标题： 非均匀介质中的非平衡马什克波问题 显示英文标题

标题： The non-equilibrium Marshak wave problem in non-homogeneous media

摘要： 我们推导了一组相似解，用于描述非均匀平面介质的非平衡马什克波问题，该介质耦合到一个随时间变化的辐射驱动源。我们在超音速情况下采用了非平衡灰度扩散近似。这些解是对最近为均匀介质开发的非平衡非线性解的推广。构建了自相似解，涉及幂律时间相关的表面温度、空间幂律密度剖面以及具有幂律温度和密度依赖的吸收系数和比能量密度的材料模型。将问题扩展到非均匀介质使一般幂律比能量密度的相似解成为可能。结果表明，解的存在依赖于特定的时间温度驱动指数和空间密度指数，而这些指数又取决于材料指数。我们还展示了如何根据不同参数分析相似解的不同定性形式。基于这些解，我们定义了一组超音速非平衡辐射热传导的非平凡基准测试。通过与灰度扩散模拟以及光学厚区域的详细隐式蒙特卡罗和离散纵标输运模拟的比较，相似解显示出极好的一致性，这凸显了这些解作为代码验证测试问题的优势。 显示英文摘要

摘要： We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion approximation in the supersonic regime. The solutions constitute a generalization of the non-equilibrium nonlinear solutions that were developed recently for homogeneous media. Self-similar solutions are constructed for a power law time dependent surface temperature, a spatial power law density profile and a material model with power law temperature and density dependent opacities and specific energy density. The extension of the problem to non-homogeneous media enables the existence of similarity solutions for a general power law specific material energy. It is shown that the solutions exist for specific values of the temporal temperature drive and spatial density exponents, which depend on the material exponents. We also illustrate how the similarity solutions take various qualitatively different forms which are analyzed with respect to various parameters. Based on the solutions, we define a set of non-trivial benchmarks for supersonic non-equilibrium radiative heat transfer. The similarity solutions are compared to gray diffusion simulations as well as to detailed implicit Monte-Carlo and discrete-ordinate transport simulations in the optically-thick regime, showing a great agreement, which highlights the benefit of these solutions as a code verification test problem.