Pseudospectral Technique Research Articles

Internal heating and distribution in electromagnetic Powell-Eyring [formula omitted]/glycerin hybridized nanomaterial with radiation and wall slip conditions

The synergistic influences of the hybridization of molybdenum disulfide (MoS2) and graphene oxide (GO) nanoparticles on electromagnetic radiation absorption and augmentation of thermal conductivity coupled with the industrial demand for an enhanced non-Newtonian working fluid spurred this study. Therefore, the study examines the radiative properties and thermal behaviour of hybridized MoS2 and GO nanoparticle systems dispersed in a glycerin Powell-Eyring fluid with wall slip conditions. A theoretical mathematical setup is modelled for the nanoparticle thermophysical characteristics with viscous dissipation and heat generation under the influence of the electromagnetic Riga plate. The model is transformed into an invariant dimensionless form and solved utilizing the pseudo-spectral collocation technique. The effect of fluid rheology, nanoparticle concentration, and fluid-wall slip conditions interface on radiative heat transfer and thermal propagation is investigated. The results reveal momentous augments in radiation absorption and thermal conductivity of about 4.13% to 10.22% due to MoS2 and GO hybridized nanoparticles. Also, it was found that thermal transport is enhanced close to the solid boundary wall slip, leading to an improve heat distribution rate. Hence, this study contributes to the interplay complexity between external stimuli, fluid dynamics, and nanoparticle morphology in thermal systems, offering insights into the advanced materials synthesis, thermal management systems, and optimization and design of nanoparticle fluid enhancement applications.

Alternative split-step method for solving linearly coupled nonlinear Schrödinger equations

In this paper we introduce an alternative method for solving linearly coupled nonlinear Schrödinger equations by using a split-step approach. This methodology involves approximating the nonlinear part of the evolution operator, allowing it to be solved exactly, which significantly enhances computational efficiency. The dispersive component is addressed using a spectral method, ensuring accuracy in the treatment of linear terms. As a reference, we compare our results with those obtained using the Runge-Kutta method implemented using a pseudo-spectral technique. Our findings indicate that the proposed split-step method achieves precision comparable to that of the Runge-Kutta method while nearly doubling computational efficiency. Numerical simulations include the evolution of a single soliton in each field and a collision between two solitons, demonstrating the robustness and effectiveness of our approach.

Nonlinear stability analysis of thermal convection in a fluid layer with slip flow and general temperature boundary condition

The current article presents a comprehensive analysis of the influence of inconstant viscosity into thermal convection, incorporating the influence of generalized velocity (slip boundary condition) and temperature boundary conditions (physically represent imperfectly conducting boundary) within a fluid layer. Slip boundary conditions are often considered more practical than no-slip conditions (Neto et al. (2003)). Therefore, in the present work, slip boundary condition is used to discuss the effect of temperature and pressure dependent viscosity. Both linear and nonlinear stability analyses are explored, revealing a noteworthy finding: the precise alignment of the nonlinear stability boundary with the linear instability threshold. Additionally, the exchange of stability is illustrated, indicating that convection exclusively manifests in a stationary mode. The findings are derived across a spectrum of boundary scenarios, ranging from free-free to rigid-free, and rigid-rigid boundaries, encompassing both isothermal and adiabatic conditions. Notably, the slip length parameter exhibits a destabilizing effect, while convection is observed to occur more swiftly under adiabatic boundary conditions compared to isothermal conditions. The Chebyshev pseudo-spectral technique is applied to solve the eigenvalue problems obtained from linear and nonlinear stability analysis.

Analysis of laminated shells using pseudospectrals and the Reissner-Mixed Variational Theorem

In this paper, we combine the Carrera’s Unified Formulation CUF and a pseudospectral technique for predicting the static deformations and free vibrations behaviour of thin and thick cross-ply laminated shells. For the first time, the Reissner-Mixed Variational Theorem is used together with pseudospectrals to achieve a highly accurate technique. The accuracy and efficiency of this numerical technique for static and vibration problems are demonstrated through numerical examples.

