Search Results (834)

The present paper treats the problem of steady laminar MHD flow of an incompressible viscous fluid for mixed convection stagnation-point flow over a vertical stretching sheet in the presence of an externally magnetic field. By means of the Optimal Auxiliary Functions Method (OAFM), the resulting nonlinear ODEs are semi-analytically solved. The impact of various physical parameters, such as the velocity ratio parameter A, the Prandtl number $Pr$, and the Hartmann number $Ha$, on the behavior of velocity and temperature profiles is analyzed. Both assisting ($\lambda >0$) and opposing ($\lambda <0$) flows are considered. The influence of these parameters is tabulated and graphically presented. The originality of this work lies in the development of effective semi-analytical solutions and in the excellent agreement between these solutions and the corresponding numerical solutions. This highlights the accuracy of the proposed method applied to steady laminar MHD flow. A comparative analysis underlines the advantages of the OAFM compared to the iterative method. The obtained results confirm that the OAFM represents a competitive mathematical tool to explore a large class of nonlinear problems with applications in engineering. Full article

We derive one-dimensional (1D) analytical solutions for the transport equations of incompressible magnetohydrodynamic (MHD) turbulence, including the Elsässer energies and the correlation lengths. The solutions are suitable for an arbitrary given background convection speed and Alfvén speed profiles but require near equipartition of turbulent kinetic energy and magnetic field energy. These analytical solutions provide a simple tool to investigate the evolution of turbulence and resulting energetic particle diffusion coefficients in various space and astrophysical environments that possess simple geometry. Full article

A physics-informed neural network (PINN) framework is developed to model the large deformation and coupled electromechanical response of dielectric elastomer tubes for energy harvesting. The system integrates incompressible neo-Hookean elasticity with radial electric loading and compressible gas inflation, leading to nonlinear equilibrium equations with deformation-dependent boundary conditions. By embedding the governing equations and boundary conditions directly into its loss function, the PINN enables accurate, mesh-free solutions without requiring labeled data. It captures realistic pressure–volume interactions that are difficult to address analytically or through conventional numerical methods. The results show that internal volume increases by over 290% during inflation at higher reference pressures, with residual stretch after deflation reaching 9.6 times the undeformed volume. The axial force, initially tensile, becomes compressive at high voltages and pressures due to electromechanical loading and geometric constraints. Harvested energy increases strongly with pressure, while voltage contributes meaningfully only beyond a critical threshold. To ensure stable training across coupled stages, the network is optimized using the Optuna algorithm. Overall, the proposed framework offers a robust and flexible tool for predictive modeling and design of soft energy harvesters. Full article

In this study, pressure gradient effects on heat transfer from block-like electronic chips are investigated computationally. The pressure gradient is provided by the slope given to the upper plate and starts just before the first block. Tilt angles of −2°, 0°, 2°, 4° and 6° have been used. Air is used as the fluid, and it enters the duct at a constant speed with a uniform velocity profile. Calculations were made for Re numbers (Re = 6000, 9015, and 11,993) defined according to the channel height. For this purpose, conservation and SST k-ω turbulence model equations are solved by using ANSYS-Fluent 20.1 software for two-dimensional, incompressible, and turbulent flow conditions. Velocity, temperature, pressure, and turbulence kinetic energy distributions were obtained and compared for the considered slope angles. The effects of all changing conditions on heat transfer were discussed by calculating local and average Nusselt values, the reattachment lengths after the last block were calculated by plotting, and a comparison was made by plotting the pressure values on the block in the middle of the channel and at the top of the channel. Full article

