Difference Method Research Articles

A comprehensive review on the Dynamical behavior of heat and fluid flow mechanism: Thermal performance across different geometries

The prominent novelty of current review is to exhibit the fluctuating and oscillatory convective heat transfer properties along various geometries with magnetic force, variable density, Prandtl number, buoyancy force and magnetic Prandtl number effects. The significance of present work is to illustrate a comprehensive review on transient convective heat transfer. Transient convective heat transfer plays an essential role in various technological and environmental applications, including climate control, structure safety, engines, thermal control, computer heating and cooling, and energy safety. The literature primarily focuses on steady temperature and velocity domains, with few studies exploring time-varying fluid flow in forced, natural, or mixed convective mechanisms with different methods. In current review, justification of results was performed by using oscillating stokes conditions directly in partial differential models. The similarity variables and stream functions are used in literature but in current review, the primitive variable transformation is used with implicit form of finite difference method and Gaussian elimination technique through FORTRAN and Tecplot-360 programming tools. The governing model is reduced into steady, real and imaginary form to explore steady and oscillating convective heat transmission. Transient flows have gained significance due to their ability to achieve large oscillating convective heat transfer rates. Compared with steady movement, oscillating flows exhibit higher velocity variations along the heated surface. Periodic flow produces an improved transient surface heat transmission rate than steady flow. Predicting and controlling transients in thermal exchangers requires a concept of transient forced convection heat transport. Transient convective thermal transmission solutions are important for ensuring the effectiveness and reliability of electrical components, nuclear and thermal power stations, heat-generating engines, steam turbines, condensation systems, catalytic converters, heat shielding for spacecraft, electrical devices, internal combustion engines, air conditioning and refrigerator components, cooling networks for batteries, generators, and transformers. It is found that the frequency of convective heat transport enhances through periodic and oscillating stokes variables. It was depicted that the higher amplitude in convective heat transfer was displayed for each choice of magnetic force parameter around two angles π/4 and π of circular magnetized surface. It was depicted that the maximum transient convective heat transmission was reported along vertical angle π/2 with buoyancy force, Prandtl and magnetic Prandtl values.

RBF-based partition of unity methods for two-dimensional time-dependent PDEs: Numerical and theoretical aspects

This article discusses standard Radial Basis Function (RBF) partition of unity method and an enhanced version known as the direct RBF partition of unity method. We introduce the framework of these methods for the effective and accurate numerical analysis of certain two-dimensional time-dependent Partial Differential Equations (PDEs). Additionally, we conduct a convergence analysis of these methods and establish error bounds for local approximations. These error bounds are determined based on conditions associated with the eigenvalues of the Laplacian operator matrices generated by the proposed methods. To validate the accuracy and reliability of these approaches, we provide several numerical examples. We assess the consistency between theoretical and numerical results. The localized techniques introduced in this research demonstrate a significant reduction in computational cost and algorithmic complexity, achieved through the direct local procedure. Despite this computational advantage, both versions of the RBF partition of unity method exhibit a similar level of accuracy. Finally, we conduct a comparative analysis between the RBF partition of unity local methods and the RBF-generated finite differences method, offering valuable insights into the strengths and limitations of each approach.

A simplified SP3 NEM solver within a unified formulation for pin-by-pin core multi-group calculations

This study addresses the development and verification of a pin-by-pin core multigroup SP3 solver CTRP-Clouds that employs NEM (Nodal Expansion Method) and three simplified NEM methods within a unified formulation for simultaneously solving the coupling 0th and 2nd SP3 equations. In this work, the solver using this unified formulation does not only include the original NEM and its simplifications but also the EFEN (Exponential Function Expansion Nodal) method and FDM (Finite Difference Method) for the comprehensive evaluation. Also, the solver was accelerated using CMFD (Coarse Mesh Finite Difference) method and parallelized using OpenMP. The computational efficiency of different solution methods was investigated for the 2D KAIST benchmark problems and their modified one for considering 3D extension. The results showed the simplified NEM with flat leakage approximation gives acceptable accuracies of less than 1.2 % in RMS of pin-power discrepancies of all the cases with 1x1 mesh per pin-cell, with a reduction of 20 % computing time compared to the original NEM. Particularly, the calculation time of flat leakage NEM is comparable to EFEN while the pin-wise accuracy is better. Besides, the simplified NEM with 2nd-order flux expansion gives substantially improved accuracy in comparison with FDM within comparable computing time.

