An improved non-uniform fast Fourier transform method for radio imaging of coronal mass ejections

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.

A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

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.

Chebyshev finite spectral method with extended moving grids

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.

基于非均匀多级网格索引的矢量地图叠加分析算法

矢量地图叠加分析在实际场景使用中经常需要处理各种大规模复杂空间数据,因此算法整体分析效率的提升尤其重要。该文重点针对较大多边形对象和大量较小多边形对象的叠加分析使用场景,提出了一种有较强针对性的基于非均匀多级网格索引的矢量地图叠加分析(Non-uniform Multi-level Grid Index Overlay,NMGIO)算法,包括索引构建、网格过滤、叠加计算、拓扑构面4个步骤,通过对待分析数据集和叠加对象双向建立非均匀多级网格索引,利用数据的空间分布特点从根本上提升叠加分析效率。同时给出了算法整体时间复杂度和由C语言实现的原型系统叠加分析效果验证。

A non-uniform grid approach for high-resolution flood inundation simulation based on GPUs

In view of the frequent occurrence of floods due to climate change, and the fact that a large calculation domain, with complex land types, is required for solving the problem of the flood simulations, this paper proposes an optimized non-uniform grid model combined with a high-resolution model based on the graphics processing unit (GPU) acceleration to simulate the surface water flow process. For the grid division, the topographic gradient change is taken as the control variable and different optimization criteria are designed according to different land types. In the numerical model, the Godunov-type method is adopted for the spatial discretization, the TVD-MUSUL and Runge-Kutta methods are used to improve the model’s spatial and temporal calculation accuracies, and the simulation time is reduced by leveraging the GPU acceleration. The model is applied to ideal and actual case studies. The results show that the numerical model based on a non-uniform grid enjoys a good stability. In the simulation of the urban inundation, approximately 40%–50% of the urban average topographic gradient change to be covered is taken as the threshold for the non-uniform grid division, and the calculation efficiency and accuracy can be optimized. In this case, the calculation efficiency of the non-uniform grid based on the optimized parameters is 2–3 times of that of the uniform grid, and the approach can be adopted for the actual flood simulation in large-scale areas.

AUTOMATIC SEARCHING OF CONTROL POINT IN NOAA AVHRR IMAGE

This paper discusses the approaches for automatical searching of control points in the NOAA AVHRR image on the basis of data rearrangement in the form of latitude and longitude grid. The vegetation index transformation and multi-level matching strategies have been proven effective and successful as the experiments show while the control point database is established.

A non-uniform grid for triangular differential quadrature

The triangular differential quadrature method based on a non-uniform grid is proposed in the paper. Explicit expressions of the non-uniform grid point coordinates are given and the weighting coefficients of the triangular differential quadrature method are determined with the aid of area coordinates. Two typical examples are presented to testify the effectiveness of the non-uniform grid. It is shown that rapid convergence is achieved under the non-uniform grid in comparison with those from the uniform grid with the same order of approximation.

3DFD Simulation of Asymmetric Wave Field by Side-wall Acoustic Tool in Open and Cased Wells

We developed a parallelized scheme of 3D finite difference （3DFD）with non-oniform staggered grid to simulate the eccentric borehole acoustic field with side-wall acoustic logging tools in open and cased wells. Higher accuracy and lower computation cost were achieved with this scheme for modeling such an asymmetric wave field generated by a high frequency source near or on the borehole wall. We also modeled the cases with and without considering the effects of the tool body. The simulation results demonstrated that the logging tool body would attenuate the direct waves but have only little influence on the interface waves in such a borehole condition. The effects of the tool body on the wave field were significant only when the contrast of the elastic properties between tool body and borehole fluid was large.

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.

High-Order Finite Difference Schemes for the First Derivative in Von Mises Coordinates

Third- and fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional viscous fluid flow through an irregular domain. The von Mises transformation is used to transform the governing equations, and map the irregular domain onto a rectangular computational domain. Vorticity on the solid boundary is expressed in terms of the first partial derivative of the square of the speed of the flow in the computational domain, and the schemes are used to calculate the vorticity at the computational boundary grid points using up to five computational domain grid points. In all schemes developed, we study the effect of coordinate clustering on the computed results.

Possible Impact of Spatial and Temporal Non-Uniformity in Land Surface Temperature Data on Trend Estimation

The present work investigates possible impact of the non-uniformity in observed land surface temperature on trend estimation, based on Climatic Research Unit （CRU） Temperature Version 4 （CRUTEM4） monthly temperature data-sets from 1900 to 2012. The CRU land temperature data exhibit remarkable non-uniformity in spatial and temporal features. The data are characterized by an uneven spatial distribution of missing records and station density, and dis-play a significant increase of available sites around 1950. Considering the impact of missing data, the trends seem to be more stable and reliable when estimated based on data with 〈 40% missing percent, compared to the data with above 40% missing percent. Mean absolute error （MAE） between data with 〈 40% missing percent and global data is only 0.011℃ （0.014℃） for 1900-50 （1951-2012）. The associated trend estimated by reliable data is 0.087℃ decade^-1 （0.186℃ decade^-l） for 1900-50 （1951-2012）, almost the same as the trend of the global data. However, due to non-uniform spatial distribution of missing data, the global signal seems mainly coming from the regions with good data coverage, especially for the period 1900-50. This is also confirmed by an extreme test conducted with the records in the United States and Africa. In addition, the influences of spatial and temporal non-uniform features in observation data on trend estimation are significant for the areas with poor data coverage, such as Africa, while insig-nificant for the countries with good data coverage, such as the United States.

