Numerical Method Research Articles

An analysis of the textural properties of activated carbons obtained from biomass via the LBET, NLDFT and QSDFT methods

This article presents the unique research results of the comprehensive analysis of the porous structure of activated carbons obtained from biomass waste materials from the wood industry during activation in an air atmosphere. The porous structure was analysed on the basis of nitrogen and argon adsorption isotherms via complementary multi-method analysis, i.e. the new numerical clustering-based adsorption analysis, the non-local density functional theory and the quenched solid density functional theory methods. The analytical results for the prepared activated carbons were compared with analogous results obtained for commercial activated carbon. On the basis of the conducted studies it has been determined that the new numerical clustering-based adsorption analysis method gives credible and valuable information on the textural properties of activated carbons which are in strict correlation and mutually complement with the results of the analysis with the use of the quenched solid density functional theory method. The research results obtained in this paper, it has also been shown that from waste materials of the wood industry, in a relatively cheap and cleaner production process, it is possible not only to obtain carbonaceous materials almost comparable to commercial activated carbon, but also to manage the waste in accordance with the principles of a closed-loop economy and sustainable development. The paper pays also attention to the often overlooked economic and ecological aspects, which should nevertheless be taken into account when comparing different adsorbents, rather than their textural properties alone.

Equation of motion of split conductor of anchor section at icing in wind flow

The relevance of the examined problem is connected with the necessity to develop measures to combat conductor galloping and the design of power transmission lines (ETL). The purpose of the research – to analyse statistical observation data on conductor galloping and apply a mathematical model to determine the parameters of galloping, to develop effective measures to combat conductor galloping and to improve the design of power lines. A sophisticated mathematical model was developed using Mathcad software to analyze conductor galloping in overhead power lines. This model, based on the equations of motion, predicts various galloping parameters under different conditions such as wind speed, span length, and initial mechanical stress. Time diagrams were constructed to represent linear and torsional motions, revealing correlations between amplitudes and frequencies. A comprehensive statistical analysis was performed on wire characteristics and split phase parameters to evaluate their impact on galloping patterns. Numerical methods, including the Runge-Kutta method, were employed to solve the equations and compute time-dependent behaviors. Results were visualized through graphs and diagrams to facilitate interpretation. The results revealed that conductor galloping occurs at wind speeds between 5 to 18 m/s, with significant occurrences at temperatures from 0°C to -10°C. The study identified that conductor galloping occurs within a wind velocity range of 5 to 13 m/s, predominantly with wind orientations between 30˚ and 90˚. The analysis showed that the frequency of galloping closely matches the natural oscillation frequency at low wind speeds but diverges with increasing wind speed and span length. These findings provide insights into the conditions under which conductor galloping is likely to occur and can inform design and operational strategies for overhead power lines.

A novel passive method to regulate the performance of photocatalytic-Trombe wall by horizontal fins

Constrained by the inadequate percentage of ultraviolet in solar irradiation and the low transmittance of photocatalytic layer, the purification and thermal performance of photocatalytic-Trombe wall (PC-TW) need to be improved urgently. To address this, a novel passive method to regulate PC-TW performance using horizontal fins was proposed. Aiming at this innovation, by numerical method, a three dimensional model was constructed to investigate the impact of relative fins height h* and spacing s*, and the mechanism about how these parameters affect the performance was also discussed. The results indicate that: under natural ventilation strategy, compared with PC-TW without fins, the thermal efficiency ηth, purification efficiency ηHCHO and total efficiency ηtotal are improved to some extent and there exist optimal fins parameters. However, horizontal fins will instead lower the efficiencies when h* exceeds 0.4. Under forced ventilation strategy, the increase in h* contributes to all efficiencies, making ηHCHO increasing monotonically, while ηth and ηtotal present a parabolic trend. In addition, the increase in s* lowers the improved efficiencies but can still keep them in a high range. For different ventilation strategies, considering the performance and manufacturing cost, the suggested h* and s* are 0.2 and 2.5. h* and s* respectively regulate the performance by affecting the size and amount of vortex between adjacent fins, and h* has a greater impact on the performance than s*. This study not only paves a new approach for performance regulation of PC-TW, but also provides theoretical basis for structural design and operation of PC-TW with fins.

Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation

In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the generalized hydrodynamic equations of Eu, and aims to describe rarefied flows. In the non-equilibrium regime, the NCCR equations are more reliable than the Navier-Stokes equations. And the NCCR equations have an advantage of efficiency over the discrete velocity methods and stochastic particle methods. However, the NCCR model is a complicated nonlinear system. Many assumptions have been used in the schemes for solving the NCCR equations. The corresponding numerical methods may be associated with unphysical solution and instability. At the same time, it is hard to analyze the physical accuracy and stability of NCCR model due to the uncertainties in the numerical discretization. In this study, a new numerical method for solving NCCR equations is proposed and used to analyze the properties of NCCR equations. More specifically, the nonlinear equations are converted into the solutions of an objective function of a single variable. Under this formulation, the multiple solutions of the NCCR system are identified and the criteria for picking up the physical solution are proposed. Therefore, a numerical scheme for solving NCCR equations is constructed. A series of flow problems in the near continuum and low transition regimes with a large variation of Mach numbers are conducted to validate the numerical performance of proposed method and the physical accuracy of NCCR model.

Investigation and Optimization of Wave Suppression Baffles in Automobile Integrated Water Tanks

The risk of liquid agitation in pump-driven tanks within integrated tanks has significantly escalated due to the growing demands for tank integration in new-energy vehicles. In order to solve the problem of liquid sloshing in integrated tanks, this paper presents the design of a baffle structure aimed at reducing waves in integrated water tanks. The numerical simulation method of combining the level-set function with the volume of fluid (CLSVOF) has been employed, significantly enhancing the accuracy of numerical calculations related to a two-phase flow field inside an integrated tank. A comparison was made by analyzing different factors, notably baffle length (L), baffle depth (H), and baffle angle (θ), to investigate their influences in suppressing liquid agitation within the integrated water tank. Numerical computations were conducted utilizing design points acquired by the Latin hypercube sampling technique. The Kriging approximation modelling method was employed to hold down computing time. The Pareto solution was obtained by means of the non-dominated sorting genetic algorithm II, while the optimal solution set was evaluated and ranked using the multi-criteria decision-making algorithm (MCDM). The results show that increasing the baffle depth within a certain range can effectively suppress the wave height in the tank. When the baffle depth is increased to a certain value, the effect on wave-height suppression in the water tank is limited. When the baffle length and angle of the baffle exceed a certain value, it will also have the effect of suppressing the wave height in the tank. After comparing various factors of the baffle, it was ultimately found that the wave suppression effect is maximal when the length of the baffle is 13 millimeters, the depth of the baffle is 49 millimeters, and the angle of the baffle is -20 degrees. The main contribution of this study is the proposed wave-suppressing baffle structure, which provides new insights for the future structural design of integrated water tanks.

On the interplay between fluid flow characteristics and small particle deposition in turbulent wall bounded flows

This study investigates the transport and deposition of small particles (500 nm≤dp≤10 μm) in a fully developed turbulent channel flow, focusing on two fluid friction Reynolds numbers: Reτ=180 and Reτ=1000. Using the point particle–direct numerical simulation method under the assumption of one-way coupling, we study how fluid flow (carrier phase) characteristics influence particle deposition. Our findings suggest that changes in flow conditions can significantly alter the deposition behavior of particles with the same size and properties. Furthermore, we show for the first time that gravity has minimal impact on deposition dynamics only at high Reynolds numbers. This research enhances our understanding of small particle deposition and transport in turbulent flows at high Reynolds numbers, which is crucial for various industrial applications.

Viscoelastic study of cement and emulsified asphalt mortar under temperature variations based on a novel variable-order fractional Maxwell model

Cement and emulsified asphalt (CA) mortar is a critical viscoelastic component of ballastless track systems, exhibiting pronounced temperature sensitivity. However, accurately predicting the mechanical responses of CA mortar due to temperature fluctuations remains a challenge. This work proposes a novel variable-order fractional Maxwell (VOFM) model to investigate the viscoelastic properties of CA mortar under temperature variations. The VOFM model is numerically solved using a time-varying coefficient ladder (TVL) model. The VOFM model is validated by comparing with both numerical integration methods and experimental data. The basic properties of the VOFM model, the viscoelastic responses of CA mortar under varying temperatures and alternating stress are systematically investigated. The results show that the mechanical properties of VOFM model agree with the FM model when time-dependent parameters of the VOFM model correspond to that of the FM model. Moreover, high temperatures have a promoting effect on the deformation of CA mortar under both alternating and constant stress conditions. The peak amplitude of CA mortar strain under practical varying temperature and stress loading correlates with the trend of temperature changes.

