Efficient Numerical Technique Research Articles

EFFICIENT EXPLICIT NUMERICAL TECHNIQUE FOR MODELING ADVECTION DIFFUSION REACTION FOR A WATER QUALITY MODEL IN AN OPENED UNIFORM FLOW – A 1D PERSPECTIVE

This research paper presents a novel and efficient explicit numerical technique for modeling advection diffusion reactions in an opened uniform flow from a one-dimensional perspective. The proposed hybrid scheme combines the benefits of explicit finite difference schemes, resulting in an accurate and fast solution for the advection-diffusion equation in water stream problems. The effectiveness of the scheme is demonstrated through its successful implementation in the solution of the water quality problems, where the advection-diffusion equation plays a crucial role. The results obtained using this technique show improved accuracy and computational efficiency. Overall, this research offers a valuable contribution to the field of numerical modeling in water quality and provides a useful tool for researchers and practitioners working in the area of approximating the one-dimensional diffusion equation for the measurement of pollutant concentration.

A novel approach for numerical treatment of traveling wave solution of ion acoustic waves as a fractional nonlinear evolution equation on Shehu transform environment

Abstract In this paper, we develop and employ an efficient numerical technique for traveling wave solution of the Time Fractional Zakharov-Kuznetsov (TFZK) equation, also known as the nonlinear evolution equation, using the Modified Adomian Decomposition Approach (MADA) in collaboration with the cubic order convergence of the Newton-Raphson method (also known as the improvised Newton-Raphson method) on the Shehu Transform environment (STE). In the current study, the time fractional Caputo-Fabrizio Derivative (CFD) is used in singular and non-singular kernel derivatives to address the influence of fractional parameters. Some of the current numerical and analytical results are displayed utilizing 3D plots, while others are depicted in the form of a legend 2D plots for comparison. To validate the robustness of the current approach, the uniqueness, stability, and convergence analyses are described. The current result is compared to the analytical solution as well as previous solutions in order to demonstrate the efficiency of our suggested technique.

QM/AMOEBA description of properties and dynamics of embedded molecules

AbstractWe describe the development, implementation, and application of a polarizable QM/MM strategy, based on the AMOEBA polarizable force field, for calculating molecular properties and performing dynamics of molecular systems embedded in complex matrices. We show that polarizable QM/MM is a well‐understood, mature technology that can be deployed using a state‐of‐the‐art implementation that combines efficient numerical methods and linear scaling techniques. Thanks to these numerical advances and to the availability of parameters for a wide manifold of systems in the AMOEBA force field, polarizable QM/AMOEBA can be used for advanced production applications, that range from the prediction of spectroscopies to ground‐ and excited‐state multiscale ab initio molecular dynamics simulations.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Combined QM/MM Methods

EFFECTS OF MAGNETIC PARTICLES DIAMETER AND PARTICLE SPACING ON BIOMAGNETIC FLOW AND HEAT TRANSFER OVER A LINEAR/NONLINEAR STRETCHED CYLINDER IN THE PRESENCE OF MAGNETIC DIPOLE

Magnetic particles are essential in materials science, biomedical, bioengineering, heat exchangers due to their exceptional thermal conductivity and unique properties. This work aims to model and analyze the biomagnetic fluid flow and heat transfer, namely the flow of blood with magnetic particles (Fe3O[Formula: see text] induced by stretching cylinder with linear and nonlinear stretching velocities. Additionally, this study investigates the impact of particles diameter and their spacing under the influence of ferrohydrodynamics (FHD) principle. The collection of partial differential equations is transformed using similarity transformations to produce the theoretically stated ordinary differential system. An efficient numerical technique, which is further based on common finite difference method with central differencing, a tridiagonal matrix manipulation and an iterative procedure are used to solve the problem numerically. The major goal of this extensive study is to enhance heat transformation under the influence of numerous parameters. There have been numerous displays of the velocity profile, temperature distribution, local skin friction factor and rate of heat transfer in terms of the appearing physical parameters. It is observed that variation in velocity and temperature distributions is the cause of increasing the ferromagnetic interaction parameter and the size of magnetic particles. The enhancement of particle diameter causes an increment in the skin friction while the rate of heat transfer declines. For verifying purposes, a comparison is also shown with previously published scientific work and found to possess suitable accuracy.

