The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radiation diffusion and frequency-dependent diffusion equations are two simplified models that can approximate the solution to FRTE in the thick opacity regime. The frequency discretization for the two limit models highly affects the numerical accuracy. However, classical frequency discretization for FRTE considers only the absorbing coefficient. In this paper, we propose a new decomposed multi-group method for frequency discretization that is not only AP in both gray radiation diffusion and frequency-dependent diffusion limits, but also the frequency discretization of the limiting models can be tuned. Based on the decomposed multi-group method, a full AP scheme in frequency, time, and space is proposed. Several numerical examples are used to verify the performance of the proposed scheme.
翻译:FRTE的不透明性不仅取决于物质温度,而且取决于频率,其值在不同频率的不同数量级上也各不相同。灰色辐射扩散和依赖频率的传播方程式是两种简化模型,可以在厚厚的不透明制度中接近FRTE的解决方案。两种限值模型的频率离散对数值准确性有很大影响。然而,FRTE的经典频率离散只考虑吸收系数。在本文中,我们提议一种新的分解多组频率离散方法,不仅在灰色辐射扩散和依赖频率的传播限制中都是AP,而且限制模型的频率离散也可以调整。根据分解的多组方法,提出了在频率、时间和空间方面的完整AP计划。我们用几个数字示例来核查拟议的计划的执行情况。