Application of Lattice Boltzmann Method to Simulate Forest Edge

This study is focused on the forest edge flow by using numerical method.To model the effects of a forest canopy on airflow,source terms are introduced into the governing equations.The lattice Boltzmann method in conjunction with the standard k-εmodel is applied to solve the turbulent wind field.In order to perform the simulation on non-uniform grids,the Taylor series expansion and least square based lattice Boltzmann method(TLLBM)is adopted to improve the accuracy and computational efficiency.The present method and code are verified with an earlier forest edge simulation.A series of forest canopies are established to explore the impacts of canopy morphology on wind field.These canopies cover 3 canopy architectures and the Leaf Area Index(LAI)ranges from 2.0 to 4.0.The further study is carried out by adjusting the canopy foliage amount and the canopy architecture.The present study demonstrates the potential of lattice Boltzmann method to simulate the high Re number forest edge flow.The impacts of canopy morphology on zero plane displacement,aerodynamic roughness length,friction wind velocity,permeability coefficient,wall-shear stress are illustrated in detail.The results show that the canopy sub-layer wind field,especially the wind velocity profiles within and above the forest canopy,are mainly determined by canopy morphology.

R&D and application of voltage sourced converter based high voltage direct current engineering technology in China

As a new generation of direct current(DC)transmission technology,voltage sourced converter(VSC)based high voltage direct current(HVDC)has been widely developed and applied all over the world.China has also carried out a deep technical research and engineering application in this area,and at present,it has been stepped into a fast growing period.This paper gives a general review over China’s VSC based HVDC in terms of engineering technology,application and future development.It comprehensively analyzes the technical difficulties and future development orientation on the aspects of the main configurations of VSC based HVDC system,topological structures of converters,control and protection technologies,flexible DC cables,converter valve tests,etc.It introduces the applicable fields and current status of China’s VSC based HVDC projects,and analyzes the application trends of VSC based HVDC projects both in China and all over the world according to the development characteristics and demands of future power grids.

Study on 3D simulation of wave fields in acoustic reflection image logging

The borehole acoustic reflection imaging logging is a newly developed acoustic logging method that has attracted many interests. These converted and reflected waves for imaging are usually mixed up with borehole guided waves and therefore difficult to be clearly identified. To improve the downhole tool design and develop more sophisticate data processing and interpretation algorithms,studies on precisely numerical modeling of the wave fields in the acoustic reflection imaging logging are neces-sary and critical. This paper developed a parallelized scheme of 3D finite difference (3DFD) with non-uniform staggered grid and PML absorbing boundary to simulate the acoustic wave fields in isotropic and anisotropic formations. Applications of this scheme to the typical cases of isotropic and anisot-ropic formations and comparison with the results from published analytical solutions have demon-strated the validation and efficiency of the scheme. Higher accuracy and lower computation cost (3.5 times faster than the conventional schemes) have been achieved with this scheme for modeling such a complex wave fields of 60 dB dynamic range with higher frequency (10 kHz). This simulating program provides a quantitative analytical means for studying acoustic reflection imaging tool and development of the data processing and interpretation methods.

A High Order Method for Determining the Edges in the Gradient of a Function

Detection of edges in piecewise smooth functions is important in many applications.Higher order reconstruction algorithms in image processing and post processing of numerical solutions to partial differential equations require the identification of smooth domains,creating the need for algorithms that will accurately identify discontinuities in a given function as well as those in its gradient.This work expands the use of the polynomial annihilation edge detector,(Archibald,Gelb and Yoon,2005),to locate discontinuities in the gradient given irregularly sampled point values of a continuous function.The idea is to preprocess the given data by calculating the derivative,and then to use the polynomial annihilation edge detector to locate the jumps in the derivative.We compare our results to other recently developed methods.

A high-resolution gas-kinetic scheme with minimized dispersion and controllable dissipation reconstruction

In order to simulate multiscale problems such as turbulent flows effectively, the high-order accurate reconstruction based on minimized dispersion and controllable dissipation(MDCD) is implemented in the second-order accurate gas-kinetic scheme(GKS) to improve the accuracy and resolution. MDCD is firstly extended to non-uniform grids through the modification of dissipation and dispersion coefficients for uniform grids based on the local stretch ratio. Remarkable improvements in accuracy and resolution are achieved on general grids. Then a new scheme, MDCD-GKS is constructed, with the help of MDCD reconstruction, not only for conservative variables, but also for their gradients. MDCD-GKS shows good accuracy and efficiency in typical numerical tests.MDCD-GKS is also coupled with the improved delayed detached-eddy simulation(IDDES) hybrid model and applied in the fine simulation of turbulent flow around a cylinder, and the prediction is in good agreement with experiments when using the relatively coarse grid. The high accuracy and resolution of the developed GKS guarantee its high efficiency in practical applications.