We consider the lossless compression bound of any individual data sequence. Conceptually, its Kolmogorov complexity is such a bound yet uncomputable. According to Shannon’s source coding theorem, the average compression bound is $nH$, where n is the number of words and H is the entropy of an oracle probability distribution characterizing the data source. The quantity $nH\left({\widehat{\theta }}_n\right)$ obtained by plugging in the maximum likelihood estimate is an underestimate of the bound. Shtarkov showed that the normalized maximum likelihood (NML) distribution is optimal in a minimax sense for any parametric family. Fitting a data sequence—without any a priori distributional assumption—by a relevant exponential family, we apply the local asymptotic normality to show that the NML code length is $nH\left({\widehat{\theta }}_n\right)+{\displaystyle \frac{d}{2}}log{\displaystyle \frac{n}{2\pi }}+log{\int }_{\Theta }{\left|I\left(\theta \right)\right|}^{1/2}d\theta +o\left(1\right)$, where d is dictionary size, $\left|I\right(\theta \left)\right|$ is the determinant of the Fisher information matrix, and $\Theta$ is the parameter space. We demonstrate that sequentially predicting the optimal code length for the next word via a Bayesian mechanism leads to the mixture code whose length is given by $nH\left({\widehat{\theta }}_n\right)+{\displaystyle \frac{d}{2}}log{\displaystyle \frac{n}{2\pi }}+log{\displaystyle \frac{|I\left({\widehat{\theta }}_n\right){|}^{1/2}}{w\left({\widehat{\theta }}_n\right)}}+o\left(1\right)$, where $w\left(\theta \right)$ is a prior. The asymptotics apply to not only discrete symbols but also continuous data if the code length for the former is replaced by the description length for the latter. The analytical result is exemplified by calculating compression bounds of protein-encoding DNA sequences under different parsing models. Typically, compression is maximized when parsing aligns with amino acid codons, while pseudo-random sequences remain incompressible, as predicted by Kolmogorov complexity. Notably, the empirical bound becomes more accurate as the dictionary size increases. Full article

The numerical simulation of unsteady, high-Reynolds-number incompressible flows governed by the Navier–Stokes (NS) equations presents significant challenges in computational fluid dynamics, primarily concerning numerical stability and computational efficiency. Standard Galerkin finite element methods often suffer from non-physical oscillations in convection-dominated regimes, while the multiscale nature of these flows demands prohibitively high computational resources for uniformly refined meshes. This paper proposes an improved Galerkin framework that synergistically integrates a Variational Multiscale Stabilization (VMS) method with an adaptive mesh refinement (AMR) strategy to overcome these dual challenges. Based on the Ritz–Galerkin formulation with the stable Taylor–Hood ($P_2-P_1$) element, a VMS term is introduced, derived from a generalized $\theta$-scheme. This explicitly constructs a subgrid-scale model to effectively suppress numerical oscillations without introducing excessive artificial diffusion. To enhance computational efficiency, a novel a posteriori error estimator is developed based on dual residuals. This estimator provides the robust and accurate localization of numerical errors by dynamically weighting the momentum and continuity residuals within each element, as well as the flux jumps across element boundaries. This error indicator guides an AMR algorithm that combines longest-edge bisection with local Delaunay re-triangulation, ensuring optimal mesh adaptation to complex flow features such as boundary layers and vortices. Furthermore, the stability of the Taylor–Hood element, essential for stable velocity–pressure coupling, is preserved within this integrated framework. Numerical experiments are presented to verify the effectiveness of the proposed method, demonstrating its ability to achieve stable, high-fidelity solutions on adaptively refined grids with a substantial reduction in computational cost. Full article