A Reduced-Dimension Weighted Explicit Finite Difference Method Based on the Proper Orthogonal Decomposition Technique for the Space-Fractional Diffusion Equation

A kind of reduced-dimension method based on a weighted explicit finite difference scheme and the proper orthogonal decomposition (POD) technique for diffusion equations with Riemann–Liouville fractional derivatives in space are discussed. The constructed approximation method written in matrix form can not only ensure a sufficient accuracy order but also reduce the degrees of freedom, decrease storage requirements, and accelerate the computation rate. Uniqueness, stabilization, and error estimation are demonstrated by matrix analysis. The procedural steps of the POD algorithm, which reduces dimensionality, are outlined. Numerical simulations to assess the viability and effectiveness of the reduced-dimension weighted explicit finite difference method are given. A comparison between the reduced-dimension method and the classical weighted explicit finite difference scheme is presented, including the error in the L2 norm, the accuracy order, and the CPU time.

Application of signal processing techniques for the spectroscopic analysis of dolutegravir and lamivudine: a comparative assessment and greenness appraisal

HIV treatment has greatly improved over the years, with the introduction of antiretroviral drugs that target the virus and suppress its replication. Dolutegravir and lamivudine are two such antiretroviral drugs that are commonly used in HIV treatment regimens. Herein, three spectrophotometric methods manipulating ratio spectra were developed for the simultaneous analysis of dolutegravir and lamivudine in their binary mixtures. These methods include mathematical processing stages like ratio difference method or signal processing approaches such as the first derivative of the ratio spectra, and continuous wavelet transform. The developed spectrophotometric methods exploit the characteristic spectral differences between dolutegravir and lamivudine in order to quantify them simultaneously. These methods have shown promising results in terms of sensitivity and selectivity as validated per the ICH guidelines. Moreover, these methods offer a straightforward and economical alternative to more intricate analytical methodologies like high-performance liquid chromatography. By incorporating the analytical eco-scale and AGREE for greenness evaluation of the proposed methods, we can further ensure that these techniques are effective and environmentally friendly, aligning with the principles of green chemistry. This evaluation will provide a comprehensive understanding of the environmental friendliness of these spectrophotometric methods in pharmaceutical analysis.

Lattice Boltzmann study of the effect of metal foam on bubble behavior and heat transfer performance in flow boiling

Metal foams with high porosity, light weight, and large specific surface area can significantly enhance heat transfer performance. In this study, the lattice Boltzmann method coupled with the finite difference method is used to investigate the flow boiling characteristics of metal foam surface. Focus is given on the effects of Reynolds number, gravitational acceleration, wall superheat, and metal foam thickness on heat transfer performance. Studies show that increasing the Reynolds number enhances convective heat transfer on the metal foam surface but inhibits bubble nucleation. Compared with a smooth surface, the metal foam takes full advantage of the fluid shear force induced by the high-velocity fluid in the channel-center region, thereby reducing the dependence on buoyancy for bubble detachment. As the wall superheat and metal foam thickness increase, the wake effect induced by bubble detachment is enhanced. Subsequently, bubble detachment is facilitated and the liquid supply is enhanced. These results provide theoretical and applied technical guidance for the structural design of novel metal foam surfaces.

