Linear high order finite difference methods with essentially non-oscillatory limiters for hyperbolic conservation laws

Dynamic response analysis of mooring cables for floating offshore wind turbines under ocean currents using a perturbation-based finite difference method

Developing and analyzing fourth order finite difference method in time and space for Maxwell’s equations

Purpose The purpose of this study is to reveal the influence mechanism of centrifugal inertial effect on the dynamic tracking stability of spiral groove dry gas seal (S-DGS) and to explore the interaction between the special effects of the flow field under high-parameter conditions. Design/methodology/approach The real-gas behavior of carbon dioxide (CO2) is expressed by the Virial equation, and the occurrence of exit choked flow is determined when the exit velocity reaches the sound speed. Perturbation and finite difference methods are used to calculate dynamic gas film characteristic coefficients, and then an axial dynamic model for S-DGS is developed considering centrifugal inertia, choked flow and real-gas effects, which is analytically solved to obtain the axial tracking performance of CO2 S-DGS. Findings The centrifugal inertia effect suppresses the axial tracking capability of the stationary ring in pumping-inward S-DGS, while enhancing it in pumping-outward S-DGS. The real-gas effect primarily influences the inertia effect through gas density, and affects the choked flow effect via dynamic gas film characteristic coefficients. The choked flow effect impacts the real-gas effect through the inlet–outlet pressure differential and affects the inertia effect via dynamic gas film thickness. The inertia effect mainly influences both the real-gas effect and the choked flow effect through gas flow resistance. Originality/value Divergent impacts of centrifugal inertia effect on axial tracking performance of two S-DGSs are revealed, and the complex interaction mechanisms of three special effects on dynamic leakage rate are further investigated, providing a critical theoretical foundation for optimizing the sealing performance of S-DGS.

This paper introduces a novel stochastic Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model tailored to study transportation-related infections. The model is analyzed both theoretically and computationally, offering new insights into the dynamics of disease spread in interconnected urban environments. Theoretically, we employ a Lyapunov function to establish the existence of a global positive solution and demonstrate that the solution is stochastically ultimately bounded (SUB) and stochastically permanent. Additionally, we derive a crucial sufficient condition to determine when the infectious disease may die out in the two cities under study. In the numerical analysis, we implement two distinct computational methods: the stochastic Euler-Maruyama (SEM) method and the stochastic nonstandard finite difference (SNSFD) method, to validate the theoretical findings of the studied model. When comparing the two numerical methods, our results show that the SNSFD method outperforms the SEM method in preserving key dynamic characteristics, such as positivity, boundedness, and stability, especially for larger temporal step sizes. This comparative analysis highlights the robustness and efficiency of the SNSFD scheme in handling complex stochastic epidemic models. The findings are illustrated with clear and detailed graphs, providing an accessible understanding of the model’s behavior under various parameter configurations. This work contributes to the field by combining theoretical rigor with innovative computational techniques, offering a comprehensive framework for studying transportation-related infectious diseases.

ABSTRACT We propose a positivity‐preserving computational method for the ternary Allen–Cahn (tAC) equation. To solve the tAC equation, we apply the operator splitting method. The tAC equation is decomposed into nonlinear and linear components. The nonlinear term is discretized using a finite difference method (FDM) combined with an explicit–implicit scheme. The resulting cubic polynomial admits a unique real solution under appropriate time step conditions. The unique solution is obtained by applying the analytical formula for solving cubic polynomials. The linear term, representing the diffusion equation, is discretized using a fully implicit FDM. The resulting tridiagonal matrix is solved by using the Thomas algorithm, which is a direct method for such systems. We analytically prove the positivity‐preserving property of the proposed numerical method. To validate the performance of the proposed algorithm, several standard computational tests are conducted, and the results confirm the accuracy and effectiveness of the proposed algorithm.

