We study the problem of radiative heat (Marshak) waves using advanced approximate approaches. Supersonic radiative Marshak waves that are propagating into a material are radiation dominated (i.e., hydrodynamic motion is negligible), and can be described by the Boltzmann equation. However, the exact thermal radiative transfer problem is a non-trivial one, and there still exists a need for approximations that are simple to solve. The discontinuous asymptotic P₁ approximation, which is a combination of the asymptotic P₁ and the discontinuous asymptotic diffusion approximations, was tested in previous work via theoretical benchmarks. Here, we analyze a fundamental and typical experiment of a supersonic Marshak wave propagation in a low-density SiO₂ foam cylinder, embedded in gold walls. First, we offer a simple analytic model that grasps the main effects dominating the physical system. We find the physics governing the system to be dominated by a simple, one-dimensional effect, based on the careful observation of the different radiation temperatures that are involved in the problem. The model is completed with the main two-dimensional effect which is caused by the loss of energy to the gold walls. Second, we examine the validity of the discontinuous asymptotic P₁ approximation, comparing to exact simulations with good accuracy. Specifically, the heat front position, as a function of the time, is reproduced perfectly in comparison to exact Boltzmann solutions.

我们使用先进的近似方法研究辐射热（Marshak）波的问题。传播到材料中的超音速辐射Marshak波以辐射为主（即，流体动力运动可忽略不计），可以用玻耳兹曼方程描述。然而，确切的热辐射传递问题是不平凡的，并且仍然需要简单解决的近似方法。在以前的工作中，通过理论基准测试了不连续渐近P ₁逼近，它是渐近P ₁和不连续渐近扩散逼近的组合。在这里，我们分析了超音速Marshak波在低密度SiO _2中传播的基本和典型实验泡沫缸，嵌入金墙。首先，我们提供了一个简单的分析模型，该模型掌握了控制物理系统的主要影响。基于对问题所涉及的不同辐射温度的仔细观察，我们发现控制该系统的物理学受简单的一维效应支配。该模型具有主要的二维效应，该效应是由金壁能量损失引起的。其次，我们将不连续渐近P ₁逼近的有效性与精确度较高的精确仿真进行比较。具体而言，与精确的玻尔兹曼解相比，热前位置作为时间的函数得到了完美的再现。