Turbulence generation in the solar corona through nonlinear interaction between 3D kinetic Alfvén wave and magnetic islands

This study investigates the interaction between kinetic Alfvén waves (KAWs) and magnetic islands in solar corona region. KAWs and magnetic islands are believed to be one of the key players in the heating of the coronal plasma and particle acceleration. We have used the dynamical model for KAWs to simulate its propagation through magnetic islands. The equation is solved numerically by using the finite difference and pseudospectral technique for spatial and temporal variations. The simulation results have been studied and signatures of turbulent structures evolving with time have been observed. Turbulence plays a considerable role in tapping out magnetic energy to thermal energy. The plot of the energy spectrum as a function of wavenumber exhibits a power law behavior in the inertial range, characterized with an exponent around −5/3 . Beyond this range, the spectrum becomes steeper. In order to gain a more thorough knowledge of the physical processes that underlie the development of localized structures and to estimate the current sheet scale sizes, a semi-analytically model is also performed. The results indicate that the size of localized structures are comparable to ion gyro-radius, and different intensities of KAW further modify this length scale formed at different times. The purpose of the study is to acquire an understanding of the KAW propagation in magnetic islands and the way it contributes to the formation of turbulence and energy release in the solar corona. A comparative aspect of the non-linear interaction of 3D KAW with magnetic island and null point is also presented which shows that non-linear interaction of 3D KAW with null point, leads to rapid disorganization of the magnetic field and the creation of localized structures.

A localized Fourier collocation method for 2D and 3D elastic mechanics analysis: Theory and MATLAB code

This paper documents the first attempt to apply the localized Fourier collocation method (LFCM), a recently published meshless collocation method, for solving 2D and 3D elastostatic problems. The approach first divides the entire domain into a series of intersecting sub-domains. Within each sub-domain, the unknown functions are approximated by utilizing the pseudo-spectral Fourier collocation technique. The method integrates the merits of the rapid convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique. This combination results in a novel framework that is highly suitable for large-scale and high-precision engineering simulations. Extensive numerical experiments, involving both 2D and 3D elastostatic problems, are presented to showcase the precision and efficiency of the current method. The source codes for numerical examples studied in this work are also provided.

Dynamics of micropolar-Walters B fluids under the influence of thermal radiation and Soret–Dufour mechanisms

PurposeThe purpose of this study is to investigate the Dynamics of micropolar – water B Fluids flow simultaneously under the influence of thermal radiation and Soret–Dufour Mechanisms.Design/methodology/approachThe thermal radiation contribution, the chemical change and heat generation take fluidity into account. The flow equations are used to produce a series of dimensionless equations with appropriate nondimensional quantities. By using the spectral homotopy analysis method (SHAM), simplified dimensionless equations have been quantitatively solved. With Chebyshev pseudospectral technique, SHAM integrates the approach of the well-known method of homotopical analysis to the set of altered equations. In terms of velocity, concentration and temperature profiles, the impacts of Prandtl number, chemical reaction and thermal radiation are studied. All findings are visually shown and all physical values are calculated and tabulated.FindingsThe results indicate that an increase in the variable viscosity leads to speed and temperature increases. Based on the transport nature of micropolar Walters B fluids, the thermal conductivity has great impact on the Prandtl number and decrease the velocity and temperature. The current research was very well supported by prior literature works. The results in this paper are anticipated to be helpful for biotechnology, food processing and boiling. It is used primarily in refrigerating systems, tensile heating to large-scale heating and oil pipeline reduction.Originality/valueAll results are presented graphically and all physical quantities are computed and tabulated.

How do the Intravenously Injection of Nanoparticle and Oxytatic Bacteria Affect Through Circular Cylinder Cell for Non-Newtonian Micropolar Fluid: Mathematical Approach

In this paper, we have researched the conduct of non-Newtonian micropolar nanofluid flow through horizontal circular under the impacts of nanoparticles, oxytatic bacterial and Hall current effects. The utilizations of the current investigation are exceptionally powerful in biomedical therapies, for example, obliteration of malignant growth over biological cells by utilizing drug conveyance of nanoparticles and oxytatic microscopic organisms. If there should arise an occurrence of biological nanofluid it’s accepted to concern variable physical parameters which rely on the nanofluid temperature. Implicit Chebyshev pseudospectral (ICPS) technique by helping MATHEMATICA software has been applied to governing nonlinear system of dimensionless partial differential equations (PDEs). The nanofluid velocity, microrotation angular velocity, temperature, motile bacterial density distributions, oxygen concentration, local skin friction coefficient, Nusselt number, and wall motile density gradient distributions are delineated graphically for various variable physical parameters, likewise comparison between certain results in literature and our current output is introduced and great arrangement is found.

