement of them. We draw a new interpretation of learning dynamic changes through consecutive iterations instead of typical time-dependent problems in the use of LSTM network. [ABSTRACT FROM AUTHOR]