Application of a total variation diminishing scheme to electromagnetic hybrid particle-in-cell plasma simulation

A discretization procedure for a total variation diminishing (TVD) scheme is introduced to an electromagnetic hybrid particle-in-cell (PIC) plasma simulation code in order to improve the numerical stability and resolution when calculating the plasma flow field in which magnetic field discontinuities (for example, Rankine–Hugoniot jump conditions for shock waves) are generated. In the hybrid PIC code used in this study, ions are treated as particles and electrons are assumed to be an inertia-less (mass-less) fluid. In the numerical results of one-dimensional test simulations, the TVD scheme significantly prevents non-physical, numerical oscillations, which would ordinarily be produced in the solution when the convection term of the magnetic induction equation in the hybrid PIC code is discretized by central difference schemes at magnetic field discontinuities. Furthermore, a two-dimensional simulation of the global structure of a collision-less bow shock, which is suitable for practical use, makes it possible to clearly capture the bow shock by using the hybrid PIC code with the TVD scheme.     

Simulating magnetic positive positioning of cryogenic propellants in a transient acceleration field

A computational simulation of magnetic positive positioning (MP²) is developed to model cryogenic propellant reorientation in reduced gravity. Previous efforts have successfully incorporated an electromagnetic field model into an axisymmetric, two-dimensional, incompressible fluid flow model yielding accurate predictions of fluid motion induced by a magnetic field. To simulate MP², a three-dimensional magnetic field and magnetic force model was developed as a feature of a commercially available fluid flow model which has been well validated. The computational tool was then improved upon to model magnetically induced flows in a transient acceleration field. Simulation predictions obtained with the enhanced model are compared to available reduced gravity experiment data. Evidence is presented and conclusions are drawn that support the continued use of the simulation as viable modeling and predictive tool in the continuing study of MP².     

A nonuniform nested grid method for simulations of RF induced ionospheric turbulence

We present a numerical scheme to simulate radio-frequency (RF) induced ionospheric turbulence, in which an electromagnetic wave is injected into the overhead ionospheric plasma. At the turning point of the ordinary mode, the electromagnetic wave undergoes linear mode-conversion to electrostatic Langmuir and upper hybrid waves that can have a much shorter wavelength than the electromagnetic wave. In order to resolve both the electromagnetic and electrostatic waves, avoiding severe restrictions on the time step due to the Courant-Friedrich-Lewy (CFL) condition, the equation of motion for the plasma particles is solved on a denser grid than that for the Maxwell equations near the mode-conversion region. An interpolation scheme is employed to calculate the electromagnetic field in the equation of motion of the plasma particles, and an averaging scheme is used to calculate the current density acting as a source in the Maxwell equation. Special care has to be taken to reduce numerical recurrence effects when the wavelength of the electrostatic wave is of the same order or shorter than the coarse grid spacing of the electromagnetic wave.     

Splines and high order interpolations in plasma simulations

Higher order interpolations in plasma simulations using particles have been studied in one dimension. Various schemes including quadratic and cubic splines and interpolation with Gaussian particles are tested when the Debye length is much smaller than the grid size. It is found that the effects of aliases and numerical instabilities can be neglected when the higher order schemes are employed in the simulation. It is suggested that the combination of higher order interpolations in the direction of magnetic field and linear interpolation in the cross section may be useful for three-dimensional simulations of magnetically confined plasmas for controlled fusion.     