Efficient cross-modality feature interaction for multispectral armored vehicle detection

Detecting armed vehicles from a UAV platform is challenging due to the complexity of ground environment. This paper presents a dual-stream multispectral armored vehicle detection method to tackle this problem. First, considering that there is a paucity of datasets containing multispectral armored vehicle images, a multispectral armored vehicle detection dataset is constructed for this study. The dataset consists of 5853 pairs of RGB and infrared images, featuring a total of 15,878 instances of armored vehicles. Then, a cross-modal feature interaction module is designed to enable efficient feature interaction between multispectral images. This module uses the cross-modal channel-wise feature difference method to model the channel differences between the two modal features and obtains the cross-modal channel difference matrix. The cross-modal channel difference matrix is then employed to extract the unique features of the two modal features, allowing for efficient cross-modal feature interaction by complementing each other's unique features. Experiment results demonstrate that the proposed model has excellent detection performance and is capable of coping with various challenges brought by complex ground environments.

Non-Similar Analysis of Mixed Convection Biomagnetic Boundary Layer Flow Over a Vertical Plate with Magnetization and Localized Heating/Cooling

Theoretical and numerical investigation of an applied magnetic field on mixed convection flow of a biofluid through a vertical plate using contained heating or cooling is observed in this study. The mathematical formulation is that of the full Biomagnetic Fluid Dynamics (BFD) model which deals with on the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) principle. In this work, the study is performed on a specific biofluid, viz. human blood. Assume that the magnetization very linearly with magnetic field strength, temperature dependency of dynamic viscosity and thermal conductivity is noticed. A system of non-linear equations with appropriate boundary condition is obtained by familiarizing suitable non-dimensional variables in the physical problem. For the numerical solution, we used finite difference method which is based on an efficient technique is applied in the problem. Computations for flow profiles, local skin friction coefficient and local heat transfer coefficient are performed with the magnetic parameter Mn, the viscosity/temperature parameter θr and the thermal/conductivity parameter S∗. The effect of the localized heating or cooling is examined. The computational results presented graphically and have been validated in an appropriate manner. The study reveals that the impact of a magnetic field for blood flow in arteries is found significantly. The results presented bear the promise of valuable applications in physiology, medicine and bioengineering.

Radiative flow of cross ternary hybrid nanofluid (MoS2,TiO2, Ag/CMC-water) in a Darcy Forchheimer porous medium over a stretching cylinder with entropy minimization

Stretching cylinders play a crucial role in the plastic and metal extrusion processes. This current investigation is to examine the Darcy Forchheimer flow of Carboxymethyl cellulose (CMC)/water-based tri-hybrid nanofluid through a stretching cylinder. A composite of ternary hybrid nanofluid containing MoS2, TiO2 and Ag with CMC-water-based fluid has been added to the Crossflow model. The equations regulating motion and the equation for entropy generation are both formulated using cylindrical coordinates. The governing partial differential equations (PDEs) equations have been transformed into an ordinary differential equations (ODEs) system using a similar scaling operation. Afterward, the BVP4c function employs the finite difference method and then implements the Lobatto IIIa formula. To fully understand how the flow behaves close to the cylinder's surface, the effects of these various factors on the number of entropy generation, Bejan number, the speed of the flow, the temperature and concentration distributions have been carefully studied. The result reveals that enhancing the values of Weissenberg number We and the porosity parameter declines the velocity profile. An increment in the curvature parameter β declines the velocity gradient and temperature distribution. In addition, enhancement in the radiation parameter escalates the entropy minimization and Bejan number. Furthermore, the impact of drag friction, heat, and mass are displayed in tabular form and elaborated suitably. The outcomes are authenticated with previously published literature for accuracy and authenticity.

Electro-Osmotic Flow and Mass Transfer through a Rough Microchannel with a Modulated Charged Surface.