While early ideal consolidation theories for vertical drains focused primarily on radial flow, numerous coupled radial–vertical seepage models have since been developed to better capture complex flow behavior in practice. To overcome this limitation, a nonlinear large-strain consolidation model for vertical drains with coupled radial-vertical flow is proposed, explicitly incorporating Hansbo’s non-Darcy flow, smear effects, and soil nonlinearity. The finite difference method is then employed to obtain numerical solutions, and the reliability of the proposed numerical scheme is verified by degenerating the model to the radial consolidation case and comparing the results with the corresponding analytical solution. The results indicate that consolidation develops fastest when the permeability coefficient within the smear zone follows a parabolic distribution. Increasing the Hansbo’s flow parameter m and threshold hydraulic gradient parameter I1 markedly slows down the consolidation process, while the contribution of vertical flow is primarily confined to the early stage. In addition, larger soil nonlinearity parameters Ic and α amplify the influence of radial–vertical coupled flow. Parametric analysis further shows that when the ratio of soil layer thickness to the radius of the influence zone (H/re) exceeds 10, the effect of vertical flow becomes negligible, and the consolidation behavior can be reasonably approximated using a radial-flow-only model.

The safety of freight trains depends on the performance of braking systems, particularly on the condition of frictional components such as brake blocks and wheels in tread brakes. These components are subjected to thermal and mechanical stresses that cause wear and damage. The aim of this work is to predict the temperature field developing in the wheel–brake block contact region during braking, in order to provide a reliable numerical tool for railway safety and durability assessment. Although finite element models are widely used in the literature, this study proposes two Finite Difference models featuring first-order accuracy in time and second-order accuracy in space: a 2D axisymmetric model and a 3D model to predict the thermal behaviour of wheels and blocks. Vernersson’s analytical relation is applied in the 2D model for the determination of the circumferential temperature on the wheel tread, and the result is compared with that of the 3D model. The accuracy of the models is validated using experimental data from organic LL blocks for tread brakes provided by Trenitalia (FSI group), with an average difference of around 25°C in the worst case. The results temporal evolution shows good agreement between numerical and experimental temperatures and demonstrates that the proposed 2D approach, combined with the analytical circumferential formulation, allows an accurate characterization of the wheel thermal field with a computational time reduction of more than two orders of magnitude compared to the 3D model. Finally, the model is applied to compare the thermal features of organic LL and cast iron brake blocks simulating a bench and an entire train. The analysis highlights that the use of organic LL blocks leads to an increase in wheel circumferential temperature variation compared to cast iron blocks, resulting in a higher thermal fatigue load on the wheel tread.

ABSTRACT This paper develops a fast finite difference scheme on graded meshes for variable‐order time‐fractional diffusion equations with weak initial singularities. The proposed method combines 1 approximation with the sum‐of‐exponentials technique for kernel approximation, achieving both high accuracy and computational efficiency. We establish sharp error estimates for the scheme and rigorously prove its numerical stability and convergence using maximum principle analysis. Numerical experiments confirm the theoretical results, demonstrating that the accelerated scheme maintains optimal convergence rates while significantly reducing computational costs compared to existing approaches.

Time-fractional interface problems, found in heat transfer with discontinuous conductivities and fluid flows with surface tension forces, are challenging due to irregular interfaces and the history-dependent nature of fractional derivatives. This paper presents two numerical methods for simulating time-fractional double interface problems. The first method uses the Haar wavelet collocation technique, while the second relies on a meshless approach with radial basis functions. The fractional derivatives are replaced with the Caputo sense, the resulting first-order time derivatives are handled using the finite difference method, and the spatial operator is approximated using the two proposed methods. Gauss elimination is used to solve linear problems. Quasi-Newton linearization method is used for nonlinear problems. Both methods accommodate constant and variable coefficients, handling discontinuities and singularities in both solutions and coefficients. To evaluate the effectiveness of the proposed methods, numerical experiments are carried out. The accuracy of each method is quantified using the L∞ error norm, and a comparative analysis highlights the validity and advantages of the approaches. Moreover, the proposed schemes are rigorously analyzed to establish their stability, and the existence and uniqueness of the solutions.

