GPU-accelerated computing of three-dimensional solar wind background

High-performance computational models are required to make the real-time or faster than real-time numerical prediction of adverse space weather events and their influence on the geospace environment. The main objective in this article is to explore the application of programmable graphic processing units (GPUs) to the numerical space weather modeling for the study of solar wind background that is a crucial part in the numerical space weather modeling. GPU programming is realized for our Solar-Interplanetary-CESE MHD model (SIP-CESE MHD model) by numerically studying the solar corona/interplanetary solar wind. The global solar wind structures are obtained by the established GPU model with the magnetic field synoptic data as input. Meanwhile, the time-dependent solar surface boundary conditions derived from the method of characteristics and the mass flux limit are incorporated to couple the observation and the three-dimensional (3D) MHD model. The simulated evolution of the global structures for two Carrington rotations 2058 and 2062 is compared with solar observations and solar wind measurements from spacecraft near the Earth. The MHD model is also validated by comparison with the standard potential field source surface (PFSS) model. Comparisons show that the MHD results are in good overall agreement with coronal and interplanetary structures, including the size and distribution of coronal holes, the position and shape of the streamer belts, and the transition of the solar wind speeds and magnetic field polarities.     

基于单能窄束伽马射线算法计算高分辨率屏蔽自然伽马探测器的三维测井响应

本文应用单能窄束伽马射线理论建立高分辨率屏蔽自然伽马探测器三维测井响应的数值模拟算法.首先利用单能窄束原理,用稳态扩散方程描述伽马光子密度的空间分布,根据扩散方程基本解、放射源空间分布、探测器位置和屏蔽情况,将屏蔽探测器上的总伽马通量表示成放射性地层中的有效探测区域上的体积分和晶体表面上有效接收面的面积分形式.并根据伽马射线传播路径和探测器屏蔽情况,给出有效探测区域的解析表达式,通过数值积分法计算任意复杂情况下探测器上的自然伽马通量,获得伽马测井响应的3D数值模拟算法.并通过数值模拟结果与模型井数据的对比验证了该算法的有效性.最后通过3D数值模拟算法系统研究考察晶体形状（圆柱形晶体、方形晶体）、晶体长度、仪器在井轴中的位置（居中屏蔽探测器、贴井壁屏蔽探测器）、以及测速等不同情况下自然伽马测井响应,设计出新型高分辨率自然伽马测井仪器.     

Numerical MHD simulations of the appearance of a series of current sheets above the active region AR 0365

The first attempt at numerical MHD simulations of the appearance of several current sheets above an active region before a series of elementary flares is described. Energy accumulates in the field of each sheet that can be released during one of the flares. The computations started three days before the appearance of a series of flares, i.e., before the emergence of a new magnetic flux in the active region. The initial (potential) magnetic field was calculated by solving the Laplace equation with an oblique derivative. The boundary conditions on the photosphere were specified from maps of the measured magnetic field in the active region for various instants of time. The Peresvet program solving the full system of MHD equations with dissipative terms was used in the computations. An absolutely implicit scheme conservative relative to the magnetic flux was used. The problem of properly choosing the size of the computational domain and finding the positions of singular magnetic field lines is discussed.     

Simulating solar MHD

Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere (‘convective collapse’) are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10⁵ G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.     

Effect of a uniform magnetic field on nonlinear magnetocenvection in a rotating fluid spherical shell

Abstract

Dynamic interaction between magnetic field and fluid motion is studied through a numerical experiment of nonlinear three-dimensional magnetoconvection in a rapidly rotating spherical fluid shell to which a uniform magnetic field parallel to its spin axis is applied. The fluid shell is heated by internal heat sources to maintain thermal convection. The mean value of the magnetic Reynolds number in the fluid shell is 22.4 and 10 pairs of axially aligned vortex rolls are stably developed. We found that confinement of magnetic flux into anti-cyclonic vortex rolls was crucial on an abrupt change of the mode of magnetoconvection which occurred at Δ = 1 ～ 2, where A is the Elsasser number. After the mode change, the fluid shell can store a large amount of magnetic flux in itself by changing its convection style, and the magnetostrophic balance among the Coriolis, Lorentz and pressure forces is established. Furthermore, the toroidal/poloidal ratio of the induced magnetic energy becomes less than unity, and the magnetized anti-cyclones are enlarged due to the effect of the magnetic force. Using these key ideas, we investigated the causes of the mode change of magnetoconvection. Considering relatively large magnetic Reynolds number and a rapid rotation rate of this model, we believe that these basic ideas used to interpret the present numerical experiment can be applied to the dynamics in the Earth's and other planetary cores.     

