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Accuracy of the subsurface damage parameters calculated by the finite difference algorithm

JOURNAL OF THE EUROPEAN OPTICAL SOCIETY-RAPID PUBLICATIONS 2015年 10卷

作者： Wang, H. Fu, G. Xiao, L. Chen, H. Xiao, H. State Key Laboratory for Manufacturing Systems Engineering Mechanical Engineering School Xi’an Jiaotong UniversityXi’an Shaanxi710049 China

An important approach to characterize the full three-dimensional information of subsurface damage is to simulate the etching process of a sample reversely. The simulation starts from the morphology of the sample after the subsurface damage micro cracks being opened totally. During the etching experiment, it is possible for us to get the surface morphology at any moment. This paper presents a finite difference algorithm to simulate the morphology evolution during the etching process and then the surface's morphology of the sample at a specific time can be obtained. Comparison between the simulated morphology and the measured one provides the clue of improving the precision of the finite difference algorithm. This method is kind of the fast calculation. In addition, the accuracy of this calculation of the corrosion model needs to be ensured. In order to improve the precision of calculation, the time interval should be set as the appropriate value by comparison and analysis. In this paper, the accuracy can be calculated through comparing the simulated result with the experimental result, and the maximum error of this method can be gained.

关键词： Subsurface damage finite difference algorithm simulation accuracy

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Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators

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MATHEMATICS AND COMPUTERS IN SIMULATION 2024年 215卷 291-305页

作者： Li, Nan Wang, Xiaoping Xu, Huanying Qi, Haitao Shandong Univ Sch Math & Stat Weihai 264209 Shandong Peoples R China

The magnetohydrodynamic (MHD) flow has been concerned widely for its widespread adoption in the field of astrophysics, electronics and many other industries over the years. The purpose of this article is to introduce the variable and distributed order space fractional models to characterize the MHD flow and heat transfer of heterogeneous viscoelastic fluids in a parallel plates. Based on the central difference approximation of Riesz space fractional derivative, the Crank-Nicolson difference scheme for the governing equations is established, and the effectiveness of the algorithm is verified by two numerical examples. We examine the effects of fractional-order model parameters on the velocity and temperature, our investigation indicates that for the constant fractional model, the larger the fractional order parameter, the smaller the velocity and temperature. The variable space fractional method can be used to describe dynamic behavior with time and space dependence, while the distributed space fractional model can describe various phenomena in which the number of differential orders varies over a certain range, characterizing their complex processes over space, and it is also more suitable for simulating the fluid flow and thermal behavior of complex viscoelastic magnetic fluid. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Distributed-order space fractional model Variable-order space fractional model Magnetic field Heat transfer finite difference algorithm

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State of charge estimation by finite difference extended Kalman filter with HPPC parameters identification

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Science China(Technological Sciences) 2020年第3期63卷 410-421页

作者： HE Lin HU MinKang WEI YuJiang LIU BingJiao SHI Qin Automotive Research Institute Hefei University of TechnologyHefei 230009China School of Automotive and Transportation Engineering Hefei University of TechnologyHefei 230009China

State of charge(SOC) is a key parameter of lithium-ion battery. In this paper, a finite difference extended Kalman filter(FDEKF)with Hybrid Pulse Power Characterization(HPPC) parameters identification is proposed to estimate the SOC. The finite difference(FD) algorithm is benefit to compute the partial derivative of nonlinear function, which can reduce the linearization error generated by the extended Kalman filter(EKF). The FDEKF algorithm can reduce the computational load of controller in engineering practice without solving the Jacobian matrix. It is simple of dynamic model of lithium-ion battery to adopt a secondorder resistor-capacitor(2 RC) network, the parameters of which are identified by the HPPC. Two conditions, both constant current discharge(CCD) and urban dynamometer driving schedule(UDDS), are utilized to validate the FDEKF *** convergence rate and accuracy between the FDEKF and the EKF algorithm, it can be seen that the former is a better candidate to estimate the SOC.

关键词： state of charge lithium-ion battery parameters identification finite difference algorithm extended Kalman filter

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A Sixth-Order CEV Option Valuation algorithm on Non-uniform Spatial Grids 22nd

A Sixth-Order CEV Option Valuation Algorithm on Non-uniform ...

