This paper presents a simple approach for improving the performance of the weighted essentially nonoscillatory(WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifthor...This paper presents a simple approach for improving the performance of the weighted essentially nonoscillatory(WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifthorder WENO-JS(WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202–228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable.The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On nonuniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime,the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.展开更多
Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption ev...Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.展开更多
A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for ...A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries （KdV） equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation （nonlinear convectiondiffusion problems） and the KdV equation （single solitary and 2-solitary wave problems）, where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.展开更多
In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional...In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional relation for electromagnetic field components. Lots of characteristics are obtained for different mesh sizes and frequencies. Then the reflection coefficient caused by the non-uniform mesh can be calculated according to the theory of equivalent transmission line. By comparing it with that calculated by MWI in the uniform mesh, it is found that the evaluating error can be largely reduced and is in good agreement with that directly computed by FDTD method. And this extension of MWI can be used in the error analysis of complex mesh.展开更多
由电磁学的基本规律麦克斯韦方程差分形式即时域有限差分(Finite Different Time Domain,FDTD)导出不均匀网格的FDTD差分形式,即不均匀网格的时域有限差分法(Non Uniform Grid Finite Different TimeDomain,NU-FDTD),并提出了在腔体孔...由电磁学的基本规律麦克斯韦方程差分形式即时域有限差分(Finite Different Time Domain,FDTD)导出不均匀网格的FDTD差分形式,即不均匀网格的时域有限差分法(Non Uniform Grid Finite Different TimeDomain,NU-FDTD),并提出了在腔体孔缝电磁耦合分析中采用NU-FDTD时,网格和时间步长划分的原则是:导体边界采用局部均匀细网格法,其它空间采用渐变不均匀法。实验结果表明,这种方法不仅节省计算时间,而且精度高。展开更多
基金supported by the National Natural Science Foundation of China (Grant 11672160)the National Key Research and Development Program of China (Grant 2016YF A0401200)
文摘This paper presents a simple approach for improving the performance of the weighted essentially nonoscillatory(WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifthorder WENO-JS(WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202–228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable.The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On nonuniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime,the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.
基金supported by the grants of National Natural Science Foundation of China(42374219,42127804)the Qilu Young Researcher Project of Shandong University.
文摘Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.
基金supported by the Research Grants Council of Hong Kong (No. 522007)the National Marine Public Welfare Research Projects of China (No. 201005002)
文摘A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries （KdV） equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation （nonlinear convectiondiffusion problems） and the KdV equation （single solitary and 2-solitary wave problems）, where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.
文摘In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional relation for electromagnetic field components. Lots of characteristics are obtained for different mesh sizes and frequencies. Then the reflection coefficient caused by the non-uniform mesh can be calculated according to the theory of equivalent transmission line. By comparing it with that calculated by MWI in the uniform mesh, it is found that the evaluating error can be largely reduced and is in good agreement with that directly computed by FDTD method. And this extension of MWI can be used in the error analysis of complex mesh.
文摘由电磁学的基本规律麦克斯韦方程差分形式即时域有限差分(Finite Different Time Domain,FDTD)导出不均匀网格的FDTD差分形式,即不均匀网格的时域有限差分法(Non Uniform Grid Finite Different TimeDomain,NU-FDTD),并提出了在腔体孔缝电磁耦合分析中采用NU-FDTD时,网格和时间步长划分的原则是:导体边界采用局部均匀细网格法,其它空间采用渐变不均匀法。实验结果表明,这种方法不仅节省计算时间,而且精度高。
