量纲分析法求解辐射热传导自相似解

通过量纲分析，将辐射流体方程简化为一阶常微分方程组的形式，进而结合数值计算求得热波烧蚀自相似解。流体方程涉及的内能、状态方程表达式采用依赖于温度、密度两个参量的形式，且参数可调，适用性较广。源边界条件可为恒温、恒流、恒压、常密等情况。以恒温源为例，给出了X射线加热Au壁时烧蚀质量与烧蚀压的定标关系，与文献结果及MULTI辐射流体程序计算结果吻合较好。

Self-similar solution for thermal radiation conduction by dimensional analysis

Radiation hydrodynamic equations are reduced from a system of partial differential equations to a system of ordinary differential equations by dimensional analysis, and then self-similar solutions for heat wave ablation can be numerically obtained.The expressions for internal energy and state included in the hydrodynamic equations have power-law dependences on density and temperature, and the exponents can be changed according to different conditions. Also the source boundary conditions can be constant temperature, constant flux, constant pressure, and constant density. The scaling relations of ablation mass and ablation pressure are given for X rays heating Au plane in the constant temperature condition. Comparisons with other works and MULTI 1D simulation results show excellent agreement.