Difference Method Research Articles

Thermal recovery of heavy oil reservoirs: Modeling of flow and heat transfer characteristics of superheated steam in full-length concentric dual-tubing wells

Accurately predicting the flow and heat transfer characteristics of superheated steam (SHS) in the wellbore is essential for efficiently developing heavy oil reservoirs. However, few studies have examined SHS flow in full-length concentric dual-tubing wells (CDTWs). In this paper, firstly, based on fluid dynamics and thermodynamics theories, a mathematical model for SHS flow in vertical and horizontal wellbores is proposed. Then, this model is solved using a finite difference method for spatial discretization and an iterative technique. Finally, model verification, type curve analysis, and sensitivity analysis are conducted sequentially. The results indicate that SHS temperature and pressure are independent variables, and the effect of friction energy on temperature is greater than its impact on pressure. The injection rate has a critical value, and the critical injection rates of the main controlling factors affecting the pressure drop and temperature drop of SHS in the vertical tubing are different. When the injection rate is below the critical value, the gravitational force of the SHS helps maintain high enthalpy. The SHS should be transported to the well bottom as quickly as possible. To enhance the uniform heating effect of the reservoir and improve heat utilization efficiency, a relatively small injection rate, high injection pressure, and low injection temperature are recommended. The uniformity of SHS pressure and temperature distribution in the horizontal annulus positively correlates with the uniformity of the reservoir's heat absorption rate. Achieving more uniform SHS pressure and temperature profiles in the horizontal annulus benefits the uniform heating of the reservoir.

Systematic simulation of tumor cell invasion and migration in response to time-varying rotating magnetic field.

Cancer invasion and migration play a pivotal role in tumor malignancy, which is a major cause of most cancer deaths. Rotating magnetic field (RMF), one of the typical dynamic magnetic fields, can exert substantial mechanical influence on cells. However, studying the effects of RMF on cell is challenging due to its complex parameters, such as variation of magnetic field intensity and direction. Here, we developed a systematic simulation method to explore the influence of RMF on tumor invasion and migration, including a finite element method (FEM) model and a cell-based hybrid numerical model. Coupling with the data of magnetic field from FEM, the cell-based hybrid numerical model was established to simulate the tumor cell invasion and migration. This model employed partial differential equations (PDEs) and finite difference method to depict cellular activities and solve these equations in a discrete system. PDEs were used to depict cell activities, and finite difference method was used to solve the equations in discrete system. As a result, this study provides valuable insights into the potential applications of RMF in tumor treatment, and a series of in vitro experiments were performed to verify the simulation results, demonstrating the model's reliability and its capacity to predict experimental outcomes and identify pertinent factors. Furthermore, these findings shed new light on the mechanical and chemical interplay between cells and the ECM, offering new insights and providing a novel foundation for both experimental and theoretical advancements in tumor treatment by using RMF.

Hybrid multiscale computational approach for heat transfer in GaN semiconductors

Abstract With ongoing advancements in semiconductor technology, understanding thermal transport in semiconductor devices—where phonons are the primary charge carriers—is crucial. This involves a multiscale process in which phenomena at different scales are governed by distinct control equations, necessitating various numerical methods. In this context, this paper introduces a novel multiscale simulation method called the Second-Order Reconstruction Operator Finite Difference Lattice Boltzmann Method (ROsFDLBM). This method effectively combines the Lattice Boltzmann Method (LBM) with the Finite Difference Method (FDM). ROsFDLBM employs reconstruction operators to accurately map the relationship between distribution functions and macroscopic physical quantities, significantly reducing errors caused by the transmission of interface information. The efficacy of this coupling scheme has been confirmed through an interface-coupled thermal diffusion model. Comparative analyses have revealed that the relative error of ROsFDLBM does not exceed 1.2%, demonstrating its superior accuracy. Further simulations of GaN devices have confirmed that traditional macroscopic methods tend to underestimate the temperature in the heat source area at micro-nano scales, with discrepancies reaching up to 60.9 K. Overall, the ROsFDLBM aligns with current research findings and offers an accurate and efficient simulation strategy for addressing complex heat transfer problems.

On the numerical solution to space fractional differential equations using meshless finite differences

We derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and several examples over one dimensional irregular meshes are given.

Theoretical analysis for dynamic model of U-shaped electrothermal microactuator based on Chebyshev spectral method

Abstract This paper presents a largely and accurate analysis for dynamic model of U-shaped actuator that considers the material parameters dependent on temperature. The electro-thermal analysis for temperature distribution and thermo-mechanical analysis for deflection is carried out. The electro-thermal dynamic behaviour is described by piecewise one-dimensional (1D) heat transfer partial differential equations (PDE) for each beam of U-shaped actuator. A combination of Chebyshev spectral method for space domain and Euler forward difference method for time domain is used to solve these equations. The convergence test is first done to ensure the result convinced.

Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk

Environmental management and restoration should be designed such that the risk and uncertainty owing to nonlinear stochastic systems can be successfully addressed. We apply the robustified dynamic Orlicz risk to the modeling and analysis of environmental management and restoration to consider both the risk and uncertainty within a unified theory. We focus on the control of a jump-driven hybrid stochastic system that represents macrophyte dynamics. The dynamic programming equation based on the Orlicz risk is first obtained heuristically, from which the associated Hamilton–Jacobi–Bellman (HJB) equation is derived. In the proposed Orlicz risk, the risk aversion of the decision-maker is represented by a power coefficient that resembles a certainty equivalence, whereas the uncertainty aversion is represented by the Kullback–Leibler divergence, in which the risk and uncertainty are handled consistently and separately. The HJB equation includes a new state-dependent discount factor that arises from the uncertainty aversion, which leads to a unique, nonlinear, and nonlocal term. The link between the proposed and classical stochastic control problems is discussed with a focus on control-dependent discount rates. We propose a finite difference method for computing the HJB equation. Finally, the proposed model is applied to an optimal harvesting problem for macrophytes in a brackish lake that contains both growing and drifting populations.

Cilia-assisted flow of electrically conducting micropolar fluid in a heated curved channel under Soret and Dufour effects

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the influence of heat and mass transfer on the ciliary flow of electrical conducting micropolar fluid in a curved channel. The energy and concentration equations are modulated with viscous dissipation, Soret, and Dufour effects. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). Results for velocity, pumping phenomenon, concentration, thermal field, rate of heat transfer, streamlines, skin friction coefficient, Nusselt number, and Sherwood number are analyzed subject to pertinent parameters. The study reveals that velocity is enhanced via both the micropolar parameter and curvature parameter. Temperature enhances for larger values of Dufour and Brickman numbers. Furthermore, the radial magnetic field plays a resistive role in the trapped bolus. The findings presented in this study should prove beneficial for researchers in the domains of medicine, engineering, science, and fluid mechanics. Further, it is found that the micropolar fluid model is more suitable for biofluids like blood.

Numerical methods for scalar field dark energy in tabletop experiments and Lunar Laser Ranging

Numerous tabletop experiments have been dedicated to exploring the manifestations of screened scalar field dark energy, such as symmetron or chameleon fields. Precise theoretical predictions require simulating field configurations within the respective experiments. This paper focuses onto the less-explored environment-dependent dilaton field, which emerges in the strong coupling limit of string theory. Due to its exponential self-coupling, this field can exhibit significantly steeper slopes compared to symmetron and chameleon fields, and the equations of motion can be challenging to solve with standard machine precision. We present the first exact solution for the geometry of a vacuum region between two infinitely extended parallel plates. This solution serves as a benchmark for testing the accuracy of numerical solvers. By reparametrizing the model and transforming the equations of motion, we show how to make the model computable across the entire experimentally accessible parameter space. To simulate the dilaton field in one- and two-mirror geometries, as well as spherical configurations, we introduce a non-uniform finite difference method. Additionally, we provide an algorithm for solving the stationary Schrödinger equation for a fermion in one dimension in the presence of a dilaton field. The algorithms developed here are not limited to the dilaton field, but can be applied to similar scalar-tensor theories as well. We demonstrate such applications at hand of the chameleon and symmetron field. Our computational tools have practical applications in a variety of experimental contexts, including gravity resonance spectroscopy (q Bounce), Lunar Laser Ranging (LLR), and the upcoming Casimir and Non-Newtonian Force Experiment (cannex). A Mathematica implementation of all algorithms is provided.

Different built-in electric fields for transmission-mode GaAs photocathodes through doping engineering: Design and modeling

In order to enhance the emission performance of transmission-mode GaAs photocathodes used in optoelectronic field, different exponential doping structures are designed for the GaAs emission layer to generate different types of built-in electric fields. These built-in electric fields include the constant, increasing and decreasing types, which can help photoelectron transport toward the emission surface. By solving the one-dimensional continuity equation using the finite difference method, the electron concentration distribution and quantum efficiency of the three types of exponential doping GaAs photocathodes are derived. Meanwhile, the light absorption distributions in the emission layer are simulated by the finite difference time domain method. By comparing the optical absorption distribution and the electron concentration distribution, it is concluded that, among the three types of exponential doping structures, the exponential doping structure generating the increasing built-in electric field has the most sufficient long-wave light absorption capacity and the strongest photoelectron transport ability, thereby achieving the highest quantum efficiency. This theoretical work can help understand the mechanism of improving the photoemission performance of GaAs photocathodes through doping engineering.

