A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
L. Chacón, J. Hamilton, N. Krasheninnikova
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引用次数: 0

Abstract

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018) [17], the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.
磁化等离子体中强各向异性输运方程的鲁棒四阶有限差分离散化
我们提出了一种二阶时间隐式、四阶精确的空间离散化方案,用于热、聚变级等离子体的强各向异性热输运方程。在Du Toit等人(2018)[17]之后,该方案将混合导数扩散通量(导致缺乏离散极大值原理)转换为非线性平流通量,适用于非线性求解器友好的单调性保持限制。该方案能够实现精确的多维热输运模拟,热输运系数各向异性可达7个数量级,具有低交叉场数值误差污染和优异的算法性能,线性迭代次数与网格分辨率和网格各向异性的比例非常弱,与隐式时间步长的平方根成比例。我们提出了一种基于低阶近似的多网格预处理策略,该策略使该方案在网格细化下高效且可扩展。几个数值测试显示了预期的空间收敛率和强大的算法性能,包括二维螺旋几何中Bennett捏扭不稳定性和三维环形几何中ITER的完全非线性磁流体动力学模拟。
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来源期刊
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
期刊介绍: The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
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