A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method

This research focuses on the analysis of the competitive model used in the banking sector based on the stochastic fractional differential equation. For the approximate solution, a pseudospectral technique is utilized for the proposed model based on the stochastic Lotka–Volterra equation using a wide range of fractional order parameters in simulations. Conditions for stable and unstable equilibrium points are provided using the Jacobian. The Lotka–Volterra equation is unstable in the long term and can produce highly fluctuating dynamics, which is also one of the reasons that this equation is used to model the problems arising in finance, where fluctuations are important. For this reason, the conventional analytical and numerical methods are not the best choices. To overcome this difficulty, an automatic procedure is used to solve the resultant algebraic equation after the discretization of the operator. In order to fully use the properties of orthogonal polynomials, the proposed scheme is applied to the equivalent integral form of stochastic fractional differential equations under consideration. This also helps in the analysis of fractional differential equations, which mostly fall in the framework of their integrated form. We demonstrate that this fractional approach may be considered as the best tool to model such real-world data situations with very reasonable accuracy. Our numerical simulations further demonstrate that the use of the fractional Atangana–Baleanu operator approach produces results that are more precise and flexible, allowing individuals or companies to use it with confidence to model such real-world situations. It is shown that our numerical simulation results have a very good agreement with the real data, further showing the efficiency and effectiveness of our numerical scheme for the proposed model.

A reduced-order model based on cubic B-spline basis function and SSP Runge–Kutta procedure to investigate option pricing under jump-diffusion models

The purpose of this research is to develop a numerical method that can be used to deal with option pricing in jump-diffusion models. The proposed model is made up of a backward partial integro-differential equation with diffusion and advection factors. For the first and second order derivatives, the pseudo-spectral technique is used in conjunction with cubic B-spline functions. As a consequence, the first- and second-order derivative matrices are constructed, and an ODE system is created. Second-order Strong Stability Preserved Runge–Kutta (SSP) procedure is used to solve the ODE problem. According to what has been stated, the main model falls under the advection–diffusion classification. As a result, in order to reach the ultimate time, we need to increase both the number of collocations and the number of time steps in order to improve our results. That is why the final algebraic system of equations has been condensed using a technique known as proper orthogonal decomposition (POD). The POD-cubic B-Spline (POD-CB-S) function collocation approach can be used to describe this numerical procedure. Finally, a number of test cases are conducted to demonstrate the proposed method’s efficiency and accuracy.

Nonlinear stability analysis of double diffusive convection in a fluid saturated porous layer with variable gravity and throughflow

This paper develops a detailed study of linear and nonlinear stability analyses, for the double diffusive convection problem in a porous medium, when heating is done from below and, salting is done from below as well as from above. The linear analysis is performed using normal mode technique and nonlinear analysis is developed using energy technique. The Chebyshev pseudo-spectral technique is performed to analyze the effect of variable gravity field and throughflow on the behavior of system stability. The results obtained from linear and nonlinear analysis are compared and found that the results are in better agreement for the heated from below and salted from above system however, the comparatively less agreement is obtained for the system when both heating and salting are done from below. The direction of throughflow and gravity field have considerable effect on the stability of system. The behavior of gravity field is invariant for both the type of system heating and salting from below as well as heating from below and salting from above. The solute Rayleigh number stabilizes the system for heating from below and salting from below, however, destabilizes the system for heating from below and salting from above. In the absence of gravity field, a comparatively good agreement between thresholds is seen for Q = 0, however, the agreement is shifted towards positive value of Q or negative value of Q when gravity is found to be present in the system. Thus, effect of gravity field is dominant on the influences of throughflow on the stability of system.