The present study proposes a fast and high order numerical technique for solving a three-dimensional Caputo time-fractional reaction diffusion equation. The solution of this equation generally exhibits a weak singularity at the initial time. Due to this weak singularity, the Caputo time-fractional derivative is discretized by L2-1 σ technique on the graded mesh. A high-order compact finite difference scheme is developed for discretization of spatial derivatives. To improve the computational efficiency of the fully-discretized scheme, a fast discrete sine transform is introduced. The global L 2 convergence and H 1 stability of the present numerical method are rigorously analysed. Four examples are provided to verify the computational efficiency and accuracy of the proposed algorithm. Moreover, numerical results are compared with those acquired by an existing method in the literature to highlight the advantage of our approach.

ABSTRACT The integration of thermal energy storage media utilizing phase transition mechanisms significantly enhances the operational performance of hybrid photovoltaic-thermal collectors through the cyclical storage and release of thermal energy during isothermal phase transitions. This study introduces a novel hybrid PV/T collector incorporating parallel-arranged phase change material (PCM) module. A computational framework integrating the finite difference method with an explicit enthalpy formulation was developed to analyze the melting characteristics of the PCM at multiple positions. The results demonstrate that under a solar irradiation of 823 W/m2, a uniform melting rate of 95% was achieved across all positions, despite a maximum phase transition initiation delay of 62 minutes. Notably, superior melting uniformity was also observed under lower ambient temperatures. Furthermore, the system configuration combining a 65 L tank with a flow rate of 0.036 L/s was identified as optimal, enabling a highly consistent 95% melting rate while reducing the maximum phase transition delay to 28 minutes. The analysis of these spatial-phase transition characteristics provides critical insights for the design of stable and efficient PV/T-PCM systems.

The present study examines the hydroelastic interactions of a multi-module very large floating structure interconnected by articulated hinges and integrated with porous floating breakwaters. Unlike monolithic VLFS designs, the articulated VLFS introduce unique dynamic challenges due to connector forces and inter-module wave interference, which have not been thoroughly explored when integrated with porous wave attenuation mechanisms. The study develops a coupled numerical framework that combines a multi-domain boundary element method for wave interaction with porous structures and a finite difference method for the structural response of hinged modules. This model explicitly resolves interactions between waves, structures, and connectivity, including the effects of breakwater porosity and hinge constraint dynamics. Critical parameters such as hinge stiffness, module spacing, breakwater placement, and porosity are systematically varied to quantify their influence on inter-modular bending moments, shear forces, and wave transmission. The investigation demonstrate that articulation redistributes peak stresses, reducing maximum bending moments in individual modules by 15%–25% compared to rigid configurations, although it can amplify torsion at hinge points under oblique waves. Moreover, porous breakwaters that are strategically positioned between modules suppress wave resonance in the gaps, reducing connector forces by 30%–40% and attenuates transmitted energy by over 45%. However, to avoid detrimental wave trapping between modules, the porosity of the breakwaters must exceed 25%. The study establishes that optimal hinge design, combined with breakwaters tailored for porosity, mitigates hydroelastic penalties in multi-module systems which enables scalable VLFS deployments in exposed seas and advanced design methodologies for adaptive, large-scale floating infrastructure.

In this work, the time fractional mixed diffusion-wave equation on an unbounded domain with initial weak singularity is solved numerically. The equation is first transformed into equivalent integral-differential equation. Then we propose a fully discrete scheme based upon Laguerre Galerkin-spectral method in spatial direction and finite difference method on graded meshes in temporal direction. The unconditional stability of the proposed scheme is given. Moreover, the convergence under the regularity of the solution is proved. Numerical results are given to support the theoretical analysis.

In this work, we present a rigorous proof that a designed second-order NSFD scheme is dynamically consistent with respect to the solution of a generalized eco-epidemiological predator-prey model. More specifically, positivity of populations, equilibrium points, trapping domain, and local stability, are maintained regardless of the time step size, i.e. the method is unconditionally stable. The design of the scheme relies on the usual nonlocal approximation of the right-hand side function while the nonstandard denominator functions are defined depending not only on the time step size but also on the state variables. We prove that resulting scheme is convergent with the desired order. The proposed methodology can be used to design second-order NSFD methods for other models similar to the predator-prey model presented in this paper. Finally, we present numerical examples that support the mathematical analysis and show the advantages of the constructed NSFD schemes.

