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A UNIFORM HIGH-ORDER METHOD FOR A SINGULAR PERTURBATION PROBLEM IN CONSERVATIVE FORM
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作者 吴启光 孙晓弟 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第10期909-916,共8页
A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order pro... A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given. 展开更多
关键词 uniform high-order method singular perturbation problem initial value problem
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Explicit High-Order Method to Solve Coupled Nonlinear Schrödinger Equations
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作者 Khadijah Alamoudi Mohmmad Said Hammoudeh 《Advances in Pure Mathematics》 2021年第5期472-482,共11页
Models of the coupled nonlinear Schr<span style="white-space:nowrap;">&#246;</span>dinger equations submit various critical physical phenomena with a typical equation for optical fibres with ... Models of the coupled nonlinear Schr<span style="white-space:nowrap;">&#246;</span>dinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">&#246;</span>dinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">&#246;</span>dinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics. 展开更多
关键词 Coupled Nonlinear Schrodinger Equations Sixth Order method Interaction of Two Solitons Compact Finite Difference Runge-Kutta of Order 4 method
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High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models
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作者 Wei Zheng Yan Xu 《Communications on Applied Mathematics and Computation》 EI 2024年第1期372-398,共27页
In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe... In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving. 展开更多
关键词 Chemotaxis models Local discontinuous Galerkin(LDG)scheme Convex splitting method Variant energy quadratization method Scalar auxiliary variable method Spectral deferred correction method
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Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows
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作者 Ruihan Guo Yinhua Xia 《Communications on Applied Mathematics and Computation》 EI 2024年第1期625-657,共33页
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the... Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows. 展开更多
关键词 Two-phase incompressible flows Fully-decoupled high-order accurate Linear implicit Spectral deferred correction method Local discontinuous Galerkin method
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Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse
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作者 王源 李玉龙 +7 位作者 乔月 高娜 郭福明 陈洲 赫兰海 杨玉军 赵曦 王俊 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期433-440,共8页
We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position... We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns. 展开更多
关键词 high-order harmonic semi-integer-order spectra shift inhomogeneous field
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Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field
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作者 胡杰 王一琛 +6 位作者 景秋霜 姜威 王革文 赵逸文 肖礴 梁红静 马日 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第5期453-457,共5页
High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(... High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions. 展开更多
关键词 high-order harmonic generation Coulomb effect elliptically polarized intense laser field
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High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface
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作者 莫亚枭 张朝金 +2 位作者 鹿力成 孙启航 马力 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期459-470,共12页
Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a movi... Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves. 展开更多
关键词 high-order Bragg scattering frequency shift low-frequency acoustic field moving rough sea surface
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High-order harmonic generation of ZnO crystals in chirped and static electric fields
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作者 张玲玉 何永林 +5 位作者 谢卓璇 高芳艳 徐清芸 葛鑫磊 罗香怡 郭静 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期335-343,共9页
High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduce... High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed. 展开更多
关键词 high-order harmonic generation the semiconductor Bloch equation k-resolved inter-band harmonic spectrum four-step semiclassical model
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Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles
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作者 Wei Wang Yuchen Wang +2 位作者 Shiwei Chen Yongcang Guo Zhongjiao Shi 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第4期282-294,共13页
This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theor... This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations. 展开更多
关键词 Spinning glide-guided projectile Attitude control Sliding mode disturbance observer Fixed-time stable theory high-order fully actuated approach
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High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations
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作者 Xingying Li Yin Ji 《Journal of Applied Mathematics and Physics》 2024年第7期2452-2466,共15页
In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton ... In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons. 展开更多
关键词 Konopelchenko-Dubrovsky Equations Hirota Bilinear method M-Order Lump Solutions high-order Hybrid Solutions Interaction Behavior
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High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients
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作者 Xiyu Tan Xingying Li 《Journal of Applied Mathematics and Physics》 2024年第8期2738-2763,共26页
In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton sol... In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions. 展开更多
关键词 Variable-Coefficient YTSF Equation Hirota Bilinear method N-SOLITON Hybrid Solution
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High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations 被引量:1
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作者 Jie Du Yang Yang 《Communications on Applied Mathematics and Computation》 2023年第1期31-63,共33页
In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical ... In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme. 展开更多
关键词 Weighted essentially non-oscillatory scheme Finite difference method Stiff source DETONATIONS Bound-preserving CONSERVATIVE