The influence of temperature on physical properties of a hybrid nanofluid flow in a non-Darcy porous medium

The purpose of this paper is to debate the influences of variable thermal conductivity as well as viscosity on a hybrid nanofluid flow through a non-Darcy porous medium along a wavy surface. Two kinds of base fluids are considered; the first is water (H2O) with [Formula: see text] and the second is ethylene glycol–water mixture (C2H6O[Formula: see text]H2O) with [Formula: see text]. Furthermore, the physical properties of the base fluid have been modified via the addition of two kinds of suspended nanoparticles. The suspended nanoparticles of alumina Al2O3were firstly added to the base fluid. Then, titania TiO2suspended nanoparticles are immersed into this nanofluid to form two hybrid nanofluids (TiO[Formula: see text]Al2O3/H2O) and (TiO2-Al2O3/C2H6O2–H2O). Dupuit Forchheimer model as a non-Darcy porous medium is utilized. The mathematical model for the present physical problem with convective boundary condition is studied numerically via the Chebyshev pseudospectral (CPS) technique. Nusselt number, velocity and temperature profiles are investigated under different parameters. The present outcomes clarify that adding the alumina nanoparticle supports and improves the efficiency of the titania nanoparticle. Also, taking both of the hybrid nanofluid viscosity/thermal conductivity as variable functions of temperature has an important role to support the studies of heat transfer.

A spectral method algorithm for numerical simulations of gravitational fields

A numerical study of the Einstein field equations, based on the 3 + 1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the Arnowitt–Deser–Misner (ADM) and the conformal Baumgarte–Shapiro–Shibata–Nakamura (BSSN) approach. The numerical code is based on the Fourier decomposition, accompanied by different filtering techniques. The role of the dealiasing, as well as the influence of the filter type, has been investigated. The algorithms have been stabilized via a novel procedure that controls self-consistently the regularity of the solutions. The accuracy of the model has been validated through standard testbeds, revealing that the filtered pseudo-spectral technique is among the most accurate approaches. Finally, the procedure has been stressed via black hole dynamics and a new strategy, based on hyperviscous dissipation that suppresses spurious boundary problems, has been proposed. The model represents a valid tool of investigation, particularly suitable for the inspection of small scale nonlinear phenomena in gravitational dynamics.

Aircraft three-dimensional hardconstrained trajectory planning using pseudospectral optimization method

This paper is concerned with the three-dimensional constrained optimal path planning. To this end, an objective function is defined as the shortest trajectory length in such a way that some constraints including rough terrain avoidance, forbidden zone avoidance, initial and terminal constraints, allowable altitude constraint and maximum allowable curvature of trajectory are satisfied. These leads to a challenging problem for aircraft guidance and control that solution requires great experience, skill, accuracy, and a powerful strategy. For this purpose, pseudospectral technique, which is one of the direct methods, is applied in this paper based on the Chebyshev nodes through which the complexity of the problem is reduced by transforming the optimal control problem into the parametric optimization one. The efficacy of the proposed method is demonstrated by extensive simulations, and it is particularly verified that this method is able to produce a solution satisfying all hard constraints of the underlying problem.

High accurate pseudo-spectral Galerkin scheme for pantograph type Volterra integro-differential equations with singular kernels

Spectral and pseudo-spectral Galerkin techniques, by using the standard Jacobi polynomials, are implemented to calculate numerically the solutions of pantograph type Volterra delay integro-differential equations that have kernels with the property of weak singularity. Because of the complex structure of the considered problems, pseudo-spectral Galerkin approaches are more desirable with respect to the spectral Galerkin approaches, since they have the property of integral approximator by using high order convergent Gauss quadrature formulas. A deep and detailed analysis of convergence of the numerical solutions to the exact solutions are given under some mild conditions such as smoothness of the solutions. Some test problems are illustrated and efficiency of the suggested numerical approach is investigated with respect to a recently proposed Jacobi pseudo-spectral collocation technique via some figures and tables experimentally.

Geostationary debris mitigation using minimum time solar sail trajectories with eclipse constraints

SummaryMinimum time solar sailing trajectories are introduced using a combination of indirect and direct optimal control techniques. Here, large‐scale, multiphase optimal control problems are solved using a pseudospectral collocation technique applied to an orbital debris mitigation concept. These solutions are obtained for realistic sail dimensions, producing multirevolution, Earth‐centered trajectories while accounting for uncontrolled spacecraft dynamics in the eclipse regions. Specifically, minimum time solutions for orbit transfer and phasing maneuvers are obtained using only solar radiation pressure for propulsion and control. First, an optimal primer vector steering history is obtained through numerical approximation. Locally optimal, closed‐form solutions are then implemented based on the primer vector direction, resulting in minimum time satisfaction of desired terminal orbital conditions. In addition, a novel solution strategy is presented for multiphase optimal control problems characterized by uncontrollable dynamics with flexible phase boundaries. The maneuvers presented will be shown to enable efficient orbital debris mitigation for large‐scale debris in geostationary orbits.

