The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction di...The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.展开更多
A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the solito...A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.展开更多
We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids.For spatial discretization,the classical central difference method is utilized,while the average vector field method is app...We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids.For spatial discretization,the classical central difference method is utilized,while the average vector field method is applied for time discretization.Compared with the average vector field method on the uniform mesh,the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation.This is due to the moving mesh method,which can concentrate the grid points more densely where the solution changes drastically.Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.展开更多
内孤立波(internal solitary wave,ISW)的传播扰动声速场,进而引起声场周期起伏。本文利用数值仿真的研究手段,研究了内孤立波在不同类型的初始发射角度声线的多个声线上转折区域中传播时对声场产生的周期性影响,分析了对于声线掠射角...内孤立波(internal solitary wave,ISW)的传播扰动声速场,进而引起声场周期起伏。本文利用数值仿真的研究手段,研究了内孤立波在不同类型的初始发射角度声线的多个声线上转折区域中传播时对声场产生的周期性影响,分析了对于声线掠射角度、声能量到达时间这两个物理量的起伏频率,发现利用声学参数-时间曲线两点间的斜率与差值的偶次平方的乘积(product of the slope and the even square of the difference between two points of the acoustic parameter-time curve,PSD)处理方法更容易从这两种物理量中提取到显著的声场起伏特征。此外,讨论了高阶PSD参数对声场起伏特征提取效果的影响。结果表明,合适的高阶PSD参数可以提高PSD处理方法对声场起伏特征的提取能力。展开更多
基金supported by the National Natural Science Foundation of China(Grant No.91130013)the Open Foundation of State Key Laboratory of HighPerformance Computing of China
文摘The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.
基金Project supported by the National Natural Science Foundation of China(Grant No.11161017)the National Science Foundation of Hainan Province,China(Grant No.113001)
文摘A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.
基金the National Key R&D Program of China(Grant No.2020YFA0709800)the National Natural Science Foundation of China(Grant Nos.11901577,11971481,12071481,and 12001539)+3 种基金the Natural Science Foundation of Hunan,China(Grant Nos.S2017JJQNJJ0764 and 2020JJ5652)the fund from Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(Grant No.2018MMAEZD004)the Basic Research Foundation of National Numerical Wind Tunnel Project,China(Grant No.NNW2018-ZT4A08)the Research Fund of National University of Defense Technology(Grant No.ZK19-37)。
文摘We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids.For spatial discretization,the classical central difference method is utilized,while the average vector field method is applied for time discretization.Compared with the average vector field method on the uniform mesh,the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation.This is due to the moving mesh method,which can concentrate the grid points more densely where the solution changes drastically.Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.
文摘内孤立波(internal solitary wave,ISW)的传播扰动声速场,进而引起声场周期起伏。本文利用数值仿真的研究手段,研究了内孤立波在不同类型的初始发射角度声线的多个声线上转折区域中传播时对声场产生的周期性影响,分析了对于声线掠射角度、声能量到达时间这两个物理量的起伏频率,发现利用声学参数-时间曲线两点间的斜率与差值的偶次平方的乘积(product of the slope and the even square of the difference between two points of the acoustic parameter-time curve,PSD)处理方法更容易从这两种物理量中提取到显著的声场起伏特征。此外,讨论了高阶PSD参数对声场起伏特征提取效果的影响。结果表明,合适的高阶PSD参数可以提高PSD处理方法对声场起伏特征的提取能力。
