Numerically Research Articles

Impact of temperature-reliant thermal conductivity and viscosity variations on the convection of Jeffrey fluid in a rotating cellular porous layer

In this analysis, the collective impact of temperature-dependent thermal conductivity and viscosity variations on the convective instability of a Jeffrey fluid in a rotating layer of cellular porous material is examined using an improved Jeffrey–Darcy model. This study has significant implications for cellular foams made from plastics, ceramics and metals, in which radiative heat transmission can be taken as a diffusion practice. Utilizing the linear stability concept and Galerkin method, approximate analytical and numerical solutions accurate to one decimal place are offered. The analysis reveals that the effect of the thermal conductivity variation factor and the rotation factor is to postpone the convective wave, whereas the viscosity variation factor and the Jeffrey factor have a dual effect in the form of rotation. The range of the convective cell is reduced with cumulating thermal conductivity variation factor, viscosity variation factor, Jeffrey factor and rotation factor. In the absence of rotation, the range of the convective cell is not dependent on the Jeffrey factor or the viscosity variation factor. Furthermore, the outcomes are matched with the existing literature for the specific case of this investigation.

Dynamics of a delayed discrete-time predator prey model proposed from a nonstandard finite difference scheme

Existing literature established stability in a delayed logistic Lotka–Volterra predator- prey model in terms of equilibrium analysis. However, several researchers did not construct the time-series analysis in such models. It has also been observed that both the RK4 methods and the inbuilt ‘dde23’ MATLAB solver were unable to generate stable solutions. This motivated us to develop a nonstandard scheme to capture the numerical solutions which are well consistent with the analytical equilibrium analysis of continuous delayed predator–prey model. In this paper, we will propose a nonstandard finite difference (NSFD) scheme for a delayed predator–prey model. We shall prove that the developed scheme preserves the qualitative behavior of the system, including the local stability of the equilibrium, and stability switching for any step size h=1m,m∈Z+. It is observed that the discretized system shows the occurrence of a Neimark-Sacker bifurcation. Moreover, the convergence analysis of the numerical scheme establishes first-order convergence. The bifurcation diagram and comparison of delay τ−sequence generated by NSFD with the ones obtained by analytical means have been discussed graphically.

Treatment and delay control strategy for a non-linear rift valley fever epidemic model

Rift Valley Fever (RVF) is a viral disease affecting animals and humans, causing symptoms such as fever, liver damage, and bleeding, particularly prevalent in Africa. This study focuses on numerical solutions for a non-linear delayed dynamic epidemiological model of RVF. It extends a control problem incorporating the susceptible, infected, treated, recovered vector to analyze the impact of measures such as mosquito repellent and treatment. The goal is to examine how time delays in implementing control measures affect the dynamics of an epidemic. The model considers delay factors such as mosquito replication, hospitalization, travel restrictions, and isolation due to the lack of proper vaccination. The study explores the model’s aspects, including the reproduction number, equilibrium points, and stability. Local and global implications are examined using techniques such as the Lyapunov function and the Brauer-F lemma. Numerical analysis employs the non-standard finite difference method, establishing the local stability of the equilibrium through the effective reproduction number Rrvf and sensitivity analysis. The research highlights the importance of treatment and delay strategies in reducing RVF transmission, emphasizing the critical need for immunization and preventive measures.

Optoelectronic and photoacoustic waves in rotating excited semiconductor subjected to thermal shock

In this study, the impact of rotation on the transmission of optical acoustic waves, arising from the movement of the optical carrier within an elastic thermal environment, is examined through theoretical analysis. The theoretical framework incorporates the interaction between acoustic waves and thermomechanics to formulate governing equations specific to a semiconductor medium. The fundamental equations of the physical model, influenced by photothermal and thermoelastic principles, are deduced mathematically while considering the presence of rotation. The model studied the medium under a thermal shock wave from thermal stress resulting from light-induced temperature elevation that is not fixed but decaying over time. The mathematical model is solvable using the normal mode method. The model’s numerical solutions provide access to all physical fields within the physical domain, encompassing displacement, temperature, acoustic pressure, mechanical stress, and carrier density diffusion. Utilizing the harmonic wave method, a two-dimensional graphical representation of the rotation parameter with and without the influence of the decay parameter is obtained. The theoretical analysis involves comparison, analysis, and discussion of the effects of these parameters investigated.

