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
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
In order to know the distribution of magnetic field in a novel flow control of mold (NFC Mold) and to provide the experimental data for the electromagnetic structure design and the analysis of flow control in continuo...In order to know the distribution of magnetic field in a novel flow control of mold (NFC Mold) and to provide the experimental data for the electromagnetic structure design and the analysis of flow control in continuous casting mold, the magnetic field in a NFC Mold were measured by Tesla meter of Model CT-3. The method of vector synthesis was adopted in the measurement of magnetic fields. The results showed that the magnetic field in the NFC Mold was composed of two main magnetic areas that were symmetrical. Although there was leaking magnetic flux between the lower surface of the upper pole and the upper surface of the lower pole on the sides, it was restrained by the main magnetic fields effectively. Therefore the NFC Mold was more preferably satisfied to be used in controlling the molten steel flow in continuous casting mold.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
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.
基金the National Natural Science Foundation of China (Grant No. 59734080), the National Key Basic Research and Development Programme of China (Grant No. G1998061510) and the Project of National High Te
文摘In order to know the distribution of magnetic field in a novel flow control of mold (NFC Mold) and to provide the experimental data for the electromagnetic structure design and the analysis of flow control in continuous casting mold, the magnetic field in a NFC Mold were measured by Tesla meter of Model CT-3. The method of vector synthesis was adopted in the measurement of magnetic fields. The results showed that the magnetic field in the NFC Mold was composed of two main magnetic areas that were symmetrical. Although there was leaking magnetic flux between the lower surface of the upper pole and the upper surface of the lower pole on the sides, it was restrained by the main magnetic fields effectively. Therefore the NFC Mold was more preferably satisfied to be used in controlling the molten steel flow in continuous casting mold.
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.
