Efficient Numerical Approach Research Articles

Calculation of core loss under distorted flux density with minor hysteresis loops for laminated steel structure

Accurate prediction of core losses has been a crucial aspect in the field of electromagnetics for several decades. Extensive experimental results have shown that the core loss under harmonic excitation is more complicated than that under sinusoidal excitations, which means that the traditional core loss calculation methods are no longer applicable under distorted flux. In order to determine an efficient numerical approach when minor hysteresis loops occur, a harmonic magnetic test platform is used to study the effect of the variation of B–H properties on the iron loss and magnetic flux density of grain oriented silicon steel lamination under different supply voltages. A simple method, which could be used to predict the iron losses in thin laminations due to a number of non-sinusoidal waveforms with or without minor loops, for estimating the iron loss based on the loss separation method is proposed. The errors are substantially lower than those of conventional models while saving time.

Influence of internal pores and graphene platelets on vibration of non-uniform functionally graded columns

This paper deals with free vibration analysis of non-uniform column resting on elastic foundations and subjected to follower force at its free end. The internal pores and graphene platelets (GPLs) are distributed in the matrix according to different patterns. The model is proposed with material parameters varying in the thickness of column to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite column, it is crucial to consider porosities inside the material structure.

Numerical study of non-singular variable-order time fractional coupled Burgers’ equations by using the Hahn polynomials

In this study, an efficient numerical approach is formulated for solving a category of non-singular variable-order time fractional coupled Burgers’ equations with the aid of the Hahn polynomials. The fractional differential operators are considered in the Atangana–Baleanu–Caputo concept. The designed method converts the original system into an algebraic system which can be simply handled. In order to verify that the demonstrated algorithm is reliable and accurate, some numerical experiments have been processed. The obtained solutions manifest the effectiveness and accuracy of the presented method for solving this class of equations.

An efficient numerical approach for space fractional partial differential equations

In this research work, authors are aiming to present a computational model based on hybrid B-spline collocation method (HBCM) to solve Space Fractional Partial Differential Equation (SFPDE). The efficiency of the proposed method is shown by two test problems for various values of T. Tables and graphs are used to describe the results, which ensures that results are in an excellent agreement with analytical solution.

Long-range asymptotics of exchange energy in the hydrogen molecule

The exchange energy, i.e., the splitting ΔE between gerade and ungerade states in the hydrogen molecule, has proven very difficult in numerical calculation at large internuclear distances R, while the known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work, we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 a.u. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form ΔE ∼ R5/2e-2R, but with the leading coefficient being 2σ away from the analytically derived value.

Analysis of Metal Oxide Varistor Arresters for Protection of Multiconductor Transmission Lines Using Unconditionally-Stable Crank–Nicolson FDTD

Surge arresters may represent an efficient choice for limiting lightning surge effects, significantly reducing the outage rate of power lines. The present work firstly presents an efficient numerical approach suitable for insulation coordination studies based on an implicit Crank–Nicolson finite difference time domain method; then, the IEEE recommended surge arrester model is reviewed and implemented by means of a local implicit scheme, based on a set of non-linear equations, that are recast in a suitable form for efficient solution. The model is proven to ensure robustness and second-order accuracy. The implementation of the arrester model in the implicit Crank–Nicolson scheme represents the added value brought by the present study. Indeed, its preserved stability for larger time steps allows reducing running time by more than 60 % compared to the well-known finite difference time domain method based on the explicit leap-frog scheme. The reduced computation time allows faster repeated solutions, which need to be looked for on assessing the lightning performance (randomly changing, parameters such as peak current, rise time, tail time, location of the vertical leader channel, phase conductor voltages, footing resistance, insulator strength, etc. would need to be changed thousands of times).

Crack growth adaptive XIGA simulation in isotropic and orthotropic materials

Reliable prediction and thorough understanding of crack growth in engineering materials and structures are of challenging problems, but scientific and technical community has been continuously pursuing an efficient numerical approach to crack propagation simulation. We present in this paper a significant extension and development of the adaptive extended isogeometric analysis (XIGA) based on LR B-splines (locally refined B-splines), which facilitates the local refinement, for accurately modeling crack growth in isotropic and orthotropic media. The discontinuity and singularity of displacements and stresses induced by cracks are locally captured by special enrichment functions, for both isotropic and orthotropic media. This allows the representation of crack to be independent of the computational mesh and avoids the requirement for re-meshing in crack growth simulation. The numerical integration accuracy is improved with the use of the almost-polar integration and sub-triangle technique for the crack-tip and cut elements, respectively. The posteriori error estimator based on Zienkiewicz–Zhu error estimation is employed to define refinement domains, and thereby, drives the adaptivity. On the other hand, the maximum circumferential stress criterion is adopted to determine the direction of crack growth. Several crack growth numerical examples for both isotropic and orthotropic media are studied in different scenarios to show the performance and accuracy of the developed approach. Numerical results reveal that the present approach integrated with the adaptive local refinement scheme offers higher accuracy and convergence rate than the standard XIGA. Furthermore, the adaptive XIGA in a tandem with Nitche’s method is applied to simulate the crack growth of complicated structures. We additionally explore the effects of some numerical aspects or factors on crack path. Smaller crack growth increment could be used to improve the accuracy of crack path within a finer mesh in the adaptive XIGA.