Study on bearsing capacity and rigidity of surface throttling bearing

Abstract Based on the lubrication principle and Reynolds theory, the influence of the pressure field and structural parameters on the bearing characteristics of the surface throttle bearing is analyzed and studied by using the finite difference method. The results show that the surface throttling bearing has obvious static bearing characteristics when the shaft is not rotating; The dynamic pressure effect of oil wedge load can be seen obviously when the shaft rotates. With the increase of radius gap h0, the bearing capacity and rigidity will decrease significantly. The increase of oil supply pressure will reduce bearing capacity and rigidity. With the increase of length-diameter ratio L ¯ , the rigidity will be improved.

Brownian motion in a magneto Thermo-diffusion fluid flow over a semi-circular stretching surface

The current study explores the mass and heat transport analysis of a Casson liquid stream past a curved surface. The current model considers the effect of magnetic strength brought on by the strength of the applied uniform magnetic field. The significance of thermophoresis and Brownian motion are also taken into account using the Buongiorno nano-liquid model. The study of liquid flow over stretching sheets frequently addresses practical issues that have garnered significant attention from researchers due to their importance in various domains, including microfluidics, fibreglass production, manufacturing, transportation, metal extrusion, thermal insulation, glass production, paper manufacturing, and acoustic blasting. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity variables. These equations are numerically solved using the finite difference method (FDM). The concentration, temperature, and velocity graphs were produced by varying the different physical parameters. The upsurge in the magnetic parameter reduces the velocity profile. As the magnetic parameter increases, thermal and concentration profiles upsurge. The decrease in velocity profile can be seen as the Casson parameter rises. The intensification in values of thermophoretic parameter enhances the thermal and concentration profiles. The concentration and thermal profiles reduce as the curvature parameter upsurges.

Identification Source Term of the Distributed Order Time-Space Fractional Diffusion Equation

Abstract The inverse source problem for time-distributed order spatial fractional diffusion equations is examined in this study. The forward problem is solved by combining finite difference methods with matrix transformation techniques. The Tikhonov regularization approach is then applied to convert the inverse problem into a variational problem. The optimal perturbation approach is used to find the minimizer of the variational problem, leading to an approximation solution that depends solely on the time-dependent source term. The algorithm’s effectiveness and stability are demonstrated using numerical examples in one-dimensional domains.

A novel binary data classification algorithm based on the modified reaction-diffusion predator-prey system with Holling-II function.

In this study, we propose a modified reaction-diffusion prey-predator model with a Holling-II function for binary data classification. In the model, we use u and v to represent the densities of prey and predators, respectively. We modify the original equation by substituting the term v with f-v to obtain a stable and clear nonlinear decision surface. By employing a finite difference method for numerical solution of the original model, we conduct various experiments in two-dimensional and three-dimensional spaces to validate the feasibility of the classifier. Additionally, with consideration for wide real applications, we perform classification experiments on electroencephalogram signals, demonstrating the effectiveness and robustness of the classifier in binary data classification.

CONTACT INTERACTION OF AN UNDERGROUND PIPELINE WITH SOIL UNDER DYNAMIC IMPACTS

The interaction between a semi-infinite underground pipeline and the surrounding soil during longitudinal seismic wave propagation is examined in the article. The wave travels through the soil with its front perpendicular to the pipeline's axis, and the nonlinear laws of interaction (friction) on the surface of their contact, including the Amonton-Coulomb law, are used to solve related wave problems for the pipeline and soil. The method of characteristics and the finite difference method are sequentially used to solve these problems numerically. The implementation of the law of interaction (friction) processes is shown, depending on the parameters of the wave in soil and the mechanical characteristics of soil. It was determined that a wave in soil that involves the pipeline generates a powerful wave in the pipeline. The amplitude of this wave is many times greater than the amplitude of the wave in soil, and it propagates through the pipeline without attenuation. The dependences of the amplitude of this wave on the parameters of the law of friction, waves in soil, and the mechanical characteristics of soil are determined.