The Role of Marine Energy Production in The Development of Urban Infrastructure with Tidal Power Plants

Marine structures, designed and built to develop urban infrastructure, play a very important role in improving access to marine resources, protecting beaches, and facilitating urban and marine communications. These structures can be influential in different parts of urban development. This article, marine energy production facilities with a focus on tidal power plants, which include types of tidal power plants, how they work, the effect of power plants on urban development, design and construction, advantages and challenges, and their comparison. Together with each other. Also, the contribution of each of the tidal power plants in marine energy production facilities is shown to provide a better understanding of the users of this article. These types of structures in addition to economic development and infrastructure improvement Transportation also help to protect the environment and the sustainable use of natural resources, which is why familiarizing and investigating these types of structures and the role they play in the development of urban infrastructure is of particular importance and needs Further investigations using numerical modelling and laboratory methods will be necessary to achieve accurate and reliable engineering results

Upwind block-centered multistep differences for semiconductor device problem with heat and magnetic influences

In this paper, a mathematical model of semiconductor device with two important factors is discussed. Heat and magnetic influences are considered together. Its numerical approximation is important in information science and other technological innovation fields. The major physical unknowns (the potential, electron concentration, hole concentration, and the heat) are defined by four nonlinear PDEs: an elliptic equation, two convection-diffusion equations and a heat conductor equation. A conservative block-centered method is used to approximate the elliptic equation. The derivatives to time t, ∂∂t(⋅), are discretized by multistep differences for improving the computational accuracy. The diffusions and convection terms are treated by block-centered differences and upwind approximations, respectively. This composite numerical method is suitable for this nonlinear system. Firstly, numerical dispersion and nonphysical oscillations are avoided. Secondly, the unknowns and their adjoint vectors are obtained simultaneously. Thirdly, the law of conservation is preserved. An error estimates is derived. Finally, simple examples are given for showing the efficiency and accuracy.

Conservative wormholes in generalized [formula omitted]- function

We present an exhaustive study of wormhole configurations in κ(R,T) gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a constant redshift function that leads to a wormhole (WH) which is asymptotically non-flat. The remaining solutions were explored in two cases. Firstly, assuming a linear equation of state p(r)=ωρ(r) along with different forms of κ(R,T)-function. This proved enough to derive a shape function of the form b(r)=r0(r0r)1/ω. Secondly, by assuming specific choices of the shape function consistent with the wormhole configuration requirements. All the solutions fulfill flare-out condition, asymptotically flat and supported by phantom energy. Further, the embedding surface and its revolution has been generated using numerical method to see how the length of the throat is affected of the coupling parameters through κ(R,T) function. At the end, we have also calculated the average null energy condition, which is satisfied by all the WH models signifying minimum exotic matter is required to open the WH throats.

Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networks

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods like PINNs rely on auto differentiation and sampling collocation points, leading to a lack of interpretability and lower accuracy than traditional numerical methods. As a result, we propose a fully unsupervised approach, requiring no training data, to estimate finite difference solutions for PDEs directly via small linear convolutional neural networks. Our proposed approach uses substantially fewer parameters than similar finite difference-based approaches while also demonstrating comparable accuracy to the true solution for several selected elliptic and parabolic problems compared to the finite difference method.

Incorporating numerical method for analyzing the conduction heat transfer during solidification loading nanoparticles

Incorporating numerical method for analyzing the conduction heat transfer during solidification loading nanoparticles

Numerical Modeling of Two-Phase Fluid Filtration for Carbonate Reservoir in Two-Dimensional Formulation