State-dependent indirect pseudospectral method for nonlinear optimal control problems

The state-dependent Riccati equation (SDRE) method is an efficient approach to solve nonlinear optimal control problems (OCPs), but nonlinear necessary conditions for the first-order optimality are seldom met in the SDRE approach. In this paper, a state-dependent indirect pseudospectral (SDIP) technique is developed to design nonlinear optimal controllers. To preserve the nonlinearity of the system and reduce the computational cost as well, the state-dependent coefficient (SDC) parameterization technique is employed. Then the optimality conditions are derived under input and state constraints, and spectral methods are used to discretize the optimality conditions into a series of mixed linear complementarity problems (MLCPs). The developed SDIP method is able to handle the finite and infinite-horizon nonlinear OCPs in a unified framework. Numerical comparisons also verify the performance of the developed SDIP method.

Impacts of Newtonian heating, variable fluid properties and Cattaneo–Christov model on MHD stagnation point flow of Walters’ B fluid induced by stretching surface

MHD viscoelastic (Walters’-B) fluid flow close to the stagnation point region along an extending plate with the changeable fluid properties’ influences has been debated. Heat transfer’s features are scrutinized via Cattaneo–Christov (CC) theory. The mathematical model for the physical problem is tackled numerically via Chebyshev pseudospectral (CPS) technique. The existing outcomes are supported by recent research and have acquired a suitable agreement. The numerical outcomes reveal that temperature fields are more pronounced for Fourier’s law case. Further, the opposite behavior is noticed with the heat transfer rate. Higher values of the conjugate parameter result in an increment of the heat transfer rate and temperature field. Fluid flow’s features, as well as physical quantities, are substantially varied via variable fluid properties.

Pseudospectral discretization of delay differential equations in <i>sun-star</i> formulation: Results and conjectures

In this paper we study the pseudospectral approximation of delay differential equations formulated as abstract differential equations in the \begin{document}$ \odot* $\end{document} -space. This formalism also allows us to define rigorously the abstract variation-of-constants formula, where the \begin{document}$ \odot* $\end{document} -shift operator plays a fundamental role. By applying the pseudospectral discretization technique we derive a system of ordinary differential equations, whose dynamics can be efficiently analyzed by existing bifurcation tools. To better understand to what extent the resulting finite-dimensional system mimics the dynamics of the original infinite-dimensional one, we study the pseudospectral approximations of the \begin{document}$ \odot* $\end{document} -shift operator and of the \begin{document}$ \odot* $\end{document} -generator in the supremum norm, which is the natural choice for delay differential equations, when the discretization parameter increases. In this context there are still open questions. We collect the most relevant results from the literature and we present some conjectures, supported by various numerical experiments, to illustrate the behavior w.r.t. the discretization parameter and to indicate the direction of ongoing and future research.

Optimal Interception Technique Variation Calculus Task of Multidimensional Visual Ballistic Missiles

A strategy of manoeuvrating using inverted flight is presented to determine the optimal path for the dive stage of a hypersonic missile. The fighting incident in this document is taken into account when the hypersonic missile strikes the goal on the floor. In particular, the hypersonic rockets are first implemented by a maneuvering type called the reversed plane. The ideal route is later conceived by minimizing the attack time with the current terminal route angle, taking into consideration the limitations of the attack angle, fluid pressure, thermal transfer rate and ordinary overload. A better pseudo-spectral hp-adaptive technique with a mesh size decrease is introduced to resolve the constructed trajectory optimization issue. The paper shows the application of variation calculations in the process of anti-ballistic missile interception, to achieve the optimal concept of the open-switch control law. It provides analytical outcomes in the shape of suitable Euler-Lagrange Equations, relying on the preservation of the wind concept, for three distinct indices, using a simple racket and missile model. It also offers the computer program to simulate the intercom system quickly, with chosen parameters, parametrical assessment and simple alteration possibilities by other scientists, as published as m-Function of MATLAB in accessible code.