The investigations of asperity peaks and surface roughness on transient squeeze elastohydrodynamic lubrication

Abstract The effects of asperity peak contact pressure and surface roughness (SRN) on pure squeeze elastohydrodynamic lubrication (EHL) motion of circular contacts are investigated for fixed load by using Gauss-Seidel iteration method (GSIM) and finite difference method (FDM). The transient pressure, asperity peak contact pressure, elastic deformation, and film thickness during the pure squeeze process under distinct operating conditions in EHL regime are studied. The results indicate that the differences of the pressure and film thickness between SRNEHL model and EHL model are apparent in final stage due to elastic asperity peak contact. The asperity peak contact pressure will affect hydrodynamic pressure for fixed load, so the hydrodynamic pressure with roughness surface is smaller than that without roughness surface especially around the Hertzian contact (X=1) edge. These phenomena result in different changes in total pressure in different areas. For the contact region, the film thickness of smooth type (ST) is greater than those of circular roughness type (CRT), but this phenomenon reverses near X=1. The larger the C value, the earlier the asperity peak contact effect. Therefore, the greater the C values, the greater the asperity peak contact pressure, and the smaller the hydrodynamic pressure. The asperity peak contact effect significant changes many phenomena at contact region in squeezing final stage.

Modification of the dimensional doma method for linear elliptic equations

Currently, one of the most common methods for the numerical solution of boundary value problems are difference methods (grid method, finite difference method). These methods are well suited for solving problems in regular domains. In areas of complex structure, their use leads to a number of difficulties both in the construction of difference schemes, and in the implementation on a computer. One of the methods to overcome these difficulties is the method of fictitious regions. There are four interrelated directions in the development of the method of fictitious regions: study of various ways to continue the original problems in a fictitious area; obtaining unimprovable estimates in stronger metrics; extension of the class of problems on the application of the method of fictitious areas; construction of effective difference schemes for solving auxiliary problems constructed by the method of fictitious areas. For the first time, the fictitious domain method for the Navier-Stokes equation was studied in the work of A.N. Bugrova, Sh. Smagulov, Smagulov Sh. This article discusses the method of additional areas, which is an analogue of the method of fictitious areas for solving linear boundary value problems, but in the auxiliary problem of this method there is no small perimeter. This method is based on the variational principle of solving linear boundary value problems of elliptic type in an arbitrary region. The existence of a solution is proved by the Galerkin uniqueness method.

Comparison of the activity of IL-6 and IL22 as more inflammatory cytokines related to the pathogenesis of celiac disease between active and gluten-free diet patient

This study aimed to investigate the activity of anti-inflammatory IL-6 (aIL-6) and pro-regenerative IL-22 in celiac disease patients based on their dietary habits. By comparing cytokine levels between patients on active gluten-containing diets and those on gluten-free diets, we sought to elucidate the potential role of diet in modulating inflammatory responses and clinical outcomes in celiac disease. The study made use of an enzyme-linked immunosorbent assay (ELISA) to evaluate the serum levels of interleukins IL6 and IL22. This was performed on three different groups: Group 1, which consisted of 40 recently identified active celiac patients; Group 2, which included 20 patients following a gluten-free diet; and Group 3, which contained 40 apparently healthy individuals .the individuals included in the study had been previously confirmed as celiac patients through serology, specifically by detecting both anti-IgA and IgG antibodies against tTG and gliadin using indirect immunofluorescence. The findings revealed a notable difference in IL6 levels between the patient and control groups, with a P-value of 0.041. However, when the patient groups were compared using the least significant difference (LSD) method, there were no significant differences between Group 1 (G1) and Group 2 (G2) with a P-value of 0.101, and between Group 1 and Group 3 (G3) with a P-value of 0.720. Yet, a more pronounced difference was observed between Group2 and Group3,with a P-value less than 0.015.Regarding IL22 levels, there was a significant difference between the patient and control groups, with a P-value of 0.002. Further comparisons using the LSD method revealed no significant differences between Group 1 and Group 2, with a P-value less than 0.154. However, a highly significant difference was found between Group 1 and Group 3, with a P-value less than 0.01. Also, significant differences were observed between Group 2 and Group 3, with a P-value less than 0.012. In conclusion, there is important role of the inflammatory cytokines il-6 and il-22 in the inflammation of celiac disease and potential role for these cytokines in the pathogenesis and management of the disease. Adherence to a gluten-free diet appears to have a beneficial effect on modulating the inflammatory response and improving clinical outcomes in celiac disease..