Effect of geometric non-linearity and tip mass on the frequency bandwidth of a cantilever piezoelectric energy harvester under tip excitation

The research community is investigating a variety of approaches to convert mechanical energies to useful electrical energy in order to fulfil the ever-increasing demand for energy and fulfil the requirements of the various sectors. In this regard, numerous contributions toward increasing the capacity and efficiency of the various energy harvesting techniques have been proposed in recent times; one such promising technology is piezoelectric-based vibration energy harvesting. In the present work, the effect of geometric nonlinearity and tip mass is investigated on the operational frequency range of a cantilever nonlinear piezoelectric energy harvester. The proposed mathematical model is based on an energy-based variational approach. The methodology is formulated for the piezoelectric patched cantilever beam and, eventually solved using an efficient numerical technique . An amplitude incremental iterative algorithm is used to solve the non-linear governing equations of motion for the proposed non-linear broadband harvester along with the experimental validation. Firstly, a parametric study is performed to determine the optimum piezoelectric patch dimensions. Subsequently, the attempt is made to increase the frequency bandwidth for optimum energy harvesting by taking advantage of geometrically non-linear behaviour. Additionally, a tip mass, appropriate for the excitation level, can be added to the harvester design to make it effective for lower excitation frequency. Increased frequency bandwidth for improved energy harvesting capacity with the hardening type nonlinearity and tip mass is meaningfully shown with the help of frequency-amplitude response. Furthermore, to interpret the efficacy of nonlinear harvesters in terms of frequency band-width, power spectral density plots with improved harvesting capability are presented and compared with the conventional linear vibration energy harvester.

Different Numerical Techniques, Modeling and Simulation in Solving Complex Problems

This study investigates the performance of different numerical techniques, modeling, and simulation in solving complex problems. The study found that the Finite Element Method was found to be the most precise numerical approach for simulating the behavior of structures under loading conditions, the Finite Difference Method was found to be the most efficient numerical technique for simulating fluid flow and heat transfer problems, and the Boundary Element Method was found to be the most effective numerical technique for solving problems involving singularities, such as those found in acoustics and electromagnetics. The mathematical model established in this research was able to effectively forecast the behaviors of the system under different conditions, with an error of less than 5%. The physical model established in this research was able to replicate the behavior of the system under different conditions, with an error of less than 2%. The employment of multi-physics or multi-scale modeling was found to be effective in overcoming the limitations of traditional numerical techniques. The results of this research have significant effects for the field of numerical techniques, modeling and simulation, and can be used to guide engineers and researchers in choosing the most appropriate numerical technique for their specific problem or application.

Coupled VEM–BEM Approach for Isotropic Damage Modelling in Composite Materials

Numerical prediction of composite damage behaviour at the microscopic level is still a challenging engineering issue for the analysis and design of modern materials. In this work, we document the application of a recently developed numerical technique based on the coupling between the virtual element method (VEM) and the boundary element method (BEM) within the framework of continuum damage mechanics (CDM) to model the in-plane damage evolution characteristics of composite materials. BEM is a widely adopted and efficient numerical technique that reduces the problem dimensionality due to its underlying formulation. It substantially simplifies the pre-processing stage and decreases the computational effort without affecting the solution’s accuracy. VEM is a recent generalization to general polygonal mesh elements of the finite element method that ensures noticeable simplification in the data preparation stage of the analysis, notably for computational micro-mechanics problems, whose analysis domain often features complex geometries. The numerical technique has been applied to artificial microstructures, representing the transverse section of composite material with stiffer circular-shaped inclusions embedded in a softer matrix. BEM is used to model the inclusions that are supposed to behave within the linear elastic range, while VEM is used to model the surrounding matrix material, developing nonlinear behaviours. Numerical results are reported and discussed to validate the proposed method.

