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Journal of Computational Mathematics 2024年第2期42卷 432-453页

作者： Mahboub Baccouch Department of Mathematics University of Nebraska at OmahaOmaha NE 68182USA

In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.

关键词： Boundary-value problems finite-difference method Additive white noise Wiener process Mean-square convergence Wong-Zakai approximation

Numerical Solution of a Problem of Thermal Stresses of a Magnetothermoelastic Cylinder with Rotation by finite-difference method

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Computers, Materials & Continua 2021年第9期68卷 3339-3352页

作者： F.S.Bayones A.M.Abd-Alla A.M.Farhan Department of Mathematics and Statistics College of ScienceTaif UniversityTaif21944Saudi Arabia Department of Mathematics Faculty of ScienceSohag UniversityEgypt Physics Department Faculty of ScienceJazan UniversityJazanSaudi Arabia Physics Department Faculty of ScienceZagazig UniversityZagazigEgypt

The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.

关键词： Thermoelasticity thermal stress finite-difference method non-homogeneous material rotation magnetic field

P-and S-wavefield simulations using both the firstand second-order separated wave equations through a high-order staggered grid finite-difference method

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Earthquake Science 2013年第2期26卷 83-98页

作者： Chao-ying Bai Xin Wang Cai-xia Wang Department of Geophysics College of Geology Engineering and Geomatics Chang'an University Institute of Computing Geophysics Chang'an University

In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations： the first-order （velocity-stress） and the second- order （displacement-stress） separate elastic wave equa- tions, with the first-order （velocity-stress） and the second- order （displacement-stress） full （or mixed） elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.

关键词： finite-difference method Staggeredgrid First-order separate elastic wave equation Second-order separate elastic wave equation Multiple arrival tracking

Construction of Conservative Numerical Fluxes for the Entropy Split method

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Communications on Applied Mathematics and Computation 2023年第2期5卷 653-678页

作者： Björn Sjögreen H.C.Yee Multid Analyses AB GothenburgSweden NASA Ames Research Center Moffett FieldCA 94035USA

The entropy split method is based on the physical entropies of the thermally perfect gas Euler equations.The Euler flux derivatives are approximated as a sum of a conservative portion and a non-conservative portion in conjunction with summation-by-parts(SBP)difference boundary closure of(Gerritsen and Olsson in J Comput Phys 129:245-262,1996;Olsson and Oliger in RIACS Tech Rep 94.01,1994;Yee et al.in J Comp Phys 162:33-81,2000).Sj?green and Yee(J Sci Comput)recently proved that the entropy split method is entropy conservative and stable.Stand-ard high-order spatial central differencing as well as high order central spatial dispersion relation preserving(DRP)spatial differencing is part of the entropy stable split methodol-ogy framework.The current work is our first attempt to derive a high order conservative numerical flux for the non-conservative portion of the entropy splitting of the Euler flux derivatives.Due to the construction,this conservative numerical flux requires higher oper-ations count and is less stable than the original semi-conservative split method.However,the Tadmor entropy conservative(EC)method(Tadmor in Acta Numerica 12:451-512,2003)of the same order requires more operations count than the new construction.Since the entropy split method is a semi-conservative skew-symmetric splitting of the Euler flux derivative,a modified nonlinear filter approach of(Yee et al.in J Comput Phys 150:199-238,1999,J Comp Phys 162:3381,2000;Yee and Sj?green in J Comput Phys 225:910934,2007,High Order Filter methods for Wide Range of Compressible flow Speeds.Proceedings of the ICOSAHOM09,June 22-26,Trondheim,Norway,2009)is proposed in conjunction with the entropy split method as the base method for problems containing shock waves.Long-time integration of 2D and 3D test cases is included to show the com-parison of these new approaches.

关键词： finite-difference method Entropy conservation Entropy splitting Shock capturing

Geometric grid network and third-order compact scheme for solving nonlinear variable coefficients 3D elliptic PDEs

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International Journal of Modeling, Simulation, and Scientific Computing 2018年第6期9卷 72-99页

作者： Navnit Jha Venu Gopal Bhagat Singh Department of Mathematics South Asian University ChanakyapuriNew Delhi 110070India The School of Mathematical Sciences University of Science and Technology of China Hefei Anhui 230026P.R.China

By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.

关键词： finite-difference method nonuniform grid compact operator monotone matrix sine-Gordon equation elliptic Allen-Cahn equation.

NUMERICAL SIMULATION OF DROP MIGRATION IN CHANNEL FLOW UNDER ZERO-GRAVITY

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Acta Mechanica Sinica 2004年第3期20卷 199-205页

作者：柳涛陆夕云 Department of Modern Mechanics University of Science and Technology of ChinaHefei 230026China

The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finite- difference method coupled with the front-tracking technique.The objectives of this study are to examine the effectiveness of the present approach for predicting the migration of drops in a shear flow and to investigate the behavior of the drop migration in the channel flow under zero-gravity.To validate the present calculation,some typical results are compared with available computational and theoretical data,which confirms that the present approach is reliable in predicting the drop migration. With respect to the drop migration in the channel flow at finite Reynolds numbers,the drops either move to an equilibrium lateral position or undergo an oscillatory motion under different conditions. The effects of some typical parameters,e.g.,the Reynolds number,the Weber number,the viscosity ratio and the density ratio of the drop fluid to the suspending medium,and the drop size,on the migration of drops are discussed and analyzed.

