High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of ...High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).展开更多
In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as...In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.展开更多
In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model(HOIM) is utilized to describe the...In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model(HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors(PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.展开更多
Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with ...Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.展开更多
Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuz...Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.展开更多
The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order differ...The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.展开更多
In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident bou...In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.展开更多
A high-order splitting scheme for the advection-diffusion equation of pollutants is proposed in this paper. The multidimensional advection-diffusion equation is splitted into several one-dimensional equations that are...A high-order splitting scheme for the advection-diffusion equation of pollutants is proposed in this paper. The multidimensional advection-diffusion equation is splitted into several one-dimensional equations that are solved by the scheme. Only three spatial grid points are needed in each direction and the scheme has fourth-order spatial accuracy. Several typically pure advection and advection-diffusion problems are simulated. Numerical results show that the accuracy of the scheme is much higher than that of the classical schemes and the scheme can he efficiently solved with little programming effort.展开更多
The femtosecond filamentation in the classical and high-order Kerr （HOK） models is numerically investigated by adopting multi-photon ionization （MPI） cross section with different values. It is found that in the ca...The femtosecond filamentation in the classical and high-order Kerr （HOK） models is numerically investigated by adopting multi-photon ionization （MPI） cross section with different values. It is found that in the case that the MPI cross section is relatively small, there exists a big difference between the electron density as well as clamped intensity calculated in the classical model and those calculated in the HOK one, while in the case that the MPI cross section is relatively large, the electron density and clamped intensity calculated in the two models are nearly in agreement with each other, and under this circumstance, even if the higher-order nonlinear terms do exist, the free-charge generation and the associated defocusing in a filament are enough to mask their effects. The different behaviors of the maximum intensity and on-axis electron density at the collapse position with the pulse duration provides an approach to determine which effect plays the dominant defocusing role. These results demonstrate that it is ionization that results in the difference between the two models.展开更多
Efficient and robust solution strategies are developed for discontinuous Galerkin （DG） discretization of the Navier-Stokes （NS） and Reynolds-averaged NS （RANS） equations on structured/unstructured hybrid meshes....Efficient and robust solution strategies are developed for discontinuous Galerkin （DG） discretization of the Navier-Stokes （NS） and Reynolds-averaged NS （RANS） equations on structured/unstructured hybrid meshes. A novel line-implicit scheme is devised and implemented to reduce the memory gain and improve the computational eificiency for highly anisotropic meshes. A simple and effective technique to use the mod- ified Baldwin-Lomax （BL） model on the unstructured meshes for the DC methods is proposed. The compact Hermite weighted essentially non-oscillatory （HWENO） limiters are also investigated for the hybrid meshes to treat solution discontinuities. A variety of compressible viscous flows are performed to examine the capability of the present high- order DG solver. Numerical results indicate that the designed line-implicit algorithms exhibit weak dependence on the cell aspect-ratio as well as the discretization order. The accuracy and robustness of the proposed approaches are demonstrated by capturing com- plex flow structures and giving reliable predictions of benchmark turbulent problems.展开更多
A novel general stability analysis scheme based on a non-Lyapunov framework is explored. Several easy-to-check sufficient conditions for exponential p-stability are formulated in terms of M-matrices. Stability analysi...A novel general stability analysis scheme based on a non-Lyapunov framework is explored. Several easy-to-check sufficient conditions for exponential p-stability are formulated in terms of M-matrices. Stability analysis of applied second-order It? equations with delay is provided as well. The linearization technique, in combination with the tests obtained in this paper, can be used for local stability analysis of a wide class of nonlinear stochastic differential equations.展开更多
We investigate high-order harmonic generation （HHG） ofLi＋ ion driven by an intense infrared （IR） laser field in corn-bination with a weak XUV pulse. To achieve this, we first construct an accurate single-active e...We investigate high-order harmonic generation （HHG） ofLi＋ ion driven by an intense infrared （IR） laser field in corn-bination with a weak XUV pulse. To achieve this, we first construct an accurate single-active electron angular-momentumdependent model potential of Li＋ ion, by which the accurate singlet energy levels of Li＋ for the ground state and excited states with higher quantum numbers can be obtained. Then, we solve numerically the three dimensional time-dependent Schr/Sdinger equation of Li＋ ion by means of the generalized pseudospectral method to obtain HHG. Our results show that the strength of assisted XUV is not amplified during the harmonic generation process, but the yield of HHG power spectrum in the whole plateau has a significant enhancement. Furthermore, the optimal phase delay between the IR and XUV pulses allows the production of ultrabroadband supercontinuum spectra. By superposing some harmonics, a strong new single 27-attosecond ultrashort pulse can be obtained.展开更多
In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The valid...In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.展开更多
In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an outp...In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.展开更多
We numerically investigate the high-order harmonic generation with two-colour optical field, taking into consideration the propagation effects. Some harmonics can be dramatically enhanced at a certain delay between th...We numerically investigate the high-order harmonic generation with two-colour optical field, taking into consideration the propagation effects. Some harmonics can be dramatically enhanced at a certain delay between the fundamental pulse and its second harmonics. Choice of the enhanced harmonics can be realised by changing the time delay between the two laser pulses.展开更多
Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the ...Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the enhanced high-order spectral method,which solves the fully nonlinear potential flow equations with a free surface within periodic unbounded 3-D domains. The numerical model is validated against a fifth-order Stokes solution for regular waves. Laboratory-scale freak waves are observed with wave components having equal amplitudes. Investigations of the appearance and propagation of freak-wave events in a 3-D open wavefield defined by a directional wave spectrum are then realized.展开更多
In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of ...In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.展开更多
Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wa...Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wave interaction is evaluated by comparison of the calculated results with experimental and theoretical data. Based on the modification of the Longuet-Higgins model, four wave models for generation of freak waves （a. extreme wave model ＋ random wave model; b. extreme wave model ＋ regular wave model; e. phase interval modulation wave focusing model; d. number modulation wave focusing model with the same phase） are proposed. By use of different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time.展开更多
A global transport model is proposed in which a multimoment constrained finite volume （MCV） scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom （DOFs） within each element to ...A global transport model is proposed in which a multimoment constrained finite volume （MCV） scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom （DOFs） within each element to build a 2D cubic reconstruction polynomial. The time evolution equations for DOFs are derived from constraint conditions on moments of line-integrated averages （LIA）, point values （PV）, and values of first-order derivatives （DV）. The Yin-Yang grid eliminates polar singularities and results in a quasi-uniform mesh. A limiting projection is designed to remove nonphysical oscillations around discontinuities. Our model was tested against widely used benchmarks; the competitive results reveal that the model is accurate and promising for developing general circulation models.展开更多
文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).
基金supported by the General Program (No.60774022)the State Key Program of National Natural Science Foundation of China(No.60834001)the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University (No.RCS2009ZT011)
文摘In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.
基金supported by National Basic Research Program of China(973 Program)(No.2012CB316400)National Natural Science Foundation of China(Nos.61171034 and 61273134)
文摘In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model(HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors(PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.
基金supported by China Scholarship Council and partially by the National "863" Program of China under contract No. 2007AA06Z218.
文摘Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.
基金supported by the National Natural Science Foundation of China(61309022)
文摘Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.
基金Foundation items： National Basic Research Program of China （2009CB723801） National Natural Science Foundation of China （11072259）
文摘The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51309050 and 51221961)the National Basic Research Program of China(973 Program,Grant Nos.2013CB036101 and 2011CB013703)
文摘In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.
文摘A high-order splitting scheme for the advection-diffusion equation of pollutants is proposed in this paper. The multidimensional advection-diffusion equation is splitted into several one-dimensional equations that are solved by the scheme. Only three spatial grid points are needed in each direction and the scheme has fourth-order spatial accuracy. Several typically pure advection and advection-diffusion problems are simulated. Numerical results show that the accuracy of the scheme is much higher than that of the classical schemes and the scheme can he efficiently solved with little programming effort.
基金supported by the National Basic Research Program of China(Grant No.2013CB922200)the National Natural Science Foundation of China(Grant Nos.11034003 and 11474129)+1 种基金the Research Fund for the Doctoral Program of Higher Education in China(Grant No.20130061110021)the Graduate Innovation Fund of Jilin University,China(Grant No.2015091)
文摘The femtosecond filamentation in the classical and high-order Kerr （HOK） models is numerically investigated by adopting multi-photon ionization （MPI） cross section with different values. It is found that in the case that the MPI cross section is relatively small, there exists a big difference between the electron density as well as clamped intensity calculated in the classical model and those calculated in the HOK one, while in the case that the MPI cross section is relatively large, the electron density and clamped intensity calculated in the two models are nearly in agreement with each other, and under this circumstance, even if the higher-order nonlinear terms do exist, the free-charge generation and the associated defocusing in a filament are enough to mask their effects. The different behaviors of the maximum intensity and on-axis electron density at the collapse position with the pulse duration provides an approach to determine which effect plays the dominant defocusing role. These results demonstrate that it is ionization that results in the difference between the two models.
基金Project supported by the National Basic Research Program of China(No.2009CB724104)
文摘Efficient and robust solution strategies are developed for discontinuous Galerkin （DG） discretization of the Navier-Stokes （NS） and Reynolds-averaged NS （RANS） equations on structured/unstructured hybrid meshes. A novel line-implicit scheme is devised and implemented to reduce the memory gain and improve the computational eificiency for highly anisotropic meshes. A simple and effective technique to use the mod- ified Baldwin-Lomax （BL） model on the unstructured meshes for the DC methods is proposed. The compact Hermite weighted essentially non-oscillatory （HWENO） limiters are also investigated for the hybrid meshes to treat solution discontinuities. A variety of compressible viscous flows are performed to examine the capability of the present high- order DG solver. Numerical results indicate that the designed line-implicit algorithms exhibit weak dependence on the cell aspect-ratio as well as the discretization order. The accuracy and robustness of the proposed approaches are demonstrated by capturing com- plex flow structures and giving reliable predictions of benchmark turbulent problems.