In this paper, we investigate the electro-osmotic flow (EOF) and mass transfer of a Newtonian fluid propelled by a pressure gradient and alternating current (AC) electric field in a parallel microchannel with sinusoidal roughness and modulated charged surfaces. The two-wall roughness is described by in-phase or out-of-phase sine functions with a small amplitude δ. By employing the method of perturbation expansion, the semi-analytical solutions of the Poisson-Boltzmann (P-B) equation based on the Debye-Hückel approximation and the modified Navier-Stokes (N-S) equation are obtained. The numerical solution of the concentration equation is obtained by the finite difference method. The effects of sinusoidal roughness, modulated charged surface, and the AC electric field on the potential field, velocity field, and concentration field are discussed. Under the influence of the modulated charged surface and sinusoidal roughness, vortices are generated. The velocity oscillates due to the effect of the AC electric field. The results indicate that solute diffusion becomes enhanced when the oscillation Reynolds number is below a specific critical value, and it slows down when the oscillation Reynolds number exceeds this critical value.

Quantitative Assessment and Validation of Groundwater Pollution Risk in Southwest Karst Area

AbstractGroundwater pollution risk assessment is a useful tool for groundwater pollution prevention and control. However, it is difficult to accurately quantify groundwater flow and contaminant fluxes in karst areas and different types of karst areas have different hydrogeological characteristics. Therefore, the assessment of groundwater pollution risk in karst areas must use different assessment indicator systems. This study developed a new methodology that modified the vulnerability assessment model PLEIK, determined pollutant fluxes considering hydrogeological conditions, and revised parameter weights using the random forest method. The resulting PLEIKD-RF model was used to assess the risk of groundwater contamination in the southwestern karst region and its validity was verified. The results showed that the groundwater pollution risk in the region was low, with 65.64% of the low and relatively low risk areas located in the middle and high mountainous regions. 11.81% of the high and relatively high risk areas were sporadically located in the western and central regions, which were mainly controlled by the distribution of the pollution sources and the karst development. The accuracy of the results of groundwater pollution risk assessment in the study area was 71.87% as verified by the horizontal difference method. The results of the sensitivity analysis indicated that accurate, detailed, and representative data on the protective layer, surface water-groundwater interactions, and pollution source loads would improve the accuracy of groundwater pollution risk zoning. This assessment method provided a reference for similar assessments and the results provide a basis for the protection and management of groundwater resources in the region.

RBF–based IMEX finite difference schemes for pricing option under liquidity switching

In this work, we introduce two accurate and efficient finite difference methods based on radial basis functions (RBF–FD) for pricing European and American options under liquidity shocks. The problem is formulated as the semi-linear complementarity and PDE systems for American and European options, respectively. In the context of temporal semi-discretization, we provide two backward difference formulas of order one and two (BDF1 & BDF2). Furthermore, we discuss the stability and convergence properties of the proposed methods. For the American option, to solve the semi-linear system of complementarity problems (LCPs), we combine the RBF-FD approaches with an operator splitting (OS) method. To illustrate the efficiency and accuracy of the suggested methods, we provide numerical examples for both European and American call options and verify them with the existing work in the literature. In numerical discussion, we show the Greeks (Delta & Gamma) plots for the American options.

Predictions of the missing excited vector heavy–light mesons: the mass difference method

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Element-based finite volume method applied to autogenous bead-on-plate GTAW process using the enthalpy energy equation

The welding process is the most used technique for metal joining. Understanding the temperature variation along the welded part during the process can prevent the appearance of failures. The experimental investigation process is quite time-consuming and costly. Therefore, numerical simulation processes based on the finite difference method, finite element method, finite volume method, or meshless Element-Free Galerkin (EFG) methods are important tools to optimize the welding process. The main goal of the present study is to show the feasibility of the Element-based Finite-Volume Method (EbFVM) approach for actual engineering applications. To solve the unsteady 2D and 3D thermal energy equation using enthalpy as an independent variable, an in-house Fortran code has been developed based on the EbFVM approach in conjunction with unstructured and structured meshes. The numerical simulations, with four types of different heat sources, were performed for applications of real welding processes with variations in density and enthalpy as a function of temperature. The results are presented in terms of thermal cycles and temperature fields. Furthermore, the developed code was confronted against experimental works from the literature, simulated and lab-controlled experiments with AISI 409 ferritic workpieces, and exact analytical solutions with thermocouples fixed in different positions. In general, the numerical results from the current investigation are in close agreement with the results from the literature and the experimental results performed by the authors. The numerical results also highlighted the differences between the 2D and 3D models for thermal cycles near the bead weld.