The rotated Cartesian coordinate method to remove the axial singularity of cylindrical coordinates in finite‐difference schemes for elastic and viscoelastic waves

When modelling the propagation of 3D non‐axisymmetric elastic and viscoelastic waves in cylindrical coordinates using the finite‐difference time‐domain method, a mathematical singularity occurs due to the presence of terms in the elastic and viscoelastic wave equations. For many years, this issue has been impeding the accurate numerical solution near the axis. In this work, we propose a simple but effective method for the treatment of this numerical singularity problem. By rotating the Cartesian coordinate system around the z‐axis in cylindrical coordinates, the numerical singularity problems in both 2D and 3D cylindrical coordinates can be removed. This algorithm has three advantages over the conventional treatment techniques: (i) the excitation source can be directly loaded at , (ii) the central difference scheme with second‐order accuracy is maintained, and (iii) the stability condition at the axis is consistent with the finite‐difference time‐domain in Cartesian coordinates. This method is verified by several 3D numerical examples. Results show that the rotating the Cartesian coordinate method is accurate and stable at the singularity axis. The improved finite‐difference time‐domain algorithm is also applied to sonic logging simulations in non‐axisymmetric formations and sources.     

Meridional circulation from differential rotation in an adiabatically stratified solar/stellar convection zone

Meridional circulation in stellar convection zones is not generally well observed, but may be critical for the workings of MHD dynamos operating in these domains. Coriolis forces from differential rotation play a large role in determining what the meridional circulation is. Here, we consider the question of whether a stellar differential rotation that is constant on cylinders concentric with the rotation axis can drive a meridional circulation. Conventional wisdom says that it can not. Using two related forms of the governing equations that respectively estimate the longitudinal components of the curl of the meridional mass flux and the vorticity, we show that such differential rotation will drive a meridional flow. This is because to satisfy anelastic mass conservation, non-spherically symmetric pressure contours must be present for all differential rotations, not just ones that depart from constancy on cylinders concentric with the rotation axis. Therefore, the fluid is always baroclinic if differential rotation is present. This is because, in anelastic systems, the perturbation pressure must satisfy a Poisson type equation, as well as an equation of state and a thermodynamic equation. We support our qualitative reasoning with numerical examples, and show that meridional circulation is sensitive to the magnitude and form of departures from rotation constant on cylinders. The effect should be present in 3D global anelastic convection simulations, particularly those for which the differential rotation driven by global convection is nearly cylindrical in profile. For solar-like differential rotation, Coriolis forces generally drive a two-celled circulation in each hemisphere, with a second, reversed flow at high latitudes. For solar like turbulent viscosities, the meridional circulation produced by Coriolis forces is much larger than observed on the Sun. Therefore, there must be at least one additional force, probably a buoyancy force, which opposes the meridional flow to bring its amplitude down to observed values.     

Large wavenumber convection in the rotating annulus

Abstract

The annulus model considers convection between concentric cylinders with sloping endwalls. It is used as a simplified model of convection in a rapidly rotating sphere. Large azimuthal wavenumbers are preferred in this problem, and this has been exploited to develop an asymptotic approach to nonlinear convection in the annulus. The problem is further reduced because the Taylor-Proudman constraint simplifies the dependence in the direction of the rotation vector, so that a nonlinear system dependent only on the radial variable and time results. As Rayleigh number is increased a sequence of bifurcations is found, from steady solutions to periodic solutions and 2-tori, typically ending in chaotic behaviour. Both the magnetic (MHD convection) and non-magnetic problem has been considered, and in the non-magnetic case our bifurcation sequence can be compared with those found by previous two-dimensional numerical simulations.     