A new method is presented for the measurement of electron inelastic mean free path (IMFP) of copper metal from the K-edge X-ray absorption fine structure (XAFS) using energies from 5 to 320 eV above the edge. The accuracy of theoretical determinations of electron IMFP at low energies is one of the key limiting factors in current XAFS modeling and Monte Carlo transport. Significant discrepancies between theoretical and experimental IMFP values have been revealed through recent studies, posing significant questions regarding the accuracy of key structural parameters extracted through XAFS analysis. Small molecules and organometallic systems, which often lack robust tabulations of key electron scattering data, are particularly susceptible to inconsistencies in the IMFP, requiring a new methodology to resolve these discrepancies. XAFS is determined using an advanced density functional theory (DFT) core of the finite difference method for XAFS (FDMX). The popular multiple-scattering approach, based on muffin-tin potentials, is shown to be inadequate for accurately calculating the fine structure. Experimental IMFP measurements are both consistent with past measurements and consistent with the latest plasmon theory. However, variation of measurements with temperature points to the need for fine spacing at room temperature and measured uncertainties of data points at low temperatures and also suggests significant temperature-dependent effects both of broadening and correlation from multiple sources. This work confirms both recent past experimental and theoretical works and points to new areas of challenge and discrepancy.

We present the finite-difference parquet method that greatly improves the applicability and accuracy of two-particle correlation approaches to interacting electron systems. This method incorporates the nonperturbative local physics from a reference solution and builds all parquet diagrams while circumventing potentially divergent irreducible vertices. Its unbiased treatment of different fluctuations is crucial for reproducing the strong-coupling pseudogap in the underdoped Hubbard model, consistent with diagrammatic Monte Carlo calculations. We reveal a strong-coupling spin-fluctuation mechanism of the pseudogap with decisive vertex corrections that encode the enhanced, energy-dependent scattering amplitude between electrons and antiferromagnetic spin fluctuations.

The primary objective of this paper is to numerically analyze the effect of circumferential V-grooves on the thermohydrodynamic performance of turbocharger thrust bearings, with a focus on lubricant temperature distribution and variation. To investigate the relationship between shaft speed and lubricant temperature, a thermohydrodynamic lubrication (THL) model was employed to obtain numerical results. The numerical methodology utilizes the finite difference method coupled with the Newton-Raphson scheme to solve the nonlinear modified Reynolds and energy equations concurrently. To ensure accuracy, steady-state numerical predictions of pressure and temperature distributions were validated against existing research. Subsequently, the numerical findings, focusing on oil pressure, friction, and oil temperature under varying shaft speeds, are thoroughly discussed. The numerical findings indicate that the implementation of grooved thrust bearings with a 5-mm clearance reduces the average lubricant temperature in the contact area by 14% at maximum operating speeds, while maintaining friction levels comparable to those of ungrooved counterparts. However, an excessive increase in groove width and depth adversely affects the bearing's load-carrying capacity and results in higher peak temperatures at the bearing plate edge, especially at widths and depths greater than 30 µm.

In this paper, the coordinate transformation method is applied to the Navier–Stokes equations expressed in terms of the stream function and vorticity formulation. An elliptical grid generator is used to construct an orthogonal curvilinear grid within an irregular domain of complex geometry, mapping the physical region onto a computational square domain. The developed algorithm is capable of generating both orthogonal and general curvilinear grids. The finite-difference scheme of the Navier–Stokes system in arbitrary orthogonal curvilinear coordinates is then solved numerically on this grid using the alternating direction method. Numerical simulations of the Roach problem are conducted at low Reynolds numbers and on grids of varying resolutions. The obtained results are compared with the reference studies of Napolitano and Orlandi, showing satisfactory agreement with the data reported by 16 other research groups. Overall, the proposed method enables efficient numerical simulation of laminar flows in domains with complex geometry. The developed approach provides high accuracy and stability and can be effectively used for the numerical analysis of applied fluid dynamics problems. Furthermore, the methodology described in this work may serve as a foundation for future studies focused on improving computational efficiency and expanding the applicability of curvilinear grid techniques in modern fluid dynamics.

Rapid enrichment and determination of fishery drugs residue in fishes and shrimps by ZnO-Ag SERS substrate.