This paper presents a three-dimensional (3D) free surface model to predict incompressible flow around a spur dike in a meandering channel bend, which is highly 3D due to the presence of curvature effects. The model solves the Reynolds-averaged Navier–Stokes (RANS) equations using an explicit projection method. The 3D grid system is built from a two-dimensional grid by adding dozens of horizontal layers in the vertical direction. Numerical simulations consider four test cases with different spur dike locations in the same meandering channel bend with the same Froude numbers as 0.22. Four turbulence models, the standard k-ε model, the k-ω model, the RNG k-ε model and a nonlinear k-ε model, are implemented in our three-dimensional free surface model. The performance of these turbulence models within the RANS framework is assessed. Comparisons between the model results and experimental data show that the nonlinear k-ε model behaves better than the three other models in general. Based on the results obtained by the nonlinear k-ε model, the highly 3D flow field downstream of the spur dike was revealed by presenting velocity vectors at representative cross-sections and streamlines at the surface and bottom layers. Meanwhile, the 3D characteristics of the downstream separation zone were also investigated. In addition, to highlight the advantage of the nonlinear turbulence model, comparisons of velocity vectors at representative cross-sections between the results obtained by the linear and nonlinear $k$-$\epsilon$ models are also presented. Full article

Wave deformation and sediment transport nearest the shoreside are among the main reasons for sand erosion and beach profile changes. In particular, identifying the areas of incident-wave breaking and longshore current generation parallel to the shoreline is important for understanding the morphological changes of coastal beaches. In this study, a two-phase incompressible flow model along with a sandy sloping topography was employed to investigate the wave deformation and longshore current generation areas in a circular wave basin model. The finite volume method (FVM) was implemented to discretize the governing equations in cylindrical coordinates, the volume-of-fluid method (VOF) was adopted to differentiate the air–water interfaces in the control cells, and the zonal embedded grid technique was employed for grid generation in the cylindrical computational domain. The water surface elevations and velocity profiles were measured in different wave conditions, and the measurements showed that the maximum water levels per wave were high and varied between cases, as well as between cross-sections in a single case. Additionally, the mean water levels were lower in the adjacent positions of the approximated wave-breaking zones. The wave-breaking positions varied between cross-sections in a single case, with the incident-wave height, mean water level, and wave-breaking position measurements indicating the influence of downstream flow variation in each cross-section on the sloping topography. The cross-shore velocity profiles became relatively stable over time, while the longshore velocity profiles predominantly moved in the alongshore direction, with smaller fluctuations, particularly during the same time period and in measurement positions near the wave-breaking zone. The computed velocity profiles also varied between cross-sections, and for the velocity profiles along the cross-shore and longshore directions nearest the wave-breaking areas where the downstream flow had minimal influence, it was presumed that there was longshore-current generation in the sloping topography nearest the shoreside. The computed results were compared with the experimental results and we observed similar characteristics for wave profiles in the same wave period case in both models. In the future, further investigations can be conducted using the presented circular wave basin model to investigate the oblique wave deformation and longshore current generation in different sloping and wave conditions. Full article

Modeling and simulation of aneurysm formation, growth, and rupture plays an essential role in a wide spectrum of application scenarios, ranging from risk stratification to stability prediction, and from clinical decision-making to treatment innovation. Unfortunately, it remains a non-trivial task due to the difficulties imposed by the complex and under-researched pathophysiological mechanisms behind the different development stages of various aneurysms. In this paper, we present a novel computational method for aneurysm simulation using smoothed particle hydrodynamics (SPH). Firstly, we consider blood in a vessel as a kind of incompressible fluid and model its flow dynamics using the SPH method; and then, to simulate aneurysm growth and rupture, the relationship between the aneurysm development and the properties of fluid particles is established by solving the motion control equation. In view of the prevalence of aneurysms in bifurcation vessels, we further enhance the capability of the model by introducing a solution for bifurcation aneurysms simulation according to Murray’s law. In addition, a CUDA parallel computing scheme is also designed to speed up the simulation process. To evaluate the performance of the proposed method, we conduct extensive experiments with different physical parameters associated with morphological characteristics of an aneurysm. The experimental results demonstrate the effectiveness and efficiency of proposed method in modeling and simulating aneurysm formation, growth, and rupture. Full article