Topology of Rayleigh–Bénard convection and magnetoconvection in plane layer

ABSTRACT

The present study aims to link the dynamics of geophysical fluid flows with their vortical structures in physical space and to study the transition of these structures due to the control parameters. The simulations are carried in a rectangular box filled with liquid gallium for three different cases, namely, Rayleigh–Bénard convection (RBC), magnetoconvection (MC) and rotating magnetoconvection (RMC). The physical setup and material properties are similar to those considered by Aurnou and Olson in their experimental work. The simulated results are validated with theoretical results of Chandrasekhar and experimental results of Aurnou and Olson. The results are also topologically verified with the help of Euler number given by Ma and Wang. For RBC, the onset is obtained at Ra greater than 1708 and at this Ra, the symmetric rolls are orientated in/along a horizontal axis. As the value of Ra increases further, the width of the horizontal rolls starts to amplify. It is observed that these two-dimensional rolls are nothing but the cross-sections of three-dimensional (3D) cylindrical rolls with wave structures. When the vertically imposed magnetic field is added to RBC, the onset of convection is delayed due to the effect of Lorentz force on the thermal buoyancy force. The presence of 3D rectangular structures is highlighted and analysed. When the magnetically influenced rectangular box rotates about vertical axis at low rotation rates in magnetoconvection model, the onset of convection gets further delayed by magnetic field, which is in general agreement with the theoretical predictions. The critical Ra increases linearly with magnetic field intensity. Coherent thermal oscillations are detected near the onset of convection, at moderate rotation rates.     

Weakly nonlinear stability to large-scale perturbations in convective magnetohydrodynamic systems without the α-effect

The problem of weakly nonlinear stability with respect to large-scale perturbations in 3-D convective magnetohydrodynamic (MHD) states in which the α-effect is absent or insignificant (e.g., because the system has symmetry relative to a center or a vertical axis) is examined. It is assumed that the MHD state whose stability is studied is free from large spatiotemporal scales and is insensitive to perturbations with the same small spatial scale as in the state under study. The equations for mean perturbation fields derived by asymptotic methods generalize the standard equations of magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). A combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms similar to advective terms arise in the inferred generalized equations.     

空间波数混合域磁异常场积分解三维数值模拟

本文提出一种空间波数混合域磁异常场三维数值模拟方法.该方法利用磁位三维空间域积分为卷积的特点,沿水平方向进行二维傅里叶变换,把空间域磁位满足的三维积分问题转化为不同波数之间相互独立的垂向一维积分问题.保留垂向为空间域,优势之一在于便于浅层单元剖分可适当加密,随着深度增加,单元剖分适当稀疏,可以准确模拟任意复杂地形和磁性体的磁异常,兼顾了计算精度与计算效率;优势之二在于一维积分垂向可离散为多个单元积分之和,每个单元采用二次形函数表征磁化强度,可得出单元积分的解析表达式,计算精度高、效率高.该方法充分利用一维形函数积分的高效和高精度、快速傅里叶变换的高效性及算法高度并行性,实现了磁异常场高效、高精度的数值模拟.设计棱柱体模型,将模型解析解与空间波数混合域法的数值解对比,结果表明该方法计算精度高、效率高.设计了组合棱柱体复杂模型,对比分析了标准FFT扩边法与Gauss-FFT法的计算精度与计算效率,总结了标准FFT的扩边系数选取策略.针对任意复杂地形条件下的磁异常模拟问题,本文提出一种适用于起伏地形条件下的磁异常场快速计算方法,并对其有效性进行了验证.     

Temporal Variations of the Magnetic Flux in the Solar Photosphere

The problem of the transport and transformation of magnetic fields from the generation zone to the photosphere is studied in this paper. For this purpose, the temporal variations of parameters of bipolar magnetic regions are analyzed based on the magnetic synoptic maps of the Wilcox Solar Observatory (WSO) for the declining phase of cycle 22. A 150-day modulation of the magnetic flux value in bipolar regions and a variation in their rotation velocity with a duration of 80–100 days have been found. Such variations in the parameters are interpreted as a result of action of supergiant and giant convection cells. The magnetic flux from the generation zone emerges through the local channels formed by the supergiant convection cells. From the level of 0.95 R_Sun, the flux is redistributed by giant cells, which form bipolar magnetic regions on the photosphere.     

