Search Results (83)

This study investigates natural convection of liquid metal in an annular enclosure with a square cross-section using three-dimensional numerical simulations. Liquid metals, with low Prandtl numbers, exhibit oscillatory transitions at lower Rayleigh numbers than conventional fluids. While previous studies focused on full-circle domains where steady or irregular flows were observed, this work examines the effect of angular partitions on flow dynamics. The results reveal that periodic three-dimensional oscillatory flows arise in domains with specific angular sizes, such as quarter circles, whereas full-circle domains produce irregular or steady flows. Angular wave numbers vary spatially and temporally during transitional growth. The emergence of half-symmetric oscillatory modes highlights the role of symmetry constraints imposed by the geometry and boundary conditions. These transitions are closely tied to symmetry breaking and mode selection. A linear stability perspective helps clarify the critical factors that determine the transition type. These findings underscore that angular segmentation and periodic boundary conditions are essential for sustaining regular oscillatory convection. This study contributes to the understanding of symmetry-governed convection transitions in low-Prandtl-number fluids and has potential implications for industrial processes, such as semiconductor crystal growth, where flow uniformity and thermal stability are crucial. Full article

In this paper, we propose the MUSWENO scheme, a novel mapped weighted essentially non-oscillatory (WENO) method that employs unequal-sized stencils, for solving nonlinear degenerate parabolic equations. The new mapping function and nonlinear weights are proposed to reduce the difference between the linear weights and nonlinear weights. Smaller numerical errors and fifth-order accuracy are obtained. Compared with traditional WENO schemes, this new scheme offers the advantage that linear weights can be any positive numbers on the condition that their summation is one, eliminating the need to handle cases with negative linear weights. Another advantage is that we can reconstruct a polynomial over the large stencil, while many classical high-order WENO reconstructions only reconstruct the values at the boundary points or discrete quadrature points. Extensive examples have verified the good representations of this scheme. 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 study investigates the organized flow structures and turbulence quantities in a transitional oscillatory boundary-layer flow over a smooth bed using a DNS model set up by the open-source framework Nektar++ (v5.2.0). The present model was validated against the results of a previous study involving a bypass transition mechanism in the intermittently turbulent regime. To trigger the initial perturbations, a roughness element was placed on the bed and removed at the very moment a two-dimensional vortex tube, caused by an inflectional-point shear-layer instability, was observed on it. Then, the turbulent spots where the flow experienced intense fluctuations in an otherwise laminar boundary layer were identified from the bed shear-stress distribution on the bed, which served as a reliable indicator of turbulence. These flow features emerged as the first sign of the initiation of turbulence. Several measurement points were selected to follow the bed shear-stress variations and to observe the spatial and temporal development of turbulent spots at a low-wave Reynolds number, $Re=1.8\times {10}^5$. Along with these observations, phase-resolved turbulence quantities were also investigated over successive half-cycles for the first time in the literature to understand how turbulence develops and spreads over the flow domain. The results show that the turbulence generated in the near-bed region becomes stronger in the deceleration stage due to the adverse pressure gradient and diffuses away from the bed during the subsequent phases of the developing oscillatory boundary-layer flow. The findings related to the turbulence quantities also indicate that the turbulence gradually evolves and spreads into the fluid domain in successive half-cycles. Full article

Various numerical techniques have been developed to address multiple problems in computational fluid dynamics (CFD). The finite volume method (FVM) is a numerical technique used for solving partial differential equations that represent conservation laws by dividing the domain into control volumes and ensuring flux balance at their boundaries. Its conservative characteristics and capability to work with both structured and unstructured grids make it suitable for addressing issues related to fluid flow, heat transfer, and diffusion. This article introduces an FVM for the linear advection and nonlinear Burgers’ equations through a fifth-order targeted essentially non-oscillatory (TENO5) scheme. Numerical experiments showcase the precision and effectiveness of TENO5, emphasizing its benefits for computational fluid dynamics (CFD) simulations. Full article