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22nd International Conference on Computational Science and its Applications (ICCSA)

作者： Thakoor, Nawdha Univ Mauritius Dept Math Moka Mauritius

ISBN: (纸本)9783031105364;9783031105357

Due to its ability to fit skew implied volatility profiles of market option prices, the constant elasticity of variance (CEV) model overcomes a short-coming of the constant volatility assumption used by the Black-Scholes log-normal model. Although the CEV model has an analytical formula for European options, the presence of the non-central Chi-square distribution in the formula brings instability in the computation of European option prices for certain parameter ranges. For efficient valuation of the option prices for all realistic option parameters, a sixth-order finite difference method is proposed in this work. The computational procedure employs a seven-point discretisation of the space derivatives on non-uniform grids together with a mesh-refinement technique around the option's strike price. This new technique is very fast and is shown to achieve sixth-order numerical convergence ratios. The stability of the finite difference method is demonstrated through its capability to generate accurate prices for strongly negative elasticity factors. The numerical method is thus a superior technique to existing methods for numerical computations of CEV option prices.

关键词： Option valuation Constant elasticity of variance model finite difference algorithm Non-uniform grids

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Numerical prediction of oil film shear cavitation inception considering groove structure

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2022年第20期236卷 10440-10455页

作者： Xie, Fangwei Xu, Chunjie Zheng, Xudong Li, Yongjie Gao, Kuidong Agarwal, Ramesh K. Liu, Xiumei China Univ Min & Technol Sch Mechatron Engn 1 Daxue Rd Xuzhou Jiangsu Peoples R China Jiangsu Univ Sch Mech Engn Zhenjiang Jiangsu Peoples R China Shandong Univ Sci & Technol Shandong Prov Key Lab Mine Mech Engn Qingdao Shandong Peoples R China Washington Univ Dept Mech Engn & Mat Sci St Louis MO 63110 USA

The oil film between the friction disks of the hydro-viscous clutch is taken as the research object. Considering the groove structure of the friction disks, the mathematical model of the oil film flow field is established. The finite difference algorithm is utilized to solve the velocity, the pressure, and the pressure coefficient of the oil film. The incipient position of oil film shear cavitation under different groove structure parameters is carried out. The numerical results indicate that the groove has a great influence on the oil film velocity and pressure. The oil film cavitation inception occurs first in the upstream position of the groove area. The area fraction of cavitation inception is directly proportional to the width and depth of the groove and inversely proportional to the section parameter and inclination angle of the groove. This research provides an efficient and accurate method for predicting the oil film shear cavitation inception.

关键词： hydro-viscous clutch oil film groove structure cavitation inception finite difference algorithm

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Numerical study of pulsatile non-Newtonian blood flow and heat transfer in small vessels under a magnetic field

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INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER 2022年 133卷 105930-105930页

作者： Wang, Xiaoping Qiao, Yanli Qi, Haitao Xu, Huanying Shandong Univ Sch Math & Stat Weihai 264209 Shandong Peoples R China

The purpose of this study is to analyze the impact of magnetic field on the unsteady blood flow pass a small vessel with a pulsatile pressure gradient by treating blood as a non-Newtonian fluid, which can be described by Maxwell fluid model with fractional derivative. Also the heat transfer characteristics of the flow arising out of radiative heat flux, viscous dissipation, and electromagnetic coupling is considered. We developed a finite difference algorithm to derive the numerical solutions of the nonlinear and coupled governing equations of velocity and temperature. The stability and convergence of the numerical algorithm are tested, and it is found to be stable and convergent. The influence of various significant dynamics parameters on velocity, flow rate and temperature are deeply discussed. It is indicated that, compared with the fractional Maxwell fluid model, Newtonian fluid dynamics underestimate the velocity and temperature of blood. Applying a magnetic field or increasing thermal radiation is conducive to give a higher temperature, but they have the opposite effect on velocity and flow rate, that is, the imposed magnetic field leads to a decrease of flow rate, while on the contrary, thermal radiation will enhance the flow rate.