太阳等离子体和磁场输出源表面结构的一种MHD模型

以观测到的光球视向磁场、Ｋ－日冕亮度作为输入,以相应的统计结果为约束条件,利用磁流体力学方程组,给出了等离子体及磁场各参数在源表面上的二维分布．其结果与同期的卫星观测数据和已有的统计结果相比较,显示出相当程度的一致性．     

Cumulus cloud energetics as revealed in a numerical model of cloud dynamics: Part II. Computational results

A numerical model of atmospheric convection is used to investigate the effects of the birth, growth, and death of a cumulus cloud on the temporal and spatial characteristics of atmospheric energy content. Energy in the forms of latent and thermal enthalpy of water vapor, thermal enthalpy of dry air and of condensed liquid, and potential and kinetic energy is computed. Changes in the energy content and the vertical flux of energy are mapped in the vertical plane passing through the cloud axis and are summed horizontally and vertically over the domain to show the rearrangements.It is found that the relative importance of different forms of energy is a function of position with respect to the cloud. Energy related to the presence of water vapor accounts for most of the changes in the vicinity of the cloud. Convection tends to decrease the potential instability of the atmosphere, the amount of decrease being determined by the total energy released during condensation regardless of whether it falls as rain. The time for the departure from neutral stability to be reduced by 10 percent of its initial value is estimated to be about one hour.     

地球磁尾中不同类型磁结构的磁螺度演化特征

在二维三分量MHD数值模拟的基础上 ,对地球磁尾不同类型磁结构的形成作磁螺度分析 .研究表明 ,对于由晨昏电场产生的磁尾驱动重联过程 ,通过系统边界输运的磁螺度通量是引起系统总磁螺度变化的直接原因 .不同的初始磁螺度密度分布和磁螺度通量输运 ,可以引起中性片区域磁螺度密度分布的不同演化 ,从而导致具有不同拓扑位形磁结构的形成 .     

2001年3月2日磁通量传输事件特性的研究

2001年3月2日11:00 至11:15 UT 期间,Cluster Ⅱ在南半球极尖区晨侧附近磁鞘内探测到3个通量传输事件（简称FTEs）. 本文利用Cluster Ⅱ星簇4颗卫星观测到的磁场和等离子体资料研究了这些通量传输事件的磁场形态和粒子特征. 并利用它们探测到的空间磁场梯度资料由安培定律直接求出星簇所在区域的电流分布. 结果指出：（1）BY占优势的行星际磁场结构在磁层顶的重联可以在极尖区附近发生;（2）FTEs通量管形成初期内外总压差和磁箍缩应力不一定平衡,达到平衡有一发展过程;（3）FTEs通量管截面在L M平面内的线度约为1.89RE;（4）FTEs通量管中等离子体主要沿轴向场方向流动,整个通量管以慢于背景等离子体的速度沿磁层顶向南向尾运动;（5）FTEs通量管中不仅有轴向电流,也存在环向电流. 轴向电流基本沿轴向磁场方向流动. 轴向和环向电流在管内均呈体分布,因而轴向电流产生的环向磁场接近管心时不断减小到零,而环向电流生成的轴向场则不断增大到极值;（6）在通量管的磁鞘部分观测到磁层能量粒子流量的增强,这表明通量管通过磁层顶将磁鞘和磁层内部连通起来了.     