This study investigates wave-power extraction by an oscillating water column (OWC) device over a porous-to-rigid step bottom using linearized water-wave theory. The interaction between water waves and the OWC device is analyzed by solving the governing boundary-value problem with the eigenfunction expansion method (EEM) and the boundary element method (BEM). The study examines the effects of key parameters, including the porous effect parameter of the bottom, OWC chamber width, and barrier height, on the device’s efficiency. The results indicate that the porous effect parameter significantly influences OWC performance, affecting resonance characteristics and efficiency oscillations. A wider OWC chamber enhances oscillatory efficiency patterns, leading to multiple peaks of full and zero efficiency. The efficiency shifts towards lower wavenumbers with increasing step depth and barrier height but becomes independent of these parameters at higher wavenumbers. Additionally, incident angle plays a crucial role, decreasing efficiency at lower angles and exhibiting oscillatory behavior at higher angles. Furthermore, susceptance and conductance follow an oscillatory pattern concerning the gap between the porous bottom and the OWC chamber as well as chamber width. The porous effect parameter strongly modulates these oscillations. The findings provide new insights for enhancing OWC efficiency with complex bottom topography. Full article

The finite-difference time-domain (FDTD) method is a robust numerical approach for the three-dimensional forward modeling of airborne ground-penetrating radar responses of complex geological structures, particularly landslides. However, standard FDTD implementations encounter significant memory demands as aircraft altitude increases and when modeling high-permittivity subsurface media (e.g., water-saturated soils), often exceeding ordinary computational resources. Existing subgridding FDTD methods, tailored for simple localized target models, are also inadequate for simulating landslide models. To overcome these limitations, we thus propose a novel high-order FDTD-based subgridding algorithm that applies coarse grids to the air layer and fine grids to the subsurface medium, enabling the simulation of arbitrarily complex landslide models with significantly reduced memory consumption. This study achieves the first implementation of the high-order FDTD(2,4) method in both coarse- and fine-grid regions, which enables larger grid sizes in both regions. As a result, the proposed approach not only preserves high-order spatial accuracy but also achieves significant memory savings. To mitigate the challenges posed by higher-order difference stencils, we introduce a specialized grid configuration with an overlap zone between coarse and fine grids, supplemented by surrounding virtual nodes. The algorithm accommodates various grid refinement factors, ensuring adaptability to dielectric models with diverse permittivity values and structural complexities. By optimizing the grid refinement factor based on the subsurface medium’s maximum permittivity, simulations can be performed with minimal memory usage. Field updates within the overlapping region are followed by weighted corrections to ensure numerical stability, whereas simulations without these novel measures exhibit oscillatory artifacts. Wavefield snapshots reveal seamless transitions across grid boundaries without spurious artifacts. Numerical experiments on deposition-type landslide models and water-bearing media confirm the validity and stability of the proposed method. Notably, using the optimal grid refinement factor reduces memory consumption to less than 8% of the standard FDTD method for aquifer model simulations. Full article

The objective of this study is to develop a mathematical model capable of correctly displaying the dynamics of an individual’s cognitive activity under conditions of external information influence of different modalities. The adequacy of the model is verified by comparing the results of numerical analysis and experimental data. The mathematical basis of such a model is the apparatus of self-oscillating quantum mechanics. To describe algorithms for the processes of transmission, processing, and generation of information, the theory of information images/representations is used. Methods. This article provides a brief description of the proposed theory. The cognitive activity of an individual is represented mathematically as a one-dimensional potential hole with finite walls of different sizes. The internal potential barrier in this model can model the boundary between consciousness and subconsciousness. The authors developed a parameterization of the systems under study taking into account the proposed theory. Next, a mathematical model was developed based on the apparatus of self-oscillatory quantum mechanics. The authors formulated an equation that describes the function of the state of an information image in the process of human cognitive activity. Computer modeling of various variations of information impact was carried out. The authors also conducted a specially designed experiment. Conclusions. The authors have identified characteristic patterns of such processes and shown the oscillating nature of changes in the state function of information images and the appearance of characteristic threshold effects. A comparison of the obtained model and experimental data showed the adequacy of the developed tool (the coincidence of the general dynamics and characteristic patterns was shown). Full article