文摘A novel general stability analysis scheme based on a non-Lyapunov framework is explored. Several easy-to-check sufficient conditions for exponential p-stability are formulated in terms of M-matrices. Stability analysis of applied second-order It? equations with delay is provided as well. The linearization technique, in combination with the tests obtained in this paper, can be used for local stability analysis of a wide class of nonlinear stochastic differential equations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11465016,11664035,11764038,and 11765018)the Foundation of Northwest Normal University,China(Grant No.NWNU-LKQN-17-1)
文摘We investigate high-order harmonic generation （HHG） ofLi＋ ion driven by an intense infrared （IR） laser field in corn-bination with a weak XUV pulse. To achieve this, we first construct an accurate single-active electron angular-momentumdependent model potential of Li＋ ion, by which the accurate singlet energy levels of Li＋ for the ground state and excited states with higher quantum numbers can be obtained. Then, we solve numerically the three dimensional time-dependent Schr/Sdinger equation of Li＋ ion by means of the generalized pseudospectral method to obtain HHG. Our results show that the strength of assisted XUV is not amplified during the harmonic generation process, but the yield of HHG power spectrum in the whole plateau has a significant enhancement. Furthermore, the optimal phase delay between the IR and XUV pulses allows the production of ultrabroadband supercontinuum spectra. By superposing some harmonics, a strong new single 27-attosecond ultrashort pulse can be obtained.
基金support of the National Natural Science Foundation of China (Grants 11501495, 51541912, 51409227)the Natural Science Foundation of Jiangsu Province, China (Grants BK20130436, BK20150436)+1 种基金the Postdoctoral Science Foundation of China (Grants 2014M550310, 2015M581869, 2015T80589)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant 15KJB110025)
文摘In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.
文摘In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.
基金Project supported by Chinese Academy of Sciences,the National Natural Science Foundation (Grant Nos. 10734080,10523003,60921004,10904157,and 60978012)973 Project (Grant No. 2006CB806000)Shanghai Commission of Science and Technology(Grant Nos. 06DZ22015 and 07PJ14091)
文摘We numerically investigate the high-order harmonic generation with two-colour optical field, taking into consideration the propagation effects. Some harmonics can be dramatically enhanced at a certain delay between the fundamental pulse and its second harmonics. Choice of the enhanced harmonics can be realised by changing the time delay between the two laser pulses.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 50779004)
文摘Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the enhanced high-order spectral method,which solves the fully nonlinear potential flow equations with a free surface within periodic unbounded 3-D domains. The numerical model is validated against a fifth-order Stokes solution for regular waves. Laboratory-scale freak waves are observed with wave components having equal amplitudes. Investigations of the appearance and propagation of freak-wave events in a 3-D open wavefield defined by a directional wave spectrum are then realized.
基金Project supported by the National Basic Research Program of China (Grant No 2006CB705500)the National Natural Science Foundation of China (Grant Nos 10532060 and 10602025)+1 种基金Scientific Research Fund of Zhejiang Provincial Education Department,China (Grant No 20061634)K. C. Wong Magna Fund in Ningbo University, China
文摘In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.
基金supported by the National Natural Science Foundation of China (Grant No.50779004)
文摘Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wave interaction is evaluated by comparison of the calculated results with experimental and theoretical data. Based on the modification of the Longuet-Higgins model, four wave models for generation of freak waves （a. extreme wave model ＋ random wave model; b. extreme wave model ＋ regular wave model; e. phase interval modulation wave focusing model; d. number modulation wave focusing model with the same phase） are proposed. By use of different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time.
基金supported by National Key Technology R&D Program of China (Grant No. 2012BAC22B01)Natural Science Foundation of China (Grant Nos. 10902116, 40805045, and 41175095)Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science (Grant No. 24560187)
文摘A global transport model is proposed in which a multimoment constrained finite volume （MCV） scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom （DOFs） within each element to build a 2D cubic reconstruction polynomial. The time evolution equations for DOFs are derived from constraint conditions on moments of line-integrated averages （LIA）, point values （PV）, and values of first-order derivatives （DV）. The Yin-Yang grid eliminates polar singularities and results in a quasi-uniform mesh. A limiting projection is designed to remove nonphysical oscillations around discontinuities. Our model was tested against widely used benchmarks; the competitive results reveal that the model is accurate and promising for developing general circulation models.