An uncoupled fluid structure interaction method in the assessment of structural responses of tall buildings

This paper presents an innovative and efficient numerical approach for predicting wind induced dynamic responses of a tall building. The method uses an uncoupled fluid structure interaction (FSI) approach, where wind flow data obtained from a validated Computational Fluid Dynamics (CFD) analysis was used to obtain structural responses of the 184 m tall CAARC (Commonwealth Advisory Aeronautical Research Council) building with a typical façade. An innovative method of converting recorded pressures on the building’s surface, to time history nodal loads, was presented. This new method of pressure to load conversion enabled the use of an implicit modal time history analysis where the structure’s dynamic behaviour was predicted. This new method was critically evaluated with a full transient structural analysis. It was shown that the proposed mapping and implicit analysis technique took 45 s to perform and was able to provide similar numerical accuracy to a full transient analysis which took 2 clock hours. Also, the proposed method was capable of predicting building responses accurately in terms of mean, maximum and standard deviation quantities of displacement where comparison were made to experimental measurements. Other important characteristics such as the impact of using higher number of modes for the proposed modal superposition method is presented and discussed.

An efficient numerical approach for fractional diffusion partial differential equations

The main purpose of this manuscript is to present a new approximation method to find the numerical solution of partial differential equations with Caputo fractional derivatives. We have also included the stability analysis of the proposed technique. To illustrate the effectiveness and reliability of the method, we have examined the method with several numerical examples. The high computational efficiency of the proposed method can be seen by observing the accurate approximate solutions obtained from the process. The suggested procedure is a potent tool and it can be used to solve other similar problems in modeling real-world problems.

Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure.

A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.

Multi-level DEM study on liner wear in tumbling mills for an engineering level approach

Liner wear is one of the major problems for the design and maintaining of the tumbling mills and an effective and efficient numerical approach can significantly reduce the cost for studying liner wear. To obtain an engineering level approach, a coarse grain level wear model is proposed in this paper. A multi-level study on the liner wear was conducted to assess the adequacy of the coarse grain level approach based on the simulation results of the original-level approach - Discrete Element Method (DEM) combined with the wear model Shear Impact Energy Model (SIEM). Quasi-mono-size distribution and polydisperse size distribution were used in the simulations. The reasons for the deviations of the results predicted by the coarse grain level wear model were discussed and analyzed.

A fast and efficient numerical approach for solving advection–diffusion equations by using hybrid functions

In this paper, we developed a new and efficient numerical method for solving advection–diffusion equations. The method is based on the integration of the considered advection–diffusion equation. By integration, we transform the advection diffusion equation into the equivalent integral equation which the integral equation contains initial and boundary conditions. Afterward, the integral equation would be transformed into the system of linear algebraic equations by using a hybrid of Chebyshev and Block-pulse functions and their operational matrix of integration. The system of linear algebraic equations can be solved by direct or iterative methods. We presented some theorems to show the error approximation of the hybrid function. Three numerical examples are considered to investigate the applicability and simplicity of the method. The numerical results confirm that the method is fast, stable, and exponentially accurate.

An efficient numerical approach for simulating contact in origami assemblages.

Origami-inspired structures provide novel solutions to many engineering applications. The presence of self-contact within origami patterns has been difficult to simulate, yet it has significant implications for the foldability, kinematics and resulting mechanical properties of the final origami system. To open up the full potential of origami engineering, this paper presents an efficient numerical approach that simulates the panel contact in a generalized origami framework. The proposed panel contact model is based on the principle of stationary potential energy and assumes that the contact forces are conserved. The contact potential is formulated such that both the internal force vector and the stiffness matrix approach infinity as the distance between the contacting panel and node approaches zero. We use benchmark simulations to show that the model can correctly capture the kinematics and mechanics induced by contact. By tuning the model parameters accordingly, this methodology can simulate the thickness in origami. Practical examples are used to demonstrate the validity, efficiency and the broad applicability of the proposed model.

On the solutions to the Saint–Venant problem of heterogeneous beam-like structures with periodic microstructures

This paper presents displacement solutions of the Saint-Venant problem for linear elastic heterogeneous beam structures with arbitrarily shaped periodic microstructures. The solutions are generated by introducing unknown axially periodic displacement functions in place of the axially invariant warping functions in Ieşan's rational scheme, due to the periodic characteristics of the beam structure, while retaining the displacement fields integrated from rigid-body displacements, which represent basic kinematics in beam theories. The governing equations of the unknown functions, defined on a base cell, are then developed from equilibrium equations and boundary conditions of the periodic beam structure. Moreover, an improved FE formulation of the governing equations is presented and its efficient numerical implementation approach, which can be readily realized using FE software as a black box, is proposed with the aid of NIAH (Novel Numerical Implementation of Asymptotic homogenization) approach. To illustrate the validity of the Saint-Venant solution and the effectiveness of the numerical implementation approach, several numerical examples are presented and compared with detailed three-dimensional FE analysis for the heterogeneous beam structures in terms of stress components.