关键词： Blood flow Magnetic field Heat transfer Fractional viscoelastic fluid model finite difference algorithm

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Differentiation via Logarithmic Expansions

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2020年第1期37卷

作者： Fu, Michael C. Heidergott, Bernd Leahu, Haralambie Vazquez-Abad, Felisa J. Univ Maryland Smith Sch Business College Pk MD 20742 USA Univ Maryland Inst Syst Res College Pk MD 20742 USA Vrije Univ Amsterdam Dept Econometr & Operat Res Amsterdam Netherlands Univ Amsterdam Dept Math Amsterdam Netherlands CUNY Hunter Coll Dept Comp Sci New York NY 10021 USA Univ Melbourne Comp & Informat Syst Melbourne Vic Australia

In this note, we introduce a new finite difference approximation called the Black-Box Logarithmic Expansion Numerical Derivative (BLEND) algorithm, which is based on a formal logarithmic expansion of the differentiation operator. BLEND capitalizes on parallelization and provides derivative approximations of arbitrary precision, i.e., our analysis can be used to determine the number of terms in the series expansion to guarantee a specified number of decimal places of accuracy. Furthermore, in the vector setting, the complexity of the resulting directional derivative is independent of the dimension of the parameter.

关键词： finite difference algorithm numerical differentiation Taylor series expansions sensitivity analysis directional derivative

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Computational analysis of turbulent flow through an eccentric annulus under different temperature conditions

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INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW 2018年第9期28卷 2189-2207页

作者： Ulker, Erman Korkut, Sila Ovgu Sorgun, Mehmet Izmir Katip Celebi Univ Fac Engn & Architecture Dept Civil Engn Izmir Turkey Izmir Katip Celebi Univ Fac Engn & Architecture Dept Engn Sci Izmir Turkey

Purpose The purpose of this paper is to solve Navier-Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms. Design/methodology/approach A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one. Findings The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop. Originality/value The originality of this work is that Navier-Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.

关键词： Temperature Convergence analysis finite difference algorithm Navier-Stokes equations Annulus

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Higher-order boundary and rough surface treatment of the MMPE model in the evaluation of scattering effects

Higher-order boundary and rough surface treatment of the MMP...

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作者： Tan, Yi Ling Naval Postgraduate School

学位级别：硕士

This research aims to improve the Monterey-Miami Parabolic Equation model (MMPE) by incorporating a higher-order hybrid boundary treatment and Fred D. Tappert’s field transformational model to add surface scattering to the existing models. The impact of these two additions is investigated for improvements in accuracy and stability to the current MMPE model under rough surface conditions. Both models were treated with a Pierson-Moskowitz rough surface spectrum. It was hoped that the hybrid model would provide a reduction of the phase errors inherent to the MMPE at long range; however, no improvements were seen, and the sensitivity to depth mesh size was not reduced. This could be the result of errors in the derivation of the higher-order algorithm. The transformational model used Tappert’s field transformation to incorporate surface scattering and is thought to perform better when compared with the hybrid model by capturing higher modes of propagation. The inclusion of rough surface scattering in both models was evaluated for energy transmission across the air/water interface and beam dispersion. It was observed that the rough surface had minimal impact on energy transmission.

关键词： Acoustic propagation rough sea surface scattering acoustic scattering split-step Fourier algorithm finite difference algorithm

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Kernel Density Estimation on a Linear Network

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SCANDINAVIAN JOURNAL OF STATISTICS 2017年第2期44卷 324-345页

作者： McSwiggan, Greg Baddeley, Adrian Nair, Gopalan Univ Western Australia Sch Math & Stat Nedlands WA Australia Curtin Univ Dept Math & Stat GPO Box U1987 Perth WA 6845 Australia

This paper develops a statistically principled approach to kernel density estimation on a network of lines, such as a road network. Existing heuristic techniques are reviewed, and their weaknesses are identified. The correct analogue of the Gaussian kernel is the heat kernel', the occupation density of Brownian motion on the network. The corresponding kernel estimator satisfies the classical time-dependent heat equation on the network. This diffusion estimator' has good statistical properties that follow from the heat equation. It is mathematically similar to an existing heuristic technique, in that both can be expressed as sums over paths in the network. However, the diffusion estimate is an infinite sum, which cannot be evaluated using existing algorithms. Instead, the diffusion estimate can be computed rapidly by numerically solving the time-dependent heat equation on the network. This also enables bandwidth selection using cross-validation. The diffusion estimate with automatically selected bandwidth is demonstrated on road accident data.

关键词： bandwidth selection diffusion equal-split kernels finite difference algorithm heat equation heat kernel intensity road accidents spatial point process

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