A note on the numerical approximation of Greeks for American-style options

In this note, we consider the approximation of the Greeks Delta and Gamma of American-style options through the numerical solution of time-dependent partial differential complementarity problems (PDCPs). This approach is very attractive as it can yield accurate approximations to these Greeks at essentially no additional computational cost during the numerical solution of the PDCP for the pertinent option value function. For the temporal discretization, the Crank–Nicolson method is arguably the most popular method in computational finance. It is well-known, however, that this method can have an undesirable convergence behaviour in the approximation of the Greeks Delta and Gamma for American-style options, even when backward Euler damping (Rannacher smoothing) is employed.In this note, for the temporal discretization of the PDCP, we study an interesting family of diagonally implicit Runge–Kutta (DIRK) methods together with the two-stage Lobatto IIIC method. Through ample numerical experiments for one- and two-asset American-style options, it is shown that these methods can yield a regular second-order convergence behaviour for the option value as well as for the Greeks Delta and Gamma. A mutual comparison reveals that the DIRK method with suitably chosen parameter θ is preferable.

Numerical Technique Based on Operational Matrices of Fractional Integration Using ψ$$ \psi $$‐Shifted Chebyshev Polynomials

ABSTRACTIn this paper, we present a numerical scheme based on a modified form of shifted Chebyshev polynomials to find the numerical solution of a class of fractional differential equations. For this purpose, we work out operational matrices of fractional integration of ‐shifted Chebyshev polynomials obtained from shifted Chebyshev polynomials. Finally, the solution to the problem under consideration is obtained by solving a system of algebraic equations that results from the use of operational matrices of integration. The analysis of integer and non‐integer order differential equations is presented to show the convergence of the solution of fractional order differential equation to the corresponding solution of the integer order differential equation. At the end, we present some linear and non‐linear examples to validate the theoretical analysis. Non‐linear examples are solved using Quasilinearization and proposed numerical technique.

Comparative analysis on the radiative time-dependent water/kerosene-based Cu nanofluid through squeezing Riga plates with heat dissipation: Spectral quasilinearization technique

The time-dependent thermal management along with convective flows are vital in various heat transfer applications in engineering systems such as in automotive cooling systems, and industrial heat exchangers. Because of enhanced thermal conductivity, nanofluids are widely considered for advanced cooling systems such as electronics, aerospace, geothermal energy extraction, etc. The current analysis presents comparative results of the radiative, time-dependent flow of water/kerosene-based Copper nanofluids between squeezing Riga plates focusing on heat dissipation. Both the plates are embedded within a porous matrix and the influence of non-uniform heat source/sink and thermal convective boundary conditions is examined. Riga plates, generally utilized for their ability to generate electromagnetic fields provide greater control over the fluid flow. The problem designed with the inclusion of aforesaid factors is transformed into a non-dimensional form for the utilization of appropriate similarity functions. Further, the impacts of several effective terms on the flow profiles are presented followed by the numerical solution of the profile obtained using the spectral quasilinearization method. Moreover, some of the outstanding findings are; an increase in the fluid velocity is marked for the separation of the plates but the rate of enhancement in the case of kerosene is more pronounced than that of water. Further, irrespective to the type of fluids, the heat transfer rate enhances for the increasing heat fluid which provides the variation of thermal radiation.

Two novel linearized energy-conserving finite element schemes for nonlinear regularized long wave equation

In this paper, two linearized second-order energy-conserving schemes for the nonlinear regularized long wave (RLW) equation are introduced, the unconditional superclose and superconvergence results are presented by using the conforming finite element method (FEM). Initially, through a skillful decomposition of the nonlinear term, two linearized second-order fully discrete schemes are developed. Compared to the previous nonlinear approaches, these schemes significantly reduce the number of iterations and improve computational efficiency; moreover, they conserve energy, and ensure the boundedness of the numerical solution in the H1-norm directly, which represents an advancement over the L∞-norm boundedness reported in prior studies. Secondly, based on the boundedness of the FE solution, the Ritz projection operator and high-precision results of the linear triangular element, the error estimates for superclose and superconvergence are derived without any restrictions on the ratio between time step size Δt and spatial mesh size h. Finally, four numerical examples are provided to confirm the accuracy of the theoretical analysis and the effectiveness of the method.