3D Viscoelastic Finite-Difference Analysis of the Monopole Acoustic Logs in Cylindrical Coordinates

In this paper, a model of the heterogeneous anelastic seismic wave problem is proposed in three-dimensional (3D) cylindrical coordinates. We use the velocity-stress formula to describe the realistic attenuation properties of viscoelastic materials, derived from a rheological model of the generalized standard linear solid (GSLS). The equation system is completed by additional equations for the anelastic functions including the strain history of the material. We apply the staggered grid finite-difference (FD) method in 3D cylindrical coordinates to solve the equations. Moreover, to avoid the effect of gradual expansion of the grid size as the radius increases, we use a variable grid method to achieve compensation. In real drilling operations, the mud injected in the borehole is a fluid with viscous properties. The actual formation is also not elastic. In the synthetic data of acoustic logging while drilling (LWD), we find that the drill collar wave is not affected by the viscoelastic parameters of the formation. In contrast, the Stoneley wave is more sensitive to the viscosity of the drilling fluid. The phase and amplitude of the received waveform are affected by the drilling fluid as well as the formation viscoelasticity. Therefore, the development of the cylindrical variable-grid FD method provides a flexible and efficient numerical technique to solve 3D viscoelastic wave propagation problems, including realistic attenuation and complex geometry.

Pharmacokinetic parameter identification using a meshless method approach for transdermal drug delivery

The Localized Collocation Meshless Method (LCMM) is applied to the solution of a set of partial differential equations governing the diffusive transport of a dermally injected compound as described by the Compartmental Pharmacokinetic (CPK) model. This efficient and accurate numerical technique then provides the framework for the estimation of pharmacokinetic (PK) parameters by the comparison of two models, both containing information derived from experimental results, using the iterative Golden Section search algorithm. This comparison is quantified using a norm between the two solution spaces. While this method does provide an estimate of the effective-diffusion coefficient, it ultimately demonstrates that a simple, free-diffusion model is inadequate for quantifying the spatial and temporal distribution of a dermally-injected compound if elimination effects are not accounted for properly.

A level set based fractional order variational model for motion estimation in application oriented spectrum

In recent years, motion estimation has become prominent in the field of computer vision. This is due to its applications in various domains such as object detection, video surveillance, undersea navigation, fire damage control, particle image velocimetry etc. Therefore, in this paper, a nonlinear fractional order variational model is introduced for motion estimation in an image sequence (video). The motion estimation is performed in terms of optical flow. The objective of this work is to generalize the existing variational models from integer order to fractional order and provide the increased robustness against outliers, and furnish the dense and discontinuity preserving optical flow in various spectra such as synthetic, sintell, thermal, underwater, medical, fire and smoke and fluid image sequences. For this purpose, a level set segmentation based fractional order variational functional composed of a non-quadratic Charbonnier norm and a regularization term is propounded. This non-quadratic penalty provides an effective robustness against outliers, whereas the fractional derivative possesses a non-local character, and therefore is capable to deal with discontinuous information about texture and edges. The level set segmentation is performed on the flow field instead of images, which is a union of disjoint and independently moving regions such that each motion region contains objects of equal flow velocity. The numerical discretization of the fractional partial differential equations is employed with the help of Grünwald–Letnikov fractional derivative. The resulting nonlinear formulation is converted into a linear system and solved by an efficient numerical technique. The experimental results are carried out on 10 different application oriented spectra. The performance of the model is tested using different error measures and demonstrated against several outliers. The efficiency and accuracy of the proposed model is shown against recently published works. The graphical abstract for this algorithm is illustrated under the next section.

