In this study, we present an optimized aerodynamic design of the widely recognized wind turbine profile NREL S809. The optimization is focused on achieving the best glide ratio while preserving the basic properties of the original profile. The optimization procedure was carried out using MATLAB software. The code developed is a combination of the genetic algorithm and the XFOIL software, whose main function is to calculate the lift and drag coefficients for angles attack between [Formula: see text] and [Formula: see text] for a Reynolds number of 106. This optimization employs a parametrization method defined by two analytical equations, which accurately define a set of 2D geometries ideally adapted for representing aerodynamic profiles. The aerodynamic performance of the new optimized profile OP-21 is reviewed against the original one. The new OP-21 achieved a 20.5% rise in the maximum lift and a 34.49% gain in the glide ratio. This validates the reliability of the optimization method employed in this work. In addition, a steady-state computational fluid dynamics analysis is performed on both the S809 and the OP-21 aerodynamic profiles, employing Reynolds-averaged Navier–Stokes equations coupled with the [Formula: see text]–[Formula: see text] SST turbulence model. The results are validated through comparison with experiments.

In this paper, we investigate a two-level multiscale finite element method for the nonlinear Allen–Cahn equation. The core idea of the proposed two-level scheme is first to solve the nonlinear Allen–Cahn equation on a coarse mesh by directly using a implicit multiscale finite element method, then to solve a linear problem on a fine grid. With reasonable stability conditions, it is shown that the proposed two-level scheme is energy stable. Furthermore, by defining a new projection operator, we deduce the optimal [Formula: see text] error estimates. Some numerical examples are presented to confirm the theoretical predictions and the efficiency of the proposed two-level scheme.

In this paper, an integration of the improved smoothed particle hydrodynamics (SPH) method with physics-informed neural networks (PINNs) is presented. The improved SPH method is employed to replace automatic differentiation in computing the differential operators of the loss function within the neural network framework, facilitating accelerated neural network training and reducing computational time. Additionally, tests are conducted on two-dimensional partial differential equations (PDEs) and systems of PDEs, with comparisons made to the results obtained using automatic differentiation-based physics-informed neural network (AD-PINN) and finite difference-based physics-informed neural network (FD-PINN). The findings demonstrate that the proposed method achieves faster computation speeds, particularly when dealing with larger network layer sizes and increased equation complexity. It maintains errors within the same order of magnitude while avoiding nonphysical solutions.

Parallel Manipulators (PMs) offer enhanced rigidity and better power-to-weight ratio through their closed kinematic chains and parallel structures. This makes PMs beneficial for applications requiring high payload capacity and performing at high speeds with precise positioning. PMs that are purely based on revolute joints, e.g., 6-DOF RSS (Revolute-Spherical-Spherical), have the potential to be used for compliant manipulation tasks apart from conventional tasks such as pick-and-place, packaging and assembly. The presence of backdrivability and compliance in the revolute joints of these PMs necessitates real-time mapping of the virtual model of the robot in a digital-twin environment using forward kinematics in case the robot fails to achieve the commanded pose. Researchers encounter significant challenges while solving Forward Kinematics Problems (FKP) in real-time with high accuracy. Hence, a generalized methodology for solving FKP in 6-DOF PMs with revolute joints is considered in this work. A Neural Network (NN) model is developed to predict the end-effector coordinates in real-time with high accuracy for the given joint angles. The novelty of this research lies in the seamless integration of the NN model with real-time hardware manipulation and virtual simulation via a digital twin, enabling both physical validation and virtual representation.

In this paper, we develop an energy-conserving time integration method for the co-rotational formulation force-based beam elements, aiming to achieve unconditional stability in nonlinear dynamic analysis. The proposed method incorporates material and geometric nonlinearities, with geometric nonlinearity addressed through the co-rotational technique. To ensure energy conservation in the time-discrete system, restoring force corrections are applied to the material stress and geometric configuration. It is proved that the method achieves energy conservation for discrete systems, thereby ensuring unconditional stability in nonlinear analyses. Also, the proposed method is second-order in accuracy. Finally, the effectiveness of the proposed method is verified through three numerical examples. In particular, the simulations demonstrate that the iterations converge well at both the global structural and element levels, and the computation effort can be significantly reduced by selecting appropriate initial correction parameters. While the restoring force correction procedure increases computational costs, the method’s capacity for larger time integration steps maintains total computational cost at acceptable levels.