Efficient two–scale simulations of engineering structures using the Hashin–Shtrikman type finite element method

An efficient FE2-like numerical homogenization approach for nonlinear microstructures is proposed using the Hashin–Shtrikman type finite element (HSFE) method to solve the microscale problem. The latter combines the small computational effort of Hashin–Shtrikman type homogenization approaches with the accuracy of full-field FE-solutions. The key point is a reduced order method based on a Hashin–Shtrikman type variational formulation combined with data-clustering, which is based on offline FE-simulations of microstructures (snapshots). The presented microscopic model has significantly less microscopic degrees of freedom in comparison to the classic FE2-method. The number of stress computations within the microstructure is highly reduced. The tangent operator, which incorporates the coupling between the microscopic and macroscopic scale, is derived analytically. Different numerical examples are investigated, where a nonlinear RVE is attached to each integration point of a macrostructure. A comparison to full-field FE-simulations shows that the macro-response and local fields are well captured by the HSFE method.

A simple non-iterative uncoupled algorithm for nonlinear pore-dynamic analyses

In this work, a simple, stable, non-iterative, uncoupled formulation is proposed for nonlinear pore-dynamic analyses. Here, each phase of the coupled problem is treated separately, uncoupling the governing equations of the porous model. Thus, simpler, smaller and better conditioned systems of equations are obtained, providing a more efficient numerical approach. In addition, in the proposed technique, solution is carried out without considering any iterative computation, even when nonlinear models are regarded, further improving the effectiveness of the method. Incompressible and impermeable media may also be directly analysed by the new formulation, without requiring any special discretization procedure, as it is the case in standard analyses. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the new technique.

An efficient numerical approach to solve the space fractional FitzHugh\u2013Nagumo model

In this work, we study the numerical approximation for the space fractional FitzHugh–Nagumo model. The numerical scheme is based on the Crank–Nicolson (C–N) method in time and Legendre-spectral method in space. In addition, we prove that the numerical scheme is unconditionally stable. Numerical examples are presented to verify validity of the proposed scheme.

An efficient numerical approach to the micromorphic hyperelasticity

A computationally efficient numerical strategy called as variational differential quadrature-finite element method (VDQFEM) is developed herein for the nonlinear analysis of hyperelastic micromorphic continua. To this end, a novel formulation including microstructure effects is proposed in which high-order tensors are written in equivalent matrix or vector forms, and is then discretized in an efficient way. This feature is utilized in the coding process of numerical method. For the solution purpose, the domain is first transformed into a number of finite elements. Thereafter, a variational discretization technique called as VDQ is applied within each element. In order to employ the VDQ method, the irregular domain of the element is transformed into the regular one using the mapping technique. Finally, the assemblage procedure is performed. This approach can be used for the analysis of bodies with arbitrary geometries. By considering several numerical examples, it is revealed that the presented size-dependent formulation and numerical solution approach have a good performance to study the large deformations of hyperelastic micromorphic bodies with complex geometries.

Implementation of an efficient method of moments for treatment of soot formation and oxidation processes in three-dimensional engine simulations

In this work, an efficient numerical approach for detailed soot particle dynamics modeling in three-dimensional engine simulation is proposed. The recently developed moment projection method is incorporated into engine computational fluid dynamics codes to handle the detailed soot particle dynamics. The main advantage of moment projection method over other methods of moments is its ability to handle the soot oxidation problem which plays a significant role in determining the evolution of soot particles in engines. The new approach has been applied to study the soot formation and oxidation processes in a dual-fueled compression ignition engine operated under different conditions. Results suggest that the new approach is highly efficient with little CPU cost induced by the treatment of the detailed soot model. The integrated engine-soot model is able to correctly capture the emission trend for soot particles under different fuel injection timings. With this new approach, a detailed physical and chemical insight into the soot formation and oxidation processes inside the engines can be achieved. The findings indicate that the proposed numerical approach is a promising framework for soot modeling in three dimensional engine simulations.

Generalized multiscale multicontinuum model for fractured vuggy carbonate reservoirs

Simulating flow in a highly heterogeneous reservoir with multiscale characteristics is computationally demanding. To tackle this problem, we propose a numerical scheme based on the Generalized Multiscale Finite Element Method (GMsFEM) and a triple-continuum model. The aim is to obtain a more efficient numerical approach that can explicitly represent the interactions among different continua. To enhance the applicability of our proposed model, we combine the Discrete Fracture Model (DFM) to model the local effects of discrete fractures. In the proposed model, the GMsFEM, as an advanced model reduction technique, enables capturing the multiscale flow dynamics. This is accomplished by systematically generating an approximation space through solving a series of local snapshot and spectral problems. The resulting eigenfunctions can pass the local features to the global level when acting as basis functions in the global coarse problems. Our goal in this paper is to further improve the accuracy of flow simulation in complicated reservoirs especially for the case when multiple discrete fractures located in single coarse neighborhood. Several numerical experiments are conducted to confirm the success of our proposed method, and a rigorous convergence proof is also given.