Investigating the effect of using aluminum oxide nanofluid and twisted tapes with different twisted pitches on the heat transfer efficiency and using perceptron artificial neural networks in data prediction

This study investigates the effect of aluminum oxide nanofluid with 1% and 2% volume fractions (VFs) in four different tubes with identical bending and the uniform, low-high-low, low-high, and high-low-high longitudinal states with twist ratios of 0, 2 and 4. These tubes are affected by a constant thermal flux of 10000 W/m2 and Reynolds numbers of 2000-10000. For the numerical solution of these equations, the finite difference method on the basis of the control volume and the SIMPLEC algorithm and the K-ε-RNG method were applied for the turbulent flow modeling. The determined Nusselt number from the numerical methods were evaluated applying the perceptron neural network. The most optimal increase in the Nusselt number was in the twisted tube with twist ratio of 4 in the Reynolds number of 10,000 and VF of 1% and 2% nanofluid with increasing trend of length from low to high. The most optimal increase in Nusselt number compared to base fluid was about 25%. The sum of squared error and the relative error data obtained from the hyperbolic tangent function for the training and test data were 0.080-1.331 and 0.113-0.675, and from the sigmoid function for the training and test data were 0.093-0.392 and 0.097-0.147.

Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel

Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel

Comparison of Some Robust Methods of Difference Based Ridge Estimator in Semiparametric Regression Model

The semiparametric regression models have received a lot of attention from researchers recently because it combines parametric and nonparametric methods, it is one of the advanced topics in data analysis for various studies, which aims to find the best capabilities and a high level of efficiency. One of the most important semiparametric regression models is the partial linear regression model (PLM), which consists of a parametric component and a nonparametric component, for the purpose of estimating the parametric component, the difference method will be used to remove the nonparametric component. When the analysis hypotheses of the parametric component are not fulfilled, it will suffer from several problems, the most important of which is the problem of complete multicollinearity, besides the multicollinearity, there are also outliers in the data. In this research, the problems of multicollinearity and outliers of the semiparametric regression model were addressed, where simulation was used to generate data with different sample sizes and for different correlations and outlier ratios and for different methods such as [Difference Ridge based M robust with Nadaraya – Watson (DRMNW), Difference Ridge based S robust with Nadaraya – Watson (DRSNW), Difference Ridge based M robust with Smoothing spline (DRMSP), Difference Ridge based S robust with Smoothing spline (DRSSP)], the results showed that method Difference Ridge based M robust with Smoothing spline (DRMSP) is the best estimator.

A Comprehensive Review on the Dynamical Behavior of Heat and Fluid Flow Mechanism: Thermal Performance across Different Geometries

