This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and t...This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory(WENO)technique as well as explicit Runge-Kutta time discretization.The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair.As soon as the entropy conservative flux is derived,the dissipation term can be added to give the semidiscrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function.The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization are implemented to obtain the fully-discrete high-order entropy stable schemes.Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes.展开更多
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
Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of...Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.展开更多
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The...This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.展开更多
A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an o...A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.展开更多
In this paper,a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients.This method is based on our previous work[11]for convection-diffusion equations,w...In this paper,a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients.This method is based on our previous work[11]for convection-diffusion equations,which relies on a special kernel-based formulation of the solutions and successive convolution.However,disadvantages appear when we extend the previous method to our equations,such as inefficient choice of parameters and unprovable stability for high-dimensional problems.To overcome these difficulties,a new kernel-based formulation is designed to approach the spatial derivatives.It maintains the good properties of the original one,including the high order accuracy and unconditionally stable for one-dimensional problems,hence allowing much larger time step evolution compared with other explicit schemes.In additional,without extra computational cost,the proposed scheme can enlarge the available interval of the special parameter in the formulation,leading to less errors and higher efficiency.Moreover,theoretical investigations indicate that it is unconditionally stable for multi-dimensional problems as well.We present numerical tests for one-and two-dimensional scalar and system,demonstrating the designed high order accuracy and unconditionally stable property of the scheme.展开更多
We propose a new method to separate different orders of an all-fiber passive Q-switching stimulated Brillouin scattering（SBS） laser. We use two fiber Bragg gratings connected by two circulators for the filtering. We...We propose a new method to separate different orders of an all-fiber passive Q-switching stimulated Brillouin scattering（SBS） laser. We use two fiber Bragg gratings connected by two circulators for the filtering. We obtain a stabilized pulse laser and measure the pulse width of different orders. The first order of SBS has a central wavelength of 1549.75 nm, an average output power of 9 mW, and a pulse width of 400 ns. The pulse width of SBS is reduced by the higher-order signals with the larger fluctuations.展开更多
基金supported by the Special Project on High-performance Computing under the National Key R&D Program(No.2016YFB0200603)Science Challenge Project(No.TZ2016002)the National Natural Science Foundation of China(Nos.91630310 and 11421101),and High-Performance Computing Platform of Peking University.
文摘This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory(WENO)technique as well as explicit Runge-Kutta time discretization.The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair.As soon as the entropy conservative flux is derived,the dissipation term can be added to give the semidiscrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function.The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization are implemented to obtain the fully-discrete high-order entropy stable schemes.Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes.
基金supported by the National Natural Science Foundation of China(Grant Nos.52272358 and 62103052)。
文摘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.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19971035).
文摘Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.
文摘This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
基金Project supported by the National Natural Science Foundation of China(Nos.11601517,11502296,61772542,and 61561146395)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.
基金supported in part by AFOSR grants FA9550-12-1-0343,FA9550-12-1-0455,FA9550-15-1-0282,NSF grant DMS-1418804supported by NSFC grant 11901555supported by NSFC grant 11871448.
文摘In this paper,a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients.This method is based on our previous work[11]for convection-diffusion equations,which relies on a special kernel-based formulation of the solutions and successive convolution.However,disadvantages appear when we extend the previous method to our equations,such as inefficient choice of parameters and unprovable stability for high-dimensional problems.To overcome these difficulties,a new kernel-based formulation is designed to approach the spatial derivatives.It maintains the good properties of the original one,including the high order accuracy and unconditionally stable for one-dimensional problems,hence allowing much larger time step evolution compared with other explicit schemes.In additional,without extra computational cost,the proposed scheme can enlarge the available interval of the special parameter in the formulation,leading to less errors and higher efficiency.Moreover,theoretical investigations indicate that it is unconditionally stable for multi-dimensional problems as well.We present numerical tests for one-and two-dimensional scalar and system,demonstrating the designed high order accuracy and unconditionally stable property of the scheme.
基金Supported by the National Natural Science Foundation of China under Grant No 61675188the Open Fund of Key Laboratory Pulse Power Laser Technology of China under Grant No SKL2016KF03
文摘We propose a new method to separate different orders of an all-fiber passive Q-switching stimulated Brillouin scattering（SBS） laser. We use two fiber Bragg gratings connected by two circulators for the filtering. We obtain a stabilized pulse laser and measure the pulse width of different orders. The first order of SBS has a central wavelength of 1549.75 nm, an average output power of 9 mW, and a pulse width of 400 ns. The pulse width of SBS is reduced by the higher-order signals with the larger fluctuations.