Analytical formulae for design of one-dimensional sonic crystals with smooth geometry based on symbolic regression

Even though locally periodic structures have been studied for more than three decades, the known analytical expressions relating the waveguide geometry and the acoustic transmission are limited to a few special cases. Having an access to numerical model is a great opportunity for data-driven discovery. Our choice of cubic splines to parametrize the waveguide unit cell geometry offers enough variability for waveguide design. Using Webster equation for unit cell and Floquet-Bloch theory for periodic structures, a dataset of numerical solutions was prepared. Employing the methods of physics-informed machine learning, we have extracted analytical formulae relating the waveguide geometry and the corresponding dispersion relation or directly the bandgap widths. The results contribute to the overall readability of the system and enable a deeper understanding of the underlying principles. Specifically, it allows for assessing the influence of the waveguide geometry, offering more efficient alternative to computationally demanding numerical optimization.

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.

CFD Modeling of Film Condensation from a Steam-Air Mixture in Vertical Channels

Steam condensation in the presence of a noncondensable gas is of vital importance for passive cooling containment systems. The noncondensable gas causes a significant reduction in the condensation rate and heat transfer across the containment, which is important for postulated loss-of-coolant accidents in a nuclear reactor. In this work, computational fluid dynamics models of condensation and the adjacent single-phase steam-air mixture flow are developed for laminar and turbulent flow in vertical channels by two distinct wall condensation modeling approaches using the commercial code STAR-CCM+. The first is the fluid film model available in STAR-CCM+, which solves liquid layer governing equations with connections to the adjacent gas mixture flow. The second is a user-defined wall condensation model that neglects the fluid film and instead accounts for mass, momentum, and heat transfer via user-defined volumetric sink terms adjacent to the cold wall. The condensation models are assessed by first comparing the calculated results with the numerical solution of laminar flow, solved using a complete two-phase model that solves parabolic equations based on conservation of mass, momentum, energy, and species for each phase. Next, the results of a two-dimensional analysis are compared with COPAIN experiments and existing numerical solutions from three-dimensional analyses. The comparisons include new, detailed results that have not been reported in previous analyses of a COPAIN case. These new results include local field profiles of velocity, temperature, and air mass fraction, and local mass flux.

A Novel Approach to Solving Fractional Diffusion Equations Using Fractional Beta Derivative

This paper introduces a novel application of fractional beta derivatives in solving fractional diffusion equations with an emphasis on systems exhibiting anomalous diffusion and memory effects. The work explores the fractional beta derivative as an extension of classical fractional derivatives by incorporating a parameter β (beta) that controls the system’s memory behavior. We investigate both the analytical and numerical solutions of these equations, demonstrating the superior flexibility of fractional beta derivatives in modeling complex diffusion processes. Additionally, we provide a comparison between classical fractional derivatives and the new fractional beta approach to highlight the advantages in terms of accuracy and computational efficiency. We begin by reviewing the theoretical background of fractional derivatives and proceed to introduce the beta derivative as a modification that provides additional flexibility in modeling complex systems. Applications in fields such as control theory, signal processing, and bioengineering are highlighted. Furthermore, numerical methods for solving fractional beta differential equations are discussed, along with potential areas for future research.

Numerical Solution of Burgers Equation Using Finite Difference Methods: Analysis of Shock Waves in Aircraft Dynamics

In this research, the Lax, the Upwind, and the MacCormack finite difference methods are applied to the experimental solving of the one-dimensional (1D) unsteady Burger's Equation, a Hyperbolic Partial Differential Equation. These three numerical analysis-solving methods are implemented for accurate modeling of shock wave behavior high-speed flows that are necessary for aerospace engineering design. This research analysis proves that the MacCormack technique is the one that treats the differential equations with second-order accuracy. This method is quite preferred when it comes to numerical simulations because of its advanced level of accuracy. Although the Upwind and Lax methods are slightly less accurate, they show the development of shock waves that give visualizations to better understand the flow dynamics. Also, in this study, the impact of varying viscosity coefficients on fluid flow characteristics by using the lax (a numerical method for solving the viscous Burgers equation) is investigated. This identification of the phenomenon sheds light on the behavior of boundary layers, which, in turn, can be used to improve the design of high-speed vehicles and lead to a greater understanding of the area of ​​fluid dynamics.

