隐式-显式时间积分方案及其基于物理的预处理器在双流体托卡马克边界模拟中的应用
Implicit-Explicit time integration scheme with Physics-based preconditioning for two-fluid tokamak boundary simulations
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中文总结 AI 辅助
本文为GBS代码开发了全局刚性精确的IMEX龙格-库塔格式，隐式处理剪切阿尔芬波和平行扩散，显式处理其余项，并采用基于物理的三维预处理器，实现了远超CFL限制的时间步长，验证了算法与并行可扩展性，显著提升了数值稳定性和计算效率。
中文摘要 AI 辅助
本文在GBS代码[Ricci等人，Plasma Phys. Control. Fusion，2012]中开发并实现了一种全局刚性精确的隐式-显式(IMEX)龙格-库塔格式，用于双流体等离子体湍流模拟。由剪切阿尔芬波和平行扩散控制的最刚性现象被隐式处理，而其余非刚性项则显式推进。这种分裂使得时间步长能够远超Courant-Friedrichs-Lewy限制，同时避免全局隐式格式的全部计算成本。为了在每个时间步高效求解隐式子系统，采用了一种受磁流体动力学(MHD)领域技术启发的三维基于物理的预处理器。所得框架通过制造解方法进行验证，并展现出算法和并行可扩展性。与自适应显式龙格-库塔格式相比，在数值稳定性和计算效率方面显示出显著优势。
英文摘要
In this work, a globally stiffly accurate Implicit-Explicit (IMEX) Runge-Kutta scheme is developed and implemented in the GBS code [Ricci et al., Plasma Phys. Control. Fusion, 2012], for two-fluid plasma turbulence simulations. The stiffest phenomena, governed by shear Alfvén waves and parallel diffusion, are treated implicitly, while the remaining non-stiff terms are advanced explicitly. This splitting enables time steps well beyond the Courant-Friedrichs-Lewy limit, without incurring the full computational cost of a globally implicit formulation. To efficiently solve the implicit subsystem at each time step, a three-dimensional physics-based preconditioner, inspired by techniques developed in the magnetohydrodynamic (MHD) context, is used. The resulting framework is verified through the method of manufactured solutions and exhibits both algorithmic and parallel scalability. Significant advantages in numerical stability and computational efficiency are demonstrated with respect to an adaptive explicit Runge-Kutta scheme.
发表机构
- École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
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