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High-Order Discontinuous Galerkin Method for Hovering Rotor Simulations Based on a Rotating Reference Frame
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作者 ZHANG Tao Lü Hongqiang +1 位作者 QIN Wanglong CHEN Zhengwu 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2019年第1期57-70,共14页
An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. I... An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction. 展开更多
关键词 high-order method(HOM) discontinuous Glaerkin method(DGM) Euler equation hovering rotor simulation tip vortex
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HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM 被引量:2
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作者 刘梅林 刘少斌 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2008年第3期208-213,共6页
The Runge-Kutta discontinuous Galerkin finite element method (RK-DGFEM) is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ... The Runge-Kutta discontinuous Galerkin finite element method (RK-DGFEM) is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method (FVM). RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic (TM) wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases. 展开更多
关键词 Runge-Kutta methods finite element methods resonators basis function of high-order polynomial
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High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation
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作者 Andrew Christlieb Matthew Link +1 位作者 Hyoseon Yang Ruimeng Chang 《Communications on Applied Mathematics and Computation》 2023年第1期116-142,共27页
In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the targe... In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings. 展开更多
关键词 Semi-Lagrangian methods WENO schemes high-order splitting methods Non-polynomial basis Vlasov equation Vlasov-Poisson system
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High-order targeted essentially non-oscillatory scheme for two-fluid plasma model 被引量:1
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作者 Yuhang HOU Ke JIN +1 位作者 Yongliang FENG Xiaojing ZHENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第6期941-960,共20页
The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model,which cannot describe certain nonequilibrium phenomena by finite collisions of particles,decreasing the fidelity of the sol... The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model,which cannot describe certain nonequilibrium phenomena by finite collisions of particles,decreasing the fidelity of the solution.Based on an alternative formulation of the targeted essentially non-oscillatory(TENO)scheme,a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems.The numerical flux is constructed by the TENO interpolation of the solution and its derivatives,instead of being reconstructed from the physical flux.The present scheme is used to solve the two sets of Euler equations coupled with Maxwell's equations.The numerical methods are verified by several classical plasma problems.The results show that compared with the original TENO scheme,the present scheme can suppress the non-physical oscillations and reduce the numerical dissipation. 展开更多
关键词 PLASMA high-order scheme targeted essentially non-oscillatory(TENO)scheme two-fluid model
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Laser shaping and optical power limiting of pulsed Laguerre–Gaussian laser beams of high-order radial modes in fullerene C60 被引量:1
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作者 李杰 管文慧 +3 位作者 袁烁 赵亚男 孙玉萍 刘纪彩 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第2期273-280,共8页
We study the strong nonlinear optical dynamics of nanosecond pulsed Laguerre–Gaussian laser beams of high-order radial modes with zero orbital angular momentum propagating in the fullerene C60molecular medium. It is ... We study the strong nonlinear optical dynamics of nanosecond pulsed Laguerre–Gaussian laser beams of high-order radial modes with zero orbital angular momentum propagating in the fullerene C60molecular medium. It is found that the spatiotemporal profile of the incident pulsed Laguerre–Gaussian laser beam is strongly reshaped during its propagation in the C60molecular medium. The centrosymmetric temporal profile of the incident pulse gradually evolves into a noncentrosymmetric meniscus shape, and the on-axis pulse duration is clearly depressed. Furthermore, the field intensity is distinctly attenuated due to the field-intensity-dependent reverse saturable absorption, and clear optical power limiting behavior is observed for different orders of the input pulsed Laguerre–Gaussian laser beams before the takeover of the saturation effect;the lower the order of the Laguerre–Gaussian beam, the lower the energy transmittance. 展开更多
关键词 pulsed Laguerre–Gaussian laser beams high-order radial mode optical power limiting reverse saturable absorption
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High-order discontinuous Galerkin method for applications to multicomponent and chemically reacting flows 被引量:2
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作者 Yu Lv Matthias Ihme 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2017年第3期486-499,共14页
This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been... This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows. 展开更多
关键词 Discontinuous Galerkin method high-order schemes Reacting flows Multicomponent flows
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A high-order accurate wavelet method for solving Schrdinger equations with general nonlinearity 被引量:3
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作者 Jiaqun WANG Xiaojing LIU Youhe ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第2期275-290,共16页
A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a G... A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger (NLS) equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods. 展开更多
关键词 WAVELET Galerkin method generalized nonlinear SchrSdinger (NLS) equation high-order convergence
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A force control high-order single-step-β method (HSM) for substructure pseudo-dynamic testing 被引量:1
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作者 陈再现 王焕定 +1 位作者 王凤来 周广春 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第6期873-879,共7页
This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept... This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties. 展开更多
关键词 high-order single-step-β method(HSM) force control equivalent shear stiffness correction full-scale model
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