Tidal currents are a crucial oceanic process with significant implications for marine engineering and the sustainable use of coastal and marine resources. This paper presents the development of a finite element numerical model to simulate tidal currents. The model was mathematically formulated using the shallow water equations, which are applicable to fluid dynamics where the horizontal scale is significantly larger than the vertical scale. The finite element method was employed to discretize and solve the equations, with the bottom slope source term incorporated into the pressure equation to ensure numerical consistency. Furthermore, characteristic line theory was applied to derive the relationship between boundary tidal levels and current velocities to satisfy boundary compatibility conditions. The model was initially applied to the Qiongzhou Strait, and the results demonstrated good agreement with observed data. Subsequently, the model was implemented at Naozhou Island and its adjacent waters. The results revealed that the tidal currents around Naozhou Island exhibit oscillatory flow patterns, with the flow direction near Donghai Island oriented northeast–southwest (NE-SW) and the flow direction near Leizhou Bay oriented northwest–southeast (NW-SE). This study provides a hydrodynamic basis for marine engineering projects and the sustainable utilization of marine resources in the Naozhou Island area. Full article

The current study investigates the performance of implicit Large Eddy Simulation (iLES) incorporating an unstructured third-order Weighted Essentially Non-Oscillatory (WENO) reconstruction method, alongside conventional Large Eddy Simulation (LES) using the Wall-Adapting Local Eddy Viscosity (WALE) model, for wall-bounded flows. Specifically, iLES is applied to the flow around a NACA0012 airfoil at a Reynolds number which involves key flow phenomena such as laminar separation, transition to turbulence, and flow reattachment. Simulations are conducted using the open-source computational fluid dynamics package OpenFOAM, with a second-order implicit Euler scheme for time integration and the Pressure-Implicit Splitting Operator (PISO) algorithm for pressure–velocity coupling. The results are compared against direct numerical simulation (DNS) for the same flow conditions. Key metrics, including the pressure coefficient and reattached turbulent velocity profiles, show excellent agreement between the iLES and DNS reference results. However, both iLES and LES predict a thinner separation bubble in the transitional flow region then DNS. Notably, the iLES approach achieved a 35% reduction in mesh resolution relative to wall-resolving LES, and a 70% reduction relative to DNS, while maintaining satisfactory accuracy. The study also captures detailed instantaneous flow evolution on the airfoil’s upper surface, with evidence suggesting that three-dimensional disturbances arise from interactions between separating boundary layers near the trailing edge. Full article

The massive magnetite deposit from Takab (NW Iran) is hosted in amphibolite layers intercalated with the chemical and terrigenous sediments of the Takab BIF. A comprehensive textural and chemical study allowed three types of magnetite (Mt) to be distinguished. Mt1 forms large (≤1 mm) inhomogeneous grains surrounded and locally invaded by magnetite Mt2. Oscillatory zoning is present in Mt1 and Mt2. Mt3 forms bands aligned along fracture planes. Mt3 may contain hematite relicts and is porous in proximity to hematite. Mt1 shows variable and higher Si (up to 1.4 wt. %), Al, Ca, and Mg and lower Fe content (68 wt. %) than Mt2. Mt3 has the lowest Si (<0.3 wt. %) and highest Fe (71 wt. %) contents. The temperature of formation decreases from Mt1 (600 °C) to Mt2 (500–550 °C) and Mt3 (380–440 °C). Mt1 likely formed in a reducing Si-rich environment. The close spatial relationship, sharp compositional boundaries, similar crystallographic structure of Mt1 and Mt2, and porosity in Mt2 suggest a fluid-assisted coupled dissolution of Mt1 and precipitation of Mt2 (CDR process). Microfracturing allowed the penetration of oxidizing fluid and the formation of platy hematite bands. Mt3 (mushketovite) formed after hematite by interaction with a reducing lower temperature fluid through a redox transformation. Full article