Comparison of the Activity of IL-6 and IL22 as More Inflammatory Cytokines Related to the Pathogenesis of celiac Disease Between Active and Gluten-Free Diet Patient

This study aimed to investigate the activity of anti-inflammatory IL-6 (aIL-6) and pro-regenerative IL-22 in celiac disease patients based on their dietary habits. By comparing cytokine levels between patients on active gluten-containing diets and those on gluten-free diets, we sought to elucidate the potential role of diet in modulating inflammatory responses and clinical outcomes in celiac disease. The study made use of an enzyme-linked immunosorbent assay (ELISA) to evaluate the serum levels of interleukins IL6 and IL22. This was performed on three different groups: Group 1, which consisted of 40 recently identified active celiac patients; Group 2, which included 20 patients following a gluten-free diet; and Group 3, which contained 40 apparently healthy individuals .the individuals included in the study had been previously confirmed as celiac patients through serology, specifically by detecting both anti-IgA and IgG antibodies against tTG and gliadin using indirect immunofluorescence. The findings revealed a notable difference in IL6 levels between the patient and control groups, with a P-value of 0.041. However, when the patient groups were compared using the least significant difference (LSD) method, there were no significant differences between Group 1 (G1) and Group 2 (G2) with a P-value of 0.101, and between Group 1 and Group 3 (G3) with a P-value of 0.720. Yet, a more pronounced difference was observed between Group2 and Group3,with a P-value less than 0.015.Regarding IL22 levels, there was a significant difference between the patient and control groups, with a P-value of 0.002. Further comparisons using the LSD method revealed no significant differences between Group 1 and Group 2, with a P-value less than 0.154. However, a highly significant difference was found between Group 1 and Group 3, with a P-value less than 0.01. Also, significant differences were observed between Group 2 and Group 3, with a P-value less than 0.012. In conclusion, there is important role of the inflammatory cytokines il-6 and il-22 in the inflammation of celiac disease and potential role for these cytokines in the pathogenesis and management of the disease. Adherence to a gluten-free diet appears to have a beneficial effect on modulating the inflammatory response and improving clinical outcomes in celiac disease.

Nonlinear wave model of towed system and numerical method for its calculation

Towed systems have found wide practical applications. Notable underwater systems for the long-distance extraction of minerals (concretions) from the ocean floor extend over 5-10 km. The existing mathematical models for solving dynamic problems of such systems in various environments are not entirely accurate regarding the diversity of wave processes. This necessitates the development of refined wave models. This article presents a new quasi-linear mathematical model describing the nonlinear four-mode dynamics of a towed system in a spatially inhomogeneous field of mass and surface forces. It is described by a nonlinear system of twelve first-order partial differential equations. The principles of boundedness and hyperbolicity are satisfied. The validation of the two-mode reduction of the model is based on the numerical solution of the problem of the propagation of two waves: longitudinal and configurational. Using a numerical algorithm and a program based on the finite difference method, a comparison of two difference schemes – Crank-Nicolson and Euler – was conducted. The main limitations for applying the finite difference method used for numerical modeling of wave propagation and reflection in a towed system are the peculiarities of the defining quasi-linear equations, which are related to the necessity of simultaneous computation of variables responsible for fast and slow processes. For such systems of equations, the term "singularly perturbed system of equations" is used. These perturbations result from the significant differences in the propagation speeds of longitudinal and configurational waves at the physical level. Consequently, it is necessary to employ special time-stepping regularization and filtering methods for numerical results. This imposes certain restrictions on the ability to model real processes and on the accuracy of the obtained results, necessitating the use of implicit difference schemes and high-frequency filtering.

A Simplified Calibration Procedure for DEM Simulations of Granular Material Flow

The discrete element method (DEM) has emerged as an essential computational tool in geotechnical engineering for the simulation of granular materials, offering significant advantages over traditional continuum-based methods such as the finite element method (FEM) and the finite difference method (FDM). The DEM’s ability to model particle-level interactions, including contact forces, rotations, and particle breakage, allows for a more precise understanding of granular media behavior under various loading conditions. However, accurate DEM simulations require meticulous calibration of input parameters, such as particle density, stiffness, and friction, to effectively replicate real-world behavior. This study proposes a simplified calibration procedure, intended to be conducted prior to any granular material flow DEM modeling, based on three fundamental physical tests: bulk density, surface friction, and angle of repose. The ability of these tests, conducted on dry quartz sand, to accurately determine DEM micromechanical parameters, was validated through numerical simulation of cylinder tests with varying height-to-radius ratios. The results demonstrated that this calibration approach effectively reduced computational complexity while maintaining high accuracy, with validation errors of 0% to 12%. This research underscores the efficacy of simplified DEM calibration methods in enhancing the predictive reliability of simulations, particularly for sand modeling in geotechnical applications.