The Navier equations are reformulated to be third-order partial differential equations. New anti-Cauchy-Riemann equations can express a general solution in 2D space for incompressible materials. Based on the third-order solutions in 3D space and the Boussinesq–Galerkin method, a third-order method of fundamental solutions (MFS) is developed. For the 3D Navier equation in linear elasticity, we present three new general solutions, which have appeared in the literature for the first time, to signify the theoretical contributions of the present paper. The first one is in terms of a biharmonic function and a harmonic function. The completeness of the proposed general solution is proven by using the solvability conditions of the equations obtained by equating the proposed general solution to the Boussinesq–Galerkin solution. The second general solution is expressed in terms of a harmonic vector, which is simpler than the Slobodianskii general solution, and the traditional MFS. The main achievement is that the general solution is complete, and the number of harmonic functions, three, is minimal. The third general solution is presented by a harmonic vector and a biharmonic vector, which are subjected to a constraint equation. We derive a specific solution by setting the two vectors in the third general solution as the vectorizations of a single harmonic potential. Hence, we have a simple approach to the Slobodianskii general solution. The applications of the new solutions are demonstrated. Owing to the minimality of the harmonic functions, the resulting bases generated from the new general solution are complete and linearly independent. Numerical instability can be avoided by using the new bases. To explore the efficiency and accuracy of the proposed MFS variant methods, some examples are tested. Full article

The numerical modelling of the melt flow in Si crystal growth plays an important role for improving the resistivity distribution of crystals grown in industrial processes. However, recent series of experiments have shown that the existing numerical model—a finite volume solver with incompressible laminar approximation of the melt flow—is not always accurate enough to describe the experimental results for 4″ crystals. To improve the simulation results, material properties have been revised. For some of them, such as the Marangoni or thermal expansion coefficients, the literature suggests different values varying by more than a factor of two. Therefore, simulations using different combinations of parameters were run to perform parameter calibration. The study demonstrated that the description of induced heat on the open melting front needs to be modified to obtain the shape of phase boundaries that provides the best agreement to the experiment. It was concluded that new values should be assigned to several material properties in the model, most importantly the Marangoni coefficient $M=-1.2·{10}^{-4}{\displaystyle \frac{\mathrm{N}}{\mathrm{m}·\mathrm{K}}}$, and that an appropriate turbulence model may help to describe the dopant transport more precisely. Full article

In this study, a computational thermo-fluid dynamics simulation of a wide-slot jet impingement heating process is performed. The present configuration consists of a turbulent incompressible air jet impinging orthogonally on an isothermal cold plate at a Reynolds number of around 11,000. The two-dimensional mean turbulent flow field is numerically predicted by solving Reynolds-averaged Navier–Stokes (RANS) equations, where the two-equation eddy viscosity k-$\omega$ model is utilized for turbulence closure. As the commonly used shear stress transport variant overpredicts heat transfer at the plate due to excessive turbulent diffusion, the recently developed generalized k-$\omega$ (GEKO) model is considered for the present analysis, where the primary model coefficients are suitably tuned. Through a comparative analysis of the various solutions against one another, in addition to reference experimental and numerical data, the effectiveness of the generalized procedure in predicting both the jet flow characteristics and the heat transfer at the plate is thoroughly evaluated, while determining the optimal set of model parameters. By improving accuracy within the RANS framework, the importance of model adaptability and parameter tuning for this specific fluid engineering application is demonstrated. This study offers valuable insights for improving predictive capability in turbulent jet simulations with broad engineering implications, particularly for industrial heating or cooling systems relying on wide-slot jet impingement. Full article

