二维模式转换模型的适定性及广义平面波模拟
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
AI总结：
本文研究了二维模式转换模型的适定性问题，提出了一种基于变系数的广义平面波基函数，用于模拟波模式转换过程，并通过间断伽辽金方法进行数值模拟，验证了该模型的物理合理性。
摘要：
某些类型的电磁波在等离子体中传播时可能发生模式转换过程。在磁约束聚变中，这种现象非常有用，因为它可以加热等离子体，允许在等离子体中心附近传输热量。本文聚焦于模式转换区域周围波传播的数学模型，从理论和数值角度出发。旨在为适定方程开发特定的基函数以研究波模式转换过程。这些基函数称为广义平面波，本质上基于变系数。因此，它们特别适用于模式转换问题。本文详细描述了为所提模型设计的广义平面波。将其应用于间断伽辽金方法中，提供了该过程的数值模拟。这些首次针对该模型的二维模拟与先前研究中研究的定性方面一致。
英文摘要：
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
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