This study presents bending, frequency, and buckling analyses of multilayer functionally graded graphene nanoplatelets (GPLs)-reinforced composite (FG GPLRC) plates. To address these problems, an edge-based smoothed MITC3[Formula: see text] plate element is developed based on Reddy’s third-order shear deformation theory (TSDT). The proposed element utilizes a model of seven displacement variables, independently approximated using [Formula: see text]-type shape functions, and enhanced by a cubic function related to a bubble node at the centroid of a three-node triangular element. To reduce discrepancies in the in-plane strains among nearby elements, the in-plane strain fields are averaged over domains formed by segments connecting common edge nodes to the bubble nodes of neighboring elements, referred to as the edge-based smoothed (ES) method. The [Formula: see text]-type presented element can be applied to both thin and thick plates, as transverse shear strains are re-interpolated at six tying points to ensure spatially isotropic behavior, in accordance with the mixed interpolation tensorial component (MITC3[Formula: see text]) technique. Compared to other approaches, the proposed ES-MITC3[Formula: see text] element demonstrates excellent performance and potential for bending, free vibration, and buckling analyses of multilayer FG GPLRC plates with diverse graphene nanoplatelet (GPL) distribution patterns in the polymer matrix, varying GPL weight fractions, length-to-thickness ratios, geometries, and boundary conditions. Parametric studies indicate that GPLs significantly enhance the stiffness of functionally graded plates.

This study uses numerical simulations to investigate the complex fluid dynamics around two adjacent rotating cylinders arranged side by side. The primary focus is on understanding the influence of Reynolds number (Re), rotational speed ([Formula: see text]), gap spacing ([Formula: see text]), and compressibility effects at different Mach numbers ([Formula: see text]). Simulations were performed using ANSYS Fluent 19.0, employing a finite volume-based solver and the shear stress transport (SST) [Formula: see text]–[Formula: see text] turbulence model. The numerical methodology is validated against experimental results for flow over a single rotating cylinder and numerical studies for the two-cylinder configuration. The analysis encompasses velocity magnitude contours, pressure distributions, vorticity patterns, and drag coefficients to elucidate the intricate flow interactions over two vertically placed side-by-side cylinders. Across Reynolds numbers ranging from 50 to 200, the flow exhibits distinct transitions from laminar to turbulent regimes, characterized by forming vortices and emerging flow separation zones. Higher Reynolds numbers generally lead to more turbulent and asymmetric flow patterns, increasing drag coefficients due to intensified wake formation and vortex shedding. The cylinders’ rotational speed significantly influences flow dynamics: lower speeds favor symmetric vortex formations, while higher speeds induce complex turbulent flows with enhanced vortex shedding. Outward rotation of the cylinders accelerates flow between them, increasing velocities and drag coefficients, whereas inward rotation reduces velocities and drag coefficients due to reduced flow interactions. Alterations in the gap spacing ([Formula: see text]) between cylinders reveal critical insights: smaller gaps intensify rotational effects, enhancing vortex shedding and increasing drag coefficients, whereas larger gaps promote stable flows with reduced vortex-shedding tendencies and lower drag coefficients. Compressibility effects at Mach numbers ranging from 0.2 to 0.8 amplify wake elongation, flow compression, and asymmetric vortex shedding, contributing to higher drag coefficients in transonic and supersonic regimes. This study advances understanding of fluid dynamics around cylindrical configurations, providing insights essential for optimizing engineering designs and performance across various applications. Future research directions may involve refining models, exploring additional parameters, and advancing predictive capabilities further to enhance practical insights into similar fluid flow phenomena.

In this paper, we study a numerical approximation of the Cahn–Hilliard–magnetohydrodynamic diffuse interface model. First, based on the idea of Lagrange multiplier, we introduce an auxiliary variable, and reformulate the Cahn–Hilliard–magnetohydrodynamic system. Second, we construct a linear, decoupled, and first-order semi-discrete scheme for this system by combining the pressure-projection method and some subtle implicit–explicit treatments for nonlinear coupling terms. We also prove that the proposed scheme is unconditionally energy stable. Furthermore, error estimates are provided through rigorous theoretical analysis. Finally, we validate the efficiency of the scheme through numerical simulations.

First, a Kurchatov-type derivative-free single-parameter method without memory for solving nonlinear systems is constructed, and the convergence order of the method is proved to be third order by using the higher-order Fréchet derivative. By using the Kurchatov-type difference operator to represent the variable parameter, the method without memory develops into two Kurchatov-type methods with memory, and the convergence order of the two methods with memory can reach 3.303 and 3.414, respectively. The new Kurchatov-type methods with and without memory use LU decomposition only once per iteration and require less computational cost when applying them to solve nonlinear systems. Second, in order to enlarge the application range of the novel Kurchatov-type method, the local convergence of the new Kurchatov-type method with and without memory is proved by using the [Formula: see text]-continuity condition of the first Fréchet derivative. In this way, the influence of higher-order derivatives on the proof of convergence is avoided, and the application range of the method is expanded. In addition, the radius of convergence around the solution is obtained by theoretical proof, and the uniqueness of the solution is proved. Finally, convergence radius is calculated by solving nonlinear systems with Kurchatov-type methods in numerical experiments, and the error and calculation time of different iteration methods are compared.