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional to the area swept by the rotor blades. In this context, the dynamic loads typically observed in wind turbine towers include vibrations caused by rotating blades at the top of the tower, wind pressure, and earthquakes (less common). In offshore wind farms, wind turbine towers are also subjected to dynamic loads from waves and ocean currents. Vortex-induced vibration can be an undesirable phenomenon, as it may lead to significant adverse effects on wind turbine structures. This study presents a two-dimensional transient model for a rigid body anchored by a torsional spring subjected to a constant velocity flow. We applied a coupling of the Fourier pseudospectral method (FPM) and immersed boundary method (IBM), referred to in this study as IMERSPEC, for a two-dimensional, incompressible, and isothermal flow with constant properties—the FPM to solve the Navier–Stokes equations, and IBM to represent the geometries. Computational simulations, solved at an aspect ratio of $\varphi =4.0$, were analyzed, considering Reynolds numbers ranging from $Re=150$ to Re = 1000 when the cylinder is stationary, and $Re=250$ when the cylinder is in motion. In addition to evaluating vortex shedding and Strouhal number, the study focuses on the characterization of space–time symmetry during the galloping response. The results show a spatial symmetry breaking in the flow patterns, while the oscillatory motion of the rigid body preserves temporal symmetry. The numerical accuracy suggested that the IMERSPEC methodology can effectively solve complex problems. Moreover, the proposed IMERSPEC approach demonstrates notable advantages over conventional techniques, particularly in terms of spectral accuracy, low numerical diffusion, and ease of implementation for moving boundaries. These features make the model especially efficient and suitable for capturing intricate fluid–structure interactions, offering a promising tool for analyzing wind turbine dynamics and other similar systems. Full article

This paper investigates the existence and uniqueness of local and global solutions to the incompressible three-dimensional Navier–Stokes equations within the framework of homogeneous Lei–Lin–Gevrey spaces ${\mathcal{X}}_{a,\gamma }^{\rho }({\mathbb{R}}^3)$, where $\rho \in [-1,0),a>0$, and $\gamma \in (0,1)$. These function spaces combine the critical scaling structure of the Lei–Lin spaces with the exponential regularity of Gevrey classes, thereby enabling a refined treatment of analytic regularity and frequency localization. The main results are obtained under the assumption of small initial data in the critical Lei–Lin space ${\mathcal{X}}^{\rho }({\mathbb{R}}^3)$, extending previous works and improving regularity thresholds. In particular, we establish that for suitable initial data, the Navier–Stokes system admits unique solutions globally in time. The influence of the Gevrey parameter $\gamma$ on the high-frequency behavior of solutions is also discussed. This work contributes to a deeper understanding of regularity and decay properties in critical and supercritical regimes. Full article

In view of the problems of slow heat storage process and uneven temperature distribution in the existing phase change heat accumulator, a new type of mesh fin heat accumulator was designed and developed which increased the contact area between the phase change material (PCM) and the fins, enhanced the apparent thermal conductivity of the PCM, improved the heat storage efficiency of the heat accumulator, blocked the PCM, improved the natural convection erosion of the PCM on the upper and lower parts of the heat accumulator, and melted the PCM in each area more evenly. Fluent15.0 was used to numerically simulate the heat storage process of the mesh fins heat accumulator with the finite volume method. The composite PCM prepared by adding 10% mass fraction of expanded graphite to paraffin wax was used as the heat storage material. A 2D, non-steady-state model, incompressible fluid, and the pressure-based solution method were selected. The energy model and the solidification and melting model based on the enthalpy method were used to simulate and calculate the phase change process of PCM. The PISO algorithm was used. The influences of the structural parameters of the mesh fins on the heat storage condition of the heat accumulator were investigated by numerical simulation. The results showed that with the increase in the radius R of the mesh fin, the heat storage time decreased first and then increased. With the increases in vertical fin thickness c, mesh fins thickness δ, and vertical fins number N, the heat storage time decreased. The optimal mesh fin structure parameters were R = 33.5 mm, c = 3 mm, δ = 3 mm, and N = 8, and the heat storage time was 8086 s, which is 47.8% shorter than that of the concentric tube heat accumulator. Otherwise, with the increases in vertical fin thickness c, mesh fins thickness δ, and vertical fins number N, the PCM volume decreased, which shortened PCM melting time. Full article