拼接网格通量守恒插值算法研究

提出一种通用的拼接网格通量守恒算法应用于拼接网格"找重"过程,为拼接网格预处理提供了高效、可靠的插值方法。该算法灵活利用图形学中"多边形裁剪"原理和曲线积分公式得到拼接面上相交多边形及其面积,算法实现复杂度低,简单并健壮性较好,能够通用于结构网格和非结构网格问题。实验结果表明在大网格量、复杂拼接区域时该拼接网格插值计算方法仍能得到较理想的结果。     

Interaction of a plasma plume induced by a pulsed plasma thruster with an incident flow of rarefied magnetized plasma

A three-dimensional computational model and the results of the calculation for the dynamics of a plasma plume induced by a pulsed plasma thruster (PPT) in a magnetized flow of the ambient plasma are presented. A nonstationary expansion process of a PPT-induced plasma plume is studied in the ionospheric plasma over 100 μs after the start of a 6-microsecond plasma pulse. The parameters of the plasma plume in the PPT outlet section simulate the performance characteristics of a pulsed thruster PPT-4 (Pulsed Plasma Thruster 4 [3]) utilizing solid Teflon propellant. The magnetohydrodynamic (MHD) model of the process is based on the approximation of the ideal magnetic gas dynamics and makes it possible to predict the dynamics of a plasma bunch after the pulse termination during its interaction with the ambient medium and the magnetic field as well as the induced electric fields and currents in the vicinity of the expanding plasma     

GCLgrid: A three-dimensional geographical curvilinear grid library for computational seismology

We developed a general library for handling a class of objects we call geographical curvilinear grids (GCLgrids). A GCLgrid is a distorted, uniform grid that is georeferenced. The GCLgrid library is implemented in an object oriented system with methods that relate points in the grid to a geographic reference frame. A simple example is a spherical shell divided along latitude, longitude, and depth, but more elaborate shapes can use the same interface. Scalar and vector fields are derived from the base grid through inheritance. Two algorithms are the core of this library. First, we use the Direction Set method to search for a location in space from a starting point. This algorithm converges reasonably fast if the grid is not extremely distorted. Second, we interpolate the grid using methods known from finite element analysis. A Jacobian matrix for an 8-node cube is computed to transform a distorted cube into a unit one. Shape functions for the standard cube are used to compute interpolation coefficients. Once the interpolation coefficients are computed, we can interpolate n-element vectors almost as quickly as scalar data. We show an application of the library to travel time table calculation at regional distances. Our table interpolator was found to be 10 times faster than one based on the tau-p method and is expected to be several orders of magnitude faster than 3D ray-tracing methods. Travel time interpolation errors are reduced significantly by tabulating delay times relative to a homogenous reference model instead of absolute times. This allows much coarser grids to be used at large scales comparing to one using total time.     

基于棱边方向检测与运动补偿的视频去隔行算法

提出了一种基于棱边方向检测与运动补偿相结合的去隔行算法。首先通过Canny算子提取出棱边,将图像区分为棱边和非棱边两部分。对于棱边丢失的部分,分别在空域内沿棱边方向和时域内沿棱边移动方向插值,然后利用中值滤波得到丢失的棱边信息;对于非棱边部分,采用多级相位相关运动估计法,对当前场与前后两场计算出相应的运动矢量,然后在时域和空域中利用中值滤波计算出丢失的信号。实验结果表明,本文方法优于一般的去隔行算法,如线性空域插值等。同时本文提出了两个去隔行评价标准,可以定量检验去隔行方法的效果。     

三维湿表面自动生成算法研究

该文介绍的三维湿表面网格的自动生成算法,不但可完成型值表各站型线的等弧长插值拟合,而且还能够在沿船长方向的任意位置上进行站的加密和插值,从而自动生成三维湿表面网格。该算法的实现依赖于一套完整的图形用户界面。此界面的Unix平台Motif、C和GL编制,友好灵活,方便易用。     