The present study deals with the investigation of the oscillatory morphology of guided slow body MHD modes in inhomogeneous magnetic waveguides that appear in the solar photospheric plasmas in the forms of pores or sunspots. The eigenvalues and eigenfunctions related to these waves in an isothermal plasma are obtained numerically by solving a Sturm-Liouville problem with Dirichlet boundary conditions set at the boundary of the waveguide. Our results show that the inhomogeneities in density (pressure) and magnetic field have a strong influence on the morphology of waves, and higher-order more are sensitive to the presence of inhomogeneity. Our results suggest that he identification of modes just by a simple visual inspection can lead to a misinterpretation of the nature of modes. Full article

Libration and precession are different body forces that are ubiquitous in many rapidly rotating systems, particularly in geophysical and astrophysical flows. Libration is a modulation of the background rotation magnitude, whereas precession is a modulation of the background rotation direction. Assessing the consequences of these body forces in large-scale flows is challenging. The Ekman number, the ratio of the rotation time scale to the viscous time scale quantifying the rotation speed, is extremely small, leading to extremely thin and intense shear layers in the flows even when the amplitudes of the body forces are very small. We consider the consequences of libration and precession numerically in a geometrically simple container, a cube, which lends itself to very efficient, accurate, and robust numerical treatment, with the axis of rotation passing through opposite vertices, so that all walls of the cube are at oblique angles to the rotation axis. This results in the geometric focusing of inertial wavebeams reflecting off the walls, whereby the energy density of the wavebeams increases along with the magnitude of their wavevector. The nature of this focusing depends on the forcing frequency but not on the body force. In the inviscid setting, wavebeams form infinitesimally thin vortex sheets, and their energy density becomes unbounded upon focusing. We present linear inviscid ray tracing to set the scene for the focusing of wavebeams and then consider viscous problems at an Ekman number that is typical of current state-of-the-art laboratory experiments. We begin by considering the linear responses, which are comprised of focusing viscous shear layers, of which their details are mostly captured via ray tracing, and particular solutions accounting for the body forces. These have complicated spatio-temporal structures, which differ for libration and precession. Increasing the forcing amplitude from zero introduces nonlinear interactions, enhances the focusing effects via vortex tilting and stretching when the shear layers reflect at the walls, and also introduces temporal superharmonics and a mean flow. When the magnitude of the mean flow is within a few percent of the magnitude of the instantaneous flow, instabilities breaking the spatio-temporal symmetries set in. These are localized in the oscillatory boundary layers where the reflections are concentrated and introduce broadband dynamics in the boundary layers, with additional inertial wavebeams emitted into the interior. The details again depend on the specifics of the body forces. Full article

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid’s fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme. Full article

In this work, we investigate isothermal MHD motions of a large class of rate type fluids through a porous medium between two infinite horizontal parallel plates when a differential expression of the non-trivial shear stress is prescribed on the boundary. Exact expressions are provided for the dimensionless steady state velocities, shear stresses and Darcy’s resistances. Obtained solutions can be used to find the necessary time to touch the steady state or to bring to light certain characteristics of the fluid motion. Graphical representations showed the fluid moves slower in presence of a magnetic field or porous medium. In addition, contrary to our expectations, the volume flux across a plane orthogonal to the velocity vector per unit width of this plane is zero. Finally, based on a simple remark regarding the governing equations of velocity and shear stress for MHD motions of incompressible generalized Burgers’ fluids between infinite parallel plates, provided were the first exact solutions for MHD motions of these fluids when the two plates apply oscillatory or constant shear stresses to the fluid. This important remark offers the possibility to solve any isothermal MHD motion of these fluids between infinite parallel plates or over an infinite plate when the non-trivial shear stress is prescribed on the boundary. As an application, steady state solutions for MHD motions of same fluids have been developed when a differential expression of the fluid velocity is prescribed on the boundary. Full article