This work considers the isothermal process of incompressible viscous fluid filtration in an oil-saturated, fractured-porous reservoir. A study of the pressure and water saturation distribution process is carried out for a case in which a production well is put into operation. For this problem, i.e., a mathematical model in a two-dimensional formulation, a numerical method and a parallel algorithm are proposed. The mathematical model of two-phase filtration is written in accordance with the classical laws of continuum mechanics and Darcy’s law and also includes a function of fluid exchange between low-permeability pores and high-permeability natural fractures within the framework of the Warren–Root model. The numerical solution is based on the finite-difference method and a splitting scheme of physical processes and spatial coordinates. For a split system with respect to piezoconductivity, an implicit finite-difference scheme with fixed saturations is constructed, and with respect to saturation transfer, explicit and implicit difference schemes are constructed. For parallel implementation of the developed numerical approach, a method based on geometric parallelism is selected. Testing of the developed method is performed using the example of calculating liquid mass transfer for a wide range of parameters. To verify the model, the obtained calculated pressure curves are compared with field data recorded by a deep-well measuring device. The results allow for estimation of the distribution of reservoir pressure and water saturation depending on the permeability of the fracture set and the pore part. The obtained results allow for monitoring of well operations, reducing unexpected accident risks and optimizing the development system in order to increase oil production in fractured-porous reservoirs. Computational experiments confirm the efficiency of the developed numerical algorithm and its parallel implementation.

Reducing polynomial degree by one for inner-stage operators affects neither stability type nor accuracy order of the Runge–Kutta discontinuous Galerkin method

The Runge–Kutta (RK) discontinuous Galerkin (DG) method is a mainstream numerical algorithm for solving hyperbolic equations. In this paper, we use the linear advection equation in one and two dimensions as a model problem to prove the following results: For an arbitrarily high-order RKDG scheme in Butcher form, as long as we use the P k P^k approximation in the final stage, even if we drop the k k th-order polynomial modes and use the P k − 1 P^{k-1} approximation for the DG operators at all inner RK stages, the resulting numerical method still maintains the same type of stability and convergence rate as those of the original RKDG method. Numerical examples are provided to validate the analysis. The numerical method analyzed in this paper is a special case of the Class A RKDG method with stage-dependent polynomial spaces proposed by Chen, Sun, and Xing [arXiv preprint, arXiv:2402.15150, 2024]. Our analysis provides theoretical justifications for employing cost-effective and low-order spatial discretization at specific RK stages for developing more efficient DG schemes without affecting stability type and accuracy order of the original method.

Solution of Well-known Physical Problems with Fractional Conformable Derivative

This paper presents a new definition of fractional derivatives and integrals through the conformable derivative approach. This innovative framework offers a closer alignment with classical derivative concepts while providing a more practical and intuitive basis for fractional calculus. The new definition is applicable in two primary ranges: 0 ≤ α < 1 and n − 1 ≤ α < n, where n is a positive integer. It is shown that when α = 1, this definition corresponds precisely to the classical first-order derivative. Key benefits of this approach include its improved consistency with traditional calculus and greater computational ease, making it a useful tool for both theoretical research and practical applications. By integrating fractional calculus with conventional derivative ideas, this definition simplifies the analysis and interpretation of fractional differential equations and their solutions. Additionally, we examine the definition’s effects on stability and convergence in numerical methods and provide examples demonstrating its effectiveness and applicability.

Discontinuous galerkin method of the first order parabolic differential equation

The objective of this paper is to propose a modest numerical error analysis by applying DG finite element method for the parabolic differential equation. The DG method is an imperative numerical method with much mass compensation and more flexible meshing than other numerical methods. The DG method starts by discretizing the domain into a set of non-overlapping elements. This study gives a general introduction and discuss about the discontinuous Galerkin Method of first order parabolic problem. The parabolic problem satisfies the condition of the existence and uniqueness of DG solution. The main goal of this study is to theoretically explore the convergence of the solution of the above methods and show the validity of the results.

Physical properties of Korean normal aortic valves based on fluid–structure interactions

Recently, numerical methods such as computational fluid dynamics (CFD), have been widely used in heart valve research. The CFD approach has fewer restrictions compared to clinical and experimental methods as it involves interpretations through computer calculations, and it can be used to predict and analyze fluids. For valve numerical analysis using CFD, the mechanical properties of the valve must be defined based on the physical properties. However, most of the existing heart valve numerical analysis studies have been conducted for westerners, and only a few studies on the same topic have focused on Asians. Thus, in this paper, we aim to determine the physical property parameters suitable for defining the mechanical properties of the normal aortic valves of Koreans over time. In this study, we used a fluid−structure interaction technique for the valve simulation and applied three representative valve characteristics presented in previous aortic valve simulation studies. Herein, the valve patency rates in case of simulation and multidetector computed tomography images were compared and analyzed through statistical techniques. Our results revealed that the physical properties, such as density (1050 kg/m3), Young’s modulus (2 MPa), and Poisson’s ratio (0.3), are like those of the Korean aortic valve over time. If hemodynamic evaluation of the Korean aortic valve is performed through simulation using these conditions, it can be effective in identifying the factors of heart valve disease.