An efficient numerical technique for two-parameter singularly perturbed problems having discontinuity in convection coefficient and source term

An efficient numerical technique for two-parameter singularly perturbed problems having discontinuity in convection coefficient and source term

Impact of an effective Prandtl number model on the flow of nanofluids past an oblique stagnation point on a convective surface

The stretched surface's convective heat transfer capability can be improved by using nanoparticles. There is a significant role of the Prandtl number in determining the thermal and momentum stretching layer surfaces. It is proposed in this study that an effective Prandtl number model be used to explore the two-dimensional oblique stagnation point flow of γAl2O3−H2O and γAl2O3−C2H6O2 nanofluids moving over a convective stretching surface. The fluid in question is subjected to a thorough investigation. It is necessary to apply non-linear ordinary differential equations in order to connect the controlling partial differential equations with the boundary conditions. To solve these equations, an efficient and reliable numerical technique is used. Shooting Method with Runge Kutta-IV in Mathematica software. Visual representations of normal and tangential velocity and temperature as well as streamlines as a function of many physical parameters are shown. The results show that as the volume fraction of nanoparticles increases, the fluid flow f(y),h(y) and velocity f′(y),h′(y) all increase, whereas the flow f(y) and velocity f′(y) both increase against the stretching ratio parameter, while the flow h(y) and velocity h′(y) both decrease. When the volume percentage of nanoparticles and the Biot number are both increased, the temperature rises. However, when the stretching ratio parameter is increased, the temperature falls. Physical attributes like the local skin friction coefficient and the heat flow may be characterized in many ways. A nanofluid comprised of γAl2O3−C2H6O2 outperformed a γAl2O3−H2O nanofluid in terms of heat transfer rate. The source of zero skin friction may be observed to move to the left or right depending on the balance of obliqueness and straining motion at point xs. The computed numerical results of the current research correspond well with those accessible in the literature for the limiting scenario.

The implementation comparison between the Euler and trivial coupling schemes for achieving strong convergence

<abstract><p>This study aimed to develop efficient numerical techniques with the same accuracy level as exact solutions of stochastic differential equations (SDEs). The MATLAB program was used to find solutions for the Euler and trivial coupling methods. The results of these methods were then compared and analyzed. The results show that Euler and trivial coupling methods give the same strong convergence. Furthermore, we demonstrated that these methods achieve strong convergence with a standard order of one-half to the exact solution of the SDE. Moreover, the Euler method is characterized by its speed, ease of application and ability to find solutions through computer programs.</p></abstract>

Convergence analysis and an efficient numerical technique for the solution of Benjamin Bona Mahony partial differential equation

This study proposed a collocation based modified scheme of trigonometric cubic b-spline approach (MCTB-spline) to approximate the solution of the Benjamin Bona Mahony (BBM) partial differential equation. The MCTB-spline collocation method is used to discretise the space derivatives terms of the partial differential equation, while the finite difference method (FDM) is used to make discretised the time-variant derivatives of the BBM partial differential equation. This study also describes the convergency of the present method, which helps to illustrate the accuracy of the present scheme for the partial differential equation. A Rubin Graves linearisation process linearises BBM partially differential equations into nonlinear terms. An example has been selected for demonstration of numerical approximations and provided a comparative study with the previous scheme of different types of error norms. To validate the stability, Von-Neumann stability condition was applied on the proposed scheme. Results suggested that the present scheme achieved better results and outperformed the previous techniques used. We will apply the generalisation of the present scheme to higher order and coupled partial differential equations in the future.