Relativistic diffusion model for hadron production in p -Pb collisions at energies available at the CERN Large Hadron Collider

We investigate charged-hadron production in relativistic heavy-ion collisions of asymmetric systems within a nonequilibrium-statistical framework. Calculated centrality-dependent pseudorapidity distributions for p-Pb collisions at sNN=5.02 and 8.16 TeV are compared with data from the Large Hadron Collider. Our approach combines a relativistic diffusion model with formulations based on quantum chromodynamics while utilizing numerical solutions of a Fokker-Planck equation to account for the shift and broadening of the fragmentation sources for particle-production with respect to the stopping (net-baryon) rapidity distributions. To represent the centrality dependence of charged-hadron production in asymmetric systems over a broad region of pseudorapidities, the consideration and precise modeling of the fragmentation sources, along with the central gluon-gluon source, is found to be essential. Specifically, this results in an inversion of the particle-production amplitude from backward to forward dominance when transitioning from central to peripheral collisions, in agreement with recent ATLAS and ALICE p-Pb data at sNN=5.02TeV. Published by the American Physical Society 2024

DUFOUR, SORET AND DISSIPATION EFFECTS ON MAGNETOHYDRODYNAMIC FLOW PAST A STRETCHING PERMEABLE SHEET WITH RADIATIVE CHEMICAL REACTION ANDHEAT SOURCE

Present investigation explores the numerical solution of Magnetohydrodynamic laminar steady gray fluid flow with heat and mass transfer past a stretching permeable sheet, incorporating several factors such as heat source, viscous and joules dissipation effects, thermal radiation, chemical reactions, Soret and Dufour effects. The governing nonlinear PDEs are simplified into ODEs with the help of similarity transformations. Momentum equation is solved analytically. Non-Dimensional temperature and concentration calculated with the help of RK- shooting method with Nachtsheim-Swigert iteration method. Key results include the calculation of heat and mass transfer rates and Co-efficient of skin friction. The effects of various parameters such as magnetic field strength, suction, radiation, chemical reactions, internal heat generation and dissipative effects on the flow characteristics and other physical parameters are thoroughly investigated, highlighting their impact on the thermal and concentration profiles in the system. This comprehensive analysis provides insights into the behaviour of the fluid flow under the specified conditions, which can be useful for applications in engineering and industrial processes.

Enhanced Adomian Decomposition Method for Accurate Numerical Solutions of PDE Systems

This research addresses critical challenges in numerical solutions, which are vital for various engineering and physical fields. The Modified Adomian Decomposition Method (MADM) is proposed as a novel approach for solving linear and nonlinear partial differential equations (PDEs). MADM builds upon the Adomian Decomposition Method (ADM) by incorporating a new integral operator that significantly improves convergence rates and accuracy. Numerical examples demonstrate the effectiveness of MADM in handling complex nonlinear PDEs. Compared to traditional ADM, MADM consistently achieves more accurate and rapidly converging solutions. This enhancement is attributed to the novel integral operator, which addresses the limitations of ADM for intricate nonlinear problems. The paper outlines the application of MADM, its solution procedure, and its effectiveness through numerical examples. Comparisons with standard ADM solutions and exact solutions validate MADM's accuracy and superiority. The results suggest that MADM is a promising tool for expanding the applicability of Adomian methods in the field of solving PDEs.

Numerical solution and analysis of extended Fisher–Kolmogorov equation using an improved collocation algorithm

The paper investigated the approximate solution of the extended Fisher–Kolmogorov. For this, an advanced approach: the improved quintic B-spline collocation technique has been employed, which is an enhancement over the conventional B-spline collocation method. The B-spline interpolant of degree five has been refined through the posteriori corrections, leading to the development of the improved B-spline solution. This proposed technique demonstrates superior convergence compared to the standard B-spline method, as assessed both theoretically and numerically. In tackling the extended Fisher–Kolmogorov equation, the space discretization is conducted using the improved quintic B-spline collocation methodology (IQSCM), and for the temporal domain discretization, the Crank-Nicolson scheme is applied. The error bounds and convergence analysis is established using the Green's functions. Von-Neumann stability analysis is carried out to discuss the stability of the technique. A few examples are solved and are represented graphically which helps in determining the nature of the solution. Also, L 2 , L ∞ error norms, and order of convergence are calculated to demonstrate the contribution of the new improved technique over the standard spline collocation technique.