Field-Aligned Interpolation for Semi-Lagrangian Gyrokinetic Simulations

This work is devoted to the study of field-aligned interpolation in semi-Lagrangian codes. In the context of numerical simulations of magnetic fusion devices, this approach is motivated by the observation that gradients of the solution along the magnetic field lines are typically much smaller than along a perpendicular direction. In toroidal geometry, field-aligned interpolation consists of a 1D interpolation along the field line, combined with 2D interpolations on the poloidal planes (at the intersections with the field line). A theoretical justification of the method is provided in the simplified context of constant advection on a 2D periodic domain: unconditional stability is proven, and error estimates are given which highlight the advantages of field-aligned interpolation. The same methodology is successfully applied to the solution of the gyrokinetic Vlasov equation, for which we present the ion temperature gradient (ITG) instability as a classical test-case: first we solve this in cylindrical geometry (screw-pinch), and next in toroidal geometry (circular Tokamak). In the first case, the algorithm is implemented in Selalib (semi-Lagrangian library), and the numerical simulations provide linear growth rates that are in accordance with the linear dispersion analysis. In the second case, the algorithm is implemented in the Gysela code, and the numerical simulations are benchmarked with those employing the standard (not aligned) scheme. Numerical experiments show that field-aligned interpolation leads to considerable memory savings for the same level of accuracy; substantial savings are also expected in reactor-scale simulations.     

Normal vector generation for sampled data using fourier filtering

A three-dimensional surface is a useful graphic representation of a two-dimensional function which has been sampled on a regular grid. Shading the surface to simulate the effects of direct lighting makes visible small changes in the surface orientation, and enhances realism when the data represents a physical surface such as terrain. Shading interpolation calculations and surface patch generation techniques require the specification of a surface normal vector (or related slope information) at each sample point. These normal vectors are usually generated by averaging local data such as the normal vectors of the surfaces of a triangular mesh connecting the points. This paper describes a technique which uses Fourier filtering to generate normal vectors for two-dimensional sampled data. Images and analysis of frequency spectra are included to show how this technique preserves detail which is lost using the averaging method. Performance figures show that this enhancement of detail in the final image can be achieved for only a small increase in computation time.     

Efficient exponential compact higher order difference scheme for convection dominated problems

Present work is the development of a finite difference scheme based on Richardson extrapolation technique. It gives an exponential compact higher order scheme (ECHOS) for two-dimensional linear convection-diffusion equations (CDE). It uses a compact nine point stencil, over which the governing equations are discretized for both fine and coarse grids. The resulting algebraic systems are solved using a line iterative approach with alternate direction implicit (ADI) procedure. Combining the solutions over fine and coarse grids, initially a sixth order solution over coarse grid points is obtained. The resultant solution is then extended to finer grid by interpolation derived from the difference operator. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be monotone. The higher order accuracy and better rate of convergence of the developed algorithm have been demonstrated by solving numerous model problems.     

Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method

The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviours of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.     

基于磁共振影像层间插值的超分辨率及多视角融合

针对磁共振（MR）图像切片内分辨率高而切片间分辨率低,导致MR在冠状面和矢状面上缺乏医学诊断意义的问题,提出了一种基于层间插值及多视角融合网络的医学图像处理算法。首先,引入了层间插值模块,用来将MR体数据沿冠状和矢状方向从三维数据切割成二维图像;然后,在分别对冠状面和矢状面进行特征提取之后,通过空间矩阵滤波器动态计算权重用于任意大小的上采样因子放大图像;最后,将冠状图和矢状图在层间插值模块中得到的结果聚合成三维数据后再次沿轴状方向切割成二维图像,对得到的二维图像两两进行融合并通过轴状方向数据进行修正。实验结果表明,所提算法相较于其他超分辨率算法在×2、×3、×4尺度下的峰值信噪比（PSNR）均有1 dB左右的提升,可见所提算法有效提升了图像的重建质量。     

MHD-calculations for cometary plasmas

We present in this paper a relatively simple method for the numerical solution of the MHD-equations on a curvilinear grid. We consider the full 3D equations as well as a modified axisymmetric version. The difference scheme is based on the principle of forming backward differences along characteristics in the spatial variables. This method is used to calculate the interaction of the interplanetary magnetic field with the plasma flow around a comet. The MHD-equations are modified by source terms, which describe the transfer of mass, momentum and energy from a given background (the comet) to the plasma.     

