Exact solutions of the diffusion-convection equation in cylindrical geometry
Exact solutions of the diffusion-convection equation in cylindrical geometry
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DOI：
10.1063/1.2084887
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发表时间：
2005-10
影响因子：
2.2
通讯作者：
S. Eury;E. Harauchamps;X. Zou;G. Giruzzi
中科院分区：
文献类型：
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作者：
S. Eury;E. Harauchamps;X. Zou;G. Giruzzi
对于扩散系数、对流速度和附加阻尼项的各种函数形式，本文求出了圆柱内一维扩散-对流方程的解析解。这是对前人工作[A.克莱门松角Guivarch，S. P. Eury，X. L. Zou和G. Giruzzi，Phys. Plasmas 11，4998（2004）]，现在包括对流项，该对流项可以是常数，在空间坐标中单项增加，或者具有阶梯状变化。这种类型的方程在磁约束等离子体领域有重要的应用，在磁约束等离子体中，对流效应在粒子和能量输运中都被实验观察到。当温度梯度超过某一临界值时，微湍流会引起热扩散率、对流速度和阻尼项的急剧变化。一个通用的计划，开发连接域中的解决方案与不同的功能形式的系数…
The analytical solution of the one-dimensional diffusion-convection equation in a cylinder has been found, for various functional forms of the diffusion coefficient, convection velocity and with an additional damping term. This is a significant generalization of a previous work [A. Clemencon, C. Guivarch, S. P. Eury, X. L. Zou, and G. Giruzzi, Phys. Plasmas 11, 4998 (2004)] on the diffusion equation, including now a convection term that can be constant, monomially increasing in the space coordinate, or have step-like variations. This type of equation has important applications in the field of magnetically confined plasmas, in which convection effects are experimentally observed in both particle and energy transports. Sharp variations of heat diffusivity, convection velocity, and damping term can result from the microturbulence which develops whenever the temperature gradient exceeds a critical value. A general scheme is developed to connect solutions in domains with different functional forms of the coeff...