Exploring N-soliton solutions, multiple rogue wave and the linear superposition principle to the generalized hirota satsuma-ito equation

In this work, numerous rogue wave solution strategy (MRWSS) agreeing to the Hirota bilinear hypothesis is utilized. The said strategy to build different soliton wave solutions for the generalized Hirota-Satsuma-Ito (GHSI) condition is considered. These numerous soliton wave solutions incorporate first-order, second-order, third-order, and fourth-order waves solutions and so on, which are all depending on the starting theory of chosen capacities. For the lump solution with one most extreme or least esteem, the properties of the Hessian lattice are examined. Besides, the arrangements are contained the lump-two kink arrangements, cross-kink wave arrangements, periodic wave arrangements, and periodic-kink wave arrangements. The various classes of arrangements are gotten. We make utilize of the direct superposition procedure to find out N-soliton wave arrangements to the said condition. The appropriateness and viability of the obtained arrangements is detailed through the reenactment comes about within the shape of 3-D, density, and 2-D charts. The gotten comes about in this work are anticipated to open modern viewpoints for the traveling wave theory.

Overcoming implementation barriers to renewable energy in developing nations: A case study of Iran using MCDM techniques and monte carlo simulation

For most of the world's energy portfolio, particularly in developing countries, fossil fuels form a key dependency. The seventh aim of the United Nations' Sustainable Development Goal (SDG7) is to ensure that all people have readily available, consistent, sustainable, modern energy. Developing nations encounter a range of challenges, such as environmental concerns like air pollution and climate change, increasing energy and population demands, and limited resources. These challenges are associated with achieving net zero emissions as well as a shift to renewable, clean energy sources. Using Iran as a case study, this paper addresses the challenges to the advancement of renewable energy in developing nations. It provides strategies to overcome these challenges and raise the acceptance of environmentally friendly technologies. This study uses fuzzy logic, The Analytic Hierarchy Process (AHP), and an integrated fuzzy logic and AHP (fuzzy-AHP) to evaluate and rank numerous solutions. We conducted a Monte Carlo simulation as a sensitivity analysis method to further confirm the robustness of the proposals. This simulation aimed to find out how various criterion weights influenced the ranking of multiple strategies, thereby providing a more sophisticated knowledge of their efficiency. The results indicate that Iran's primary needs, in order of priority, are "revising governmental policies," "enhanced capacity building," and "improving financial support mechanisms." The Monte Carlo simulation underscored the sensitivity of these approaches to changes in criteria weights, therefore reinforcing the validity of these conclusions.

Dynamically regularized Lagrange multiplier schemes with energy dissipation for the incompressible Navier-Stokes equations

In this paper, we present efficient numerical schemes based on the Lagrange multiplier approach for the Navier-Stokes equations. By introducing a dynamic equation (involving the kinetic energy, the Lagrange multiplier, and a regularization parameter), we form a new system which incorporates the energy evolution process but is still equivalent to the original equations. Such nonlinear system is then discretized in time based on the backward differentiation formulas, resulting in a dynamically regularized Lagrange multiplier (DRLM) method. First- and second-order DRLM schemes are derived and shown to be unconditionally energy stable with respect to the original variables. The proposed schemes require only the solutions of two linear Stokes systems and a scalar quadratic equation at each time step. Moreover, with the introduction of the regularization parameter, the Lagrange multiplier can be uniquely determined from the quadratic equation, even with large time step sizes, without affecting accuracy and stability of the numerical solutions. Fully discrete energy stability is also proved with the Marker-and-Cell (MAC) discretization in space. Various numerical experiments in two and three dimensions verify the convergence and energy dissipation as well as demonstrate the accuracy and robustness of the proposed DRLM schemes.