A hydrostatic/non-hydrostatic grid-switching strategy for computing high-frequency,high wave number motions embedded in geophysical flows

Hydrostatic and non-hydrostatic models were used to simulate the generation of internal surges and associated soliton-like trailing waves from the non-linear steepening of low-frequency basin-scale waves. Results confirmed that the process cannot be modelled using the hydrostatic approximation. A grid-switching strategy was developed to reduce the simulation run-time of the non-hydrostatic model; a low-resolution grid using a hydrostatic computation of the flow field is dynamically switched to a high-resolution grid in the region of propagation of the leading internal surge, using a non-hydrostatic computation of the flow field. The strategy takes advantage of the small time scale required for non-hydrostatic effects to become important such that a high-resolution grid is invoked only when and where these effects become large. Run-time reduction, conservation of the interpolation scheme involved in the grid switching and strategies for field scale studies were addressed. In relation to the laboratory experiments, the grid-switching strategy predicted the phase speed and the amplitude of the leading internal surge similarly to the uniform-grid models, however, the trailing soliton-like waves lost some of their signature. All non-hydrostatic models predicted the features of the energy flux path between low- and high-frequency waves.     

Numerical simulations of the ionospheric striation model in a non-uniform magnetic field

The striation model describes the evolution of plasma clouds along and across the geomagnetic field B in the earth ionosphere. The plasma clouds drift across the ionosphere in the presence of an ambient electric field and a neutral wind. In this article we introduce new techniques to extend the simulation tools to the earth magnetic field geometry. The model moreover allows a three-dimensional representation of the plasma density evolution. The derivation of this model is recalled in the context of a non-uniform magnetic field and involves a new set of local coordinates. A numerical scheme is proposed to solve the resulting system of nonlinear partial differential equations. Numerical simulations are realized and the striation of the initial plasma cloud into a cluster of smaller clouds is obtained. The present work allows the observation of the structures along the magnetic field lines.     

Kalman-filter-based track fitting in non-uniform magnetic field with segment-wise helical track model

In the future International Linear Collider (ILC) experiment, high performance tracking is essential to its physics program including precision Higgs studies. One of major challenges for a detector such as the proposed International Large Detector (ILD) is to provide excellent momentum resolution in a magnetic field with small (but non-negligible) non-uniformity. The non-uniform magnetic field implies deviation from a helical track and hence requires the extension of a helical track model used for track fitting in a uniform magnetic field. In this paper, a segment-wise helical track model is introduced as such an extension. The segment-wise helical track model approximates the magnetic field between two nearby measurement sites to be uniform and steps between the two sites along a helix. The helix frame is then transformed according to the new magnetic field direction for the next step, so as to take into account the non-uniformity of the magnetic field. Details of the algorithm and mathematical aspects of the segment-wise helical track model in a Kalman-filter-based track fitting in the non-uniform magnetic field are elaborated. The new track model is implemented and successfully tested in the framework of the Kalman filter tracking software package, KalTest, which was originally developed for tracking in a uniform magnetic field.     

二维对流扩散方程的基于Boole和逼近的交替方向特征差分格式

51.引言关于对流扩散方程的求解,特征差分方法是其有效方法之一【1,2,3].由于采用了沿特征线离散技术,需要对网格点作插值处理,通常采用的办法是使用线性或二次插值函数.对于线性插值,直接导致误差     

Two-dimensional memory management using an avail list

A large two-dimensional fortran array is used to simulate a two-dimensional memory. The two-dimensional memory management scheme is discussed in detail, and an optimal two-dimensional scheme is established. The scheme is designed to reduce the need to copy arrays when they grow beyond their original memory allocation. Such a need arises when adaptive mesh refinement, for example, is used on a large scientific grid calculation with many multi-dimensional arrays. The memory management scheme could be realized in hardware; however, it was originally developed as a technique to speed up numerical calculations.