Harvesting strategies in ecological systems: Evaluating their efficiency in infection dominance

In population biology, the interplay between prey and predators in the presence of infection can give rise to complex dynamics. On the flip side, implementing harvesting is an infection control measure. In the present work, we use the dynamical system theory to discuss the dynamics of the harvested prey–predator system in the presence of infection in prey species. Detailed mathematical and numerical evaluations have been presented to discuss the susceptible‐free state, infection‐free state, predator‐free state, species coexistence, stability, and occurrence of various bifurcations (saddle‐node, transcritical, and Hopf bifurcation). The study reveals the impact of harvesting parameters on the dynamics. Interestingly, we observe that an infection‐free state could be achieved by varying the harvesting parameter under all three harvesting schemes (linear, quadratic, and nonlinear). Moreover, with the help of reproduction number, we claim that linear harvesting is more effective in controlling the infection than quadratic and nonlinear harvesting provided the half‐saturation constant for nonlinear harvesting is greater than a threshold value ; otherwise, nonlinear harvesting is more effective. Also, the system can support more susceptible prey in the presence of harvesting. The present theoretical study suggests different threshold values of implemented harvesting to control the disease.

Corrosion mechanisms of plasma sprayed porous coatings of Ni80Cr20 and alloy C-276 investigated by numerical and experimental method

Abstract: In this study, the corrosion performance of Ni80Cr20 and alloy C-276 (UNS N10276) coatings on 7075 aluminum alloy substrates was evaluated using a variety of performance characterization tests. Significant amounts of nickel oxide were found in the corrosion products of the two coatings that were stripped, with molybdenum in the two coatings that were not stripped effectively slowing down the corrosion rate. Both coatings selectively corrode Cr, where it is worth noting that the preferential corrosion of W elements in alloy C-276 has a positive effect on its surface protection. It is not only the amount of molybdenum content, but also the influence of the W element that leads to better corrosion resistance of alloy C-276 coating than Ni80Cr20 alloy coating. The coating spraying process due to process parameters and its own nature, etc. has caused different sizes of pores, while these pores in the corrosion process will have a certain degree of influence on the corrosion process. The size of the pore defects for the coating transverse corrosion effect was more significant, and small pore defects accelerated the corrosion process. The number of pore defects had a more significant effect on the longitudinal corrosion of the coating, and multiple pore defects slowed the corrosion process.

A Multi-Spatial Scale Ocean Sound Speed Prediction Method Based on Deep Learning

As sound speed is a fundamental parameter of ocean acoustic characteristics, its prediction is a central focus of underwater acoustics research. Traditional numerical and statistical forecasting methods often exhibit suboptimal performance under complex conditions, whereas deep learning approaches demonstrate promising results. However, these methodologies fall short in adequately addressing multi-spatial coupling effects and spatiotemporal weighting, particularly in scenarios characterized by limited data availability. To investigate the interactions across multiple spatial scales and to achieve accurate predictions, we propose the STA-ConvLSTM framework that integrates spatiotemporal attention mechanisms with convolutional long short-term memory neural networks (ConvLSTM). The core concept involves accounting for the coupling effects among various spatial scales while extracting temporal and spatial information from the data and assigning appropriate weights to different spatiotemporal entities. Furthermore, we introduce an interpolation method for ocean temperature and salinity data based on the KNN algorithm to enhance dataset resolution. Experimental results indicate that STA-ConvLSTM provides precise predictions of sound speed. Specifically, relative to the measured data, it achieved a root mean square error (RMSE) of approximately 0.57 m/s and a mean absolute error (MAE) of about 0.29 m/s. Additionally, when compared to single-dimensional spatial analysis, incorporating multi-spatial scale considerations yielded superior predictive performance.