关键词： drop migration zero-gravity front-tracking method finite-difference method

Analysis of the thermal profile of work rolls in the hot strip rolling process

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Journal of University of Science and Technology Beijing 2004年第2期11卷 173-177页

作者： XuanliZhang JieZhang XiaoyanLi HaixiaLi GangchengWei MechanicalEngineeringSchool UniversityofScienceandTechnologyBeijingBeijing100083China MechanicalEngineeringSchool UniversityofScienceandTechnologyBeijingBeijing100083China／WuhanIron＆Steel（Group）CorporationWuhan430083China

A 2-dimension axisymmetric model was developed by the finite-differencemethod, which can be used to predict the transient temperature field and thermal profile of workrolls in the hot strip rolling process. To demonstrate the accuracy and reliability of the solutiondeveloped, the calculation results were compared with the production data of a 1700 mm hot striprolling mill and good agreement was found between them. The effect of strip width and roll shiftingon the thermal expansion of the work rolls was studied. It is found that the strip width has markedeffect on the efficient thermal crown. Initially, when the rolling strip changes from narrow towide, a bigger efficient thermal crown can be quickly achieved; afterwards, when the rolling stripchanges from wide to narrow, not only the influence of uneven wear can be reduced but also theexcessive efficient thermal crown can be avoided. It is also found that the work roll shifting has adeterminate but not obvious effect on the reduction of the efficient thermal crown, and will makethe strip shape unstable without being used properly.

关键词： hot strip rolling temperature field thermal crown finite-difference method

A Rayleigh Wave Globally Optimal Full Waveform Inversion Framework Based on GPU Parallel Computing

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Journal of Geoscience and Environment Protection 2023年第3期11卷 327-338页

作者： Zhao Le Wei Zhang Xin Rong Yiming Wang Wentao Jin Zhengxuan Cao School of Geophysics and Geomatics China University of Geosciences Wuhan China Wuhan Geo-Detection Technology Co. Ltd. Wuhan China Zhejiang Design Institute of Water Conservancy & Hydro-Electric Power Co. Ltd. Hangzhou China

Conventional gradient-based full waveform inversion (FWI) is a local optimization, which is highly dependent on the initial model and prone to trapping in local minima. Globally optimal FWI that can overcome this limitation is particularly attractive, but is currently limited by the huge amount of calculation. In this paper, we propose a globally optimal FWI framework based on GPU parallel computing, which greatly improves the efficiency, and is expected to make globally optimal FWI more widely used. In this framework, we simplify and recombine the model parameters, and optimize the model iteratively. Each iteration contains hundreds of individuals, each individual is independent of the other, and each individual contains forward modeling and cost function calculation. The framework is suitable for a variety of globally optimal algorithms, and we test the framework with particle swarm optimization algorithm for example. Both the synthetic and field examples achieve good results, indicating the effectiveness of the framework. .

关键词： Full Waveform Inversion finite-difference method Globally Optimal Framework GPU Parallel Computing Particle Swarm Optimization

Numerical Analysis of Moisture Influential Depth in Concrete and Its Application in Durability Design

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Tsinghua Science and Technology 2008年第S1期13卷 7-12页

作者：李春秋李克非陈肇元 Department of Civil Engineering Tsinghua University

Determining the moisture influential depth in concrete under drying-wetting cycles is of great interest for investigation of chloride ion transport and thus the initiation of reinforcement corrosion. In this paper, the moisture transport processes during drying and wetting are modeled by diffusion and absorption. A predictor-corrector implicit scheme of finite difference method is used to solve the partial differential equations. The stability of moisture influential depth is then analyzed with the available numerical tool for both initially saturate and unsaturated concretes. The concept of equilibrium time ratio is proposed for drying-wetting cycles by the balance between water loss and intake during drying and wetting. According to this time ratio, drying-wetting cycles are classified into drying-dominated, wetting-dominated, and equilibrium ones. For drying-dominated cycles, the drying front will penetrate gradually into material while the influential depth is determined by wetting; for wetting-dominated cycles, the wetting front will progress into material while the influential depth is determined by drying. This classification has strong engineering implication and can give a more rational division of convection and diffusion zones of chloride ion transport. The case of concrete in marine splash zone is investigated to illustrate the application of influential depth in durability design of concrete structures.

关键词： concrete chloride dying-wetting cycles influential depth finite-difference method service life

DIFFRACTION OF A SOLITARY WAVE BY A THIN WEDGE

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Acta Mechanica Sinica 1988年第3期4卷 201-210页

作者： Chen Xuenong Liu Yingzhong Department of Naval Architecture and Ocean Engineering, Shanghai Jiaotong University Department of Naval Architecture and Ocean Engineering Shanghai Jiaotong University Shanghai China

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when theincident solitary wave is directed along the wedge axis. The method of multiple scales is extended to thisproblem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary andinitial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithmin which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paperare found to corroborate the Melville’s experiments not only qualitatively but also quantitatively. Themaximum run-up of our results agrees well with Funakoshi’s numerical one but it is considerably larger thanthat in Melville’s experiment. An important reason for this discrepancy is believed to be the effect of viscousboundary layer on the vertical side wall.

关键词： solitary wave Mach reflexion multiple-scale method, two-dimensional KdV equation finite-difference method