Convergence Analysis and an Efficient Numerical Technique for the Solution of Benjamin Bona Mahony (BBM) Partial Differential Equation

Convergence Analysis and an Efficient Numerical Technique for the Solution of Benjamin Bona Mahony (BBM) Partial Differential Equation

Simple yet highly efficient numerical techniques for systems of nonlinear equations

Simple yet highly efficient numerical techniques for systems of nonlinear equations

DUAL SOLUTION OF CONVECTIVE BIOMAGNETIC FLUID THROUGH PERMEABLE MOVING FLAT PLATE CONSIDERING WALL TRANSPIRATION AND MAGNETIZATION

A two-dimensional (2D) steady boundary layer flow along with heat transfer of a self-similar biomagnetic fluid over a permeable moving flat plate has been taken into consideration in this work. The flow is contemplated to be embedded by a magnetic dipole of sufficient magnetic strength. Transpiration as well as movement along the wall is also regarded. By imposing the appropriate similarity technique, the governing equations are converted into a system of coupled nondimensional equations. An efficient numerical technique has been incorporated to solve these dimensionless coupled nonlinear ordinary differential equations. The existence of dual solutions along with their stability has been established with the consideration of stability analysis. We discovered from our analysis that two solutions exist (one stable and another unstable) for the arbitrary values of transpiration, movement velocity and biomagnetic interaction parameters on flow and physical parameters. The attained results are demonstrated graphically and in tabular form. For the validity of our numerical scheme, we compared our findings with others previously published and found significant agreement.

NLFEM WITH HIGHER ORDER INTERPOLATION FUNCTION FOR EFFICIENT ANALYSIS OF IRREGULAR DOMAIN

This study proposes a new approach to developing a more efficient numerical technique by coupling the non-uniform rational B-spline (NURBS) with the higher-order polynomial basis functions under the framework of the Finite Element Method (FEM). In this technique, denoted as NURBS-Lagrange FEM (NLFEM), the NURBS basis functions are employed to represent the geometry of the problem domain, while the Lagrange interpolation functions are employed for the higher-order polynomial functions to interpolate the field variables. The NURBS is a mathematical model which provides a numerically stable algorithm to exactly represent all conic sections, and the Lagrange interpolation function allows for higher-order basis functions resulting in a faster convergence rate of analysis. By taking advantage of both models, the objective of this study is to propose a new approach, i.e., NLFEM, which can improve the accuracy of the analysis of the irregular domain with more efficient consumption of computer resources. A steady heat transfer formulation for a curved boundary problem is presented to demonstrate the validity and accuracy of the developed technique. The performance is verified against converged solutions obtained using higher-order FEM (FEM/Q9) and NURBS-Augmented FEM (NAFEM). The presented result shows that the NLFEM provides a favorable comparison against other methods. The converged solution is achieved 20% faster than the FEM/Q9 and 80 % faster than the NAFEM. This highlights the potential of the NLFEM as a new approach in numerical techniques for solving problems with irregular boundaries.

Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment

Convex and non-convex fuzzy mappings are well known to be important in the research of fuzzy optimization. Symmetry and the idea of convexity are closely related. Therefore, the concept of symmetry and convexity is important in the discussion of inequalities because of how its definition behaves. This study aims to consider new class of generalized fuzzy variational-like inequality for fuzzy mapping which is known as perturbed fuzzy mixed variational-like inequality. We also introduce strongly fuzzy mixed variational inequality, as a particular case of perturbed fuzzy mixed variational-like inequality which is also a new one. Furthermore, by using the generalized auxiliary principle technique and some new analytic techniques, some existence results and efficient numerical techniques of perturbed fuzzy mixed variational-like inequality are established. As exceptional cases, some known and new results are obtained. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

An Effective Numerical Technique for Boundary Value Problems Arising from an Adiabatic Tubular Chemical Reactor Theory

Mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic reaction are investigated by an efficient numerical technique, Fibonacci Collocation method in this study. The reaction's steady-state temperature is calculated for several values of three parameters, namely, Peclet and Damkohler numbers and the dimensionless adiabatic temperature increment. When the generated outcomes are compared with the other numerical approaches, it has been sighted that the presented method produces reliable results for this type of problems.