Three-dimensional domino model in geodynamo

The Lagrangian formalism is applied to consider temporal evolution of the ensemble of interacting magnetohydrodynamical cyclones governed by Langevin-type equations in a rotating medium. This problem is relevant for fast-rotating convective objects such as the cores of planets and a number of stars, where the Rossby numbers are far below unity and the geostrophic balance of the forces takes place. The paper presents the results of modeling for both the two-dimensional (2D) case when the cyclones can rotate relative to the rotation axis of the whole system in the vertical plane, and for the case of spatial rotation by two angles. It is shown that variations in the heat flux on the outer boundary of the spherical shell modulate the frequency of the reversals of the mean dipole magnetic field, which agrees with the three-dimensional (3D) modeling of the planetary dynamo. Applications of the model for giant planets are discussed, and an explanation for some episodes in the history of the geomagnetic field in the past is suggested.     

Two‐dimensional nonlinear diffusive numerical simulation of geomorphic modifications to cinder cones

The temporal evolution of simple landforms such as cinder cones by nonlinear diffusive processes is studied through the use of a new 2D numerical model using well‐established and accurate numerical mathematics and high‐resolution digital elevation models (DEMs). Extending 1D (profile) nonlinear diffusion analyses used in cinder cone, hillslope and fault scarp evolution studies, we have implemented a 2D numerical model with a spatially and temporally varying sediment transport rate coefficient scaled nonlinearly by the ratio of local slope to critical slope. The high accuracy and efficient numerical implementation are documented in the paper and the MATLAB toolkit developed is used to solve for the developmentof an initial 2D cone form. First, we examine the nonlinear transport rule and suggest a refinement that accounts explicitly for flux at threshold slopes. We find that the maximum diffusion (necessarily introduced in the numerical model to avoid infinite rates) at the critical slope controls the final morphology, especially approaching steady state. Secondly, solving the landscape evolution problem in 2D enables a natural accounting for sediment flux convergence or divergence in the profile. Thirdly, the boundary behavior of a given landscape element controls much of what happens in that domain and so we allow for arbitrary flux magnitude or elevation boundary conditions. Fourthly, landscapes are heterogeneous in their surface cover and so we allow for spatially and temporally varying transport rate k and we permit an arbitrary vertical displacement field within the model domain. To test the new formulation for the nonlinear term, the effect of variable diffusivity k and the numerical schemes implemented, we apply the model to cinder cones built on the flanks of Mount Etna in 2001 and 2002–2003. We explore the effects of DEM resolution with data from the 2001 cone and the utility of spatially variable diffusivity to explain the variation in erosion measured by differencing repeat light detection and ranging (LIDAR) surveys gathered in 2004 and 2007 over the 2002–2003 cone complex. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of different wind directions in relation to topography on the outbreak of convection in Northern England

The influence of different wind directions on the outbreak of convection in Northern England, was investigated with a high-resolution numerical model. The Clark model, a 3D finite-difference, non-hydrostatic model was used in this study. It was initialised with the topography of Northern England, a representation of surface characteristics, and used a routinely available meteorological sounding, typical of the unstable conditions. Results showed that convective cells were initially triggered in the lee of the elevated terrain, and that only after the convection had developed, were cells upwind of the elevated terrain produced. The windward slopes themselves seemed sheltered from convection. Under most wind directions, the central Pennines (the Forest of Trawden and the Forest of Rossendale) seemed particularly affected by convective rainfall.     

Multimoment convecting flux tube model of the polar wind system with return current and microprocesses

Multimoment fluid simulation frameworks, which effectively account for anomalous transport due to microprocesses, combine best features of small-scale kinetic and global-scale MHD models. The most practical models of this type, 1D flux tube models, have been successfully used for realistic simulations of space plasmas including polar wind and magnetosphere–ionosphere coupling processes characterized by a wide range of temporal and spatial scales. Our earlier flux tube models with field-aligned current and microprocesses have been formulated for spatially stationary flux tubes. However, horizontal convection due to electric fields is an important aspect of the high-latitude ionosphere–polar wind system and typical time scales of the polar wind upflow are comparable to the transit time across the polar cap. To take into account this important feature we have added flux tube convection to our earlier model. Using typical convecting flux tube that starts outside auroral oval, then enters and leaves downward current region, it has been shown that anomalous transport effects due to current-driven microinstabilities significantly alter dynamics of several plasma moments and should be taken into account for an accurate interpretation and prediction of the observed data. Future applications of our new model have also been discussed.