有限尺寸系统中非平衡辐射扩散的分析基准
Analytical benchmark for non-equilibrium radiation diffusion in finite size systems
摘要：
非平衡辐射扩散是惯性约束聚变、天体物理等离子体、加热炉和热交换器中重要的能量传输机制。本文给出了有限厚度平板和球壳中非平衡Marshak扩散问题的解析解。利用拉普拉斯变换方法，得到了辐射和物质能量密度随空间和时间的变化关系。积分能量密度和漏电流的变化也进行了研究。为了使辐射输运和材料能量方程线性化，假定热容与材料温度的立方成比例。稳态能量密度沿平板的深度呈线性变化，而观察到的球壳的非线性依赖。分析的能量密度与采用小网格宽度和时间步长的有限差分法得到的结果吻合较好。基准结果可用于验证平面和球面非平衡辐射扩散计算程序。
英文摘要：
Non-equilibrium radiation diffusion is an important mechanism of energy transport in Inertial Confinement Fusion, astrophysical plasmas, furnaces and heat exchangers. In this paper, an analytical solution to the non-equilibrium Marshak diffusion problem in a planar slab and spherical shell of finite thickness is presented. Using Laplace transform method, the radiation and material energy densities are obtained as a function of space and time. The variation in integrated energy densities and leakage currents are also studied. In order to linearize the radiation transport and material energy equation, the heat capacity is assumed to be proportional to the cube of the material temperature. The steady state energy densities show linear variation along the depth of the planar slab, whereas non-linear dependence is observed for the spherical shell. The analytical energy densities show good agreement with those obtained from finite difference method using small mesh width and time step. The benchmark results obtained in this work can be used to validate and verify non equilibrium radiation diffusion computer codes in both planar and spherical geometry.
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