Geometric discretization for a plasma control model
Geometric discretization for a plasma control model
复制标题
等离子体控制模型的几何离散化
DOI：
10.3182/20130204-3-fr-2033.00098
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S. Bremond
中科院分区：
文献类型：
--
作者：
L. Lefévre;R. Nouailletas;S. Bremond
摘要：我们定义了一系列几何离散化方法来简化守恒定律的一维分布参数系统，并将这些方法应用于以端口控制哈密顿量（PCH）形式编写的等离子体控制模型的简化。在这些离散方案中，变量被投影到适当的基数中，以便执行精确的空间区分。我们表明，一些光谱和能量特性因此得以保留。研究了使用拉格朗日多项式的几何（辛）配置方案。数值结果显示了在非均匀边界条件或尖锐分布式控制的情况下瞬态响应的振荡。然后导出使用贝塞尔共轭基的第二辛谱方案，该方案允许更准确地逼近本征函数并减少不需要的数值振荡。最后，根据托卡马克 Tore Supra 的实验数据验证了所提出的控制模型数值积分。
Abstract we define a family of geometric discretization methods for the reduction of a 1D distributed parameters systems of conservation laws and apply these methods to the reduction of plasma control model written in Port-Controlled Hamiltonian (PCH) form. In these discrete schemes, variables are projected into appropriate bases in order to perform exact spatial differentiation. We show that some spectral and energetical properties are therefore preserved. A geometric (symplectic) collocation scheme using Lagrange polynomials is investigated. Numerical results show oscillations in the transient response in case of non homogeneous boundary conditions or sharp distributed control. A second symplectic spectral scheme using Bessel conjugated bases is then derived which allows a more accurate approximation of eigenfunctions and reduces the unwanted numerical oscillations. Finally, the proposed numerical integration of the control model is validated against experimental data from the tokamak Tore Supra.