The prominent novelty of current review is to exhibit the fluctuating and oscillatory convective heat transfer properties along various geometries with magnetic force, variable density, Prandtl number, buoyancy force and magnetic Prandtl number effects. The significance of present work is to illustrate a comprehensive review on transient convective heat transfer. Transient convective heat transfer plays an essential role in various technological and environmental applications, including climate control, structure safety, engines, thermal control, computer heating and cooling, and energy safety. The literature primarily focuses on steady temperature and velocity domains, with few studies exploring time-varying fluid flow in forced, natural, or mixed convective mechanisms with different methods. In current review, justification of results was performed by using oscillating stokes conditions directly in partial differential models. The similarity variables and stream functions are used in literature but in current review, the primitive variable transformation is used with implicit form of finite difference method and Gaussian elimination technique through FORTRAN and Tecplot-360 programming tools. The governing model is reduced into steady, real and imaginary form to explore steady and oscillating convective heat transmission. Transient flows have gained significance due to their ability to achieve large oscillating convective heat transfer rates. Compared with steady movement, oscillating flows exhibit higher velocity variations along the heated surface. Periodic flow produces an improved transient surface heat transmission rate than steady flow. Predicting and controlling transients in thermal exchangers requires a concept of transient forced convection heat transport. Transient convective thermal transmission solutions are important for ensuring the effectiveness and reliability of electrical components, nuclear and thermal power stations, heat-generating engines, steam turbines, condensation systems, catalytic converters, heat shielding for spacecraft, electrical devices, internal combustion engines, air conditioning and refrigerator components, cooling networks for batteries, generators, and transformers. It is found that the frequency of convective heat transport enhances through periodic and oscillating stokes variables. It was depicted that the higher amplitude in convective heat transfer was displayed for each choice of magnetic force parameter around two angles π/4 and π of circular magnetized surface. It was depicted that the maximum transient convective heat transmission was reported along vertical angle π/2 with buoyancy force, Prandtl and magnetic Prandtl values.

3D reverse-time migration for pure P-wave in orthorhombic media

Compared with the transverse isotropic (TI) medium, the orthorhombic anisotropic medium has both horizontal and vertical symmetry axes and it can be approximated as a set of vertical fissures developed in a group of horizontal strata. Although the full-elastic orthorhombic anisotropic wave equation can accurately simulate seismic wave propagation in the underground media, a huge computational cost is required in seismic modeling, migration, and inversion. The conventional coupled pseudo-acoustic wave equations based on acoustic approximation can be used to significantly reduce the cost of calculation. However, these equations usually suffer from unwanted shear wave artifacts during wave propagation, and the presence of these artifacts can significantly degrade the imaging quality. To solve these problems, we derived a new pure P-wave equation for orthorhombic media that eliminates shear wave artifacts while compromising computational efficiency and accuracy. In addition, the derived equation involves pseudo-differential operators and it must be solved by 3D FFT algorithms. In order to reduce the number of 3D FFT, we utilized the finite difference and pseudo-spectral methods to conduct 3D forward modeling. Furthermore, we simplified the equation by using elliptic approximation and implemented 3D reverse-time migration (RTM). Forward modeling tests on several homogeneous and heterogeneous models confirm that the accuracy of the new equation is better than that of conventional methods. 3D RTM imaging tests on three-layer and SEG/EAGE 3D salt models confirm that the ORT media have better imaging quality.

Numerical treatment of singular ODEs using finite difference and collocation methods

Boundary value problems (BVPs) in ordinary differential equations (ODEs) with singularities arise in numerous mathematical models describing real-life phenomena in natural sciences and engineering. This motivates vivid research activities aiming to characterize the analytical properties of singular problems, to investigate convergence of the standard numerical methods when they are applied to simulate differential equation with singularities, and to provide software for their efficient numerical treatment. There are two well-known, high order numerical methods which we focus on in this paper, the finite difference schemes and the collocation methods. Those methods proved to be dependable and highly accurate in the context of regular differential equations, so the question arises how do they preform for singular problems. While, there is a strong evidence for the collocation schemes to be a robust method to solve singular systems in a stable and efficient way, finite difference schemes are still considered less suitable for this problem class.In this paper, we shall compare the performance of the code HOFiD_bvp based on the high order finite difference schemes and bvpsuite2.0 based on polynomial collocation, when the codes are applied to singular problems in ODEs. We are fully aware of the difficulties in a code comparison, so in this paper, we will try to only diagnose the potential improvements, we could address in the next update of the codes.