基于气体动理学方法的多尺度稳态热辐射计算

随着航空发动机燃烧室内燃气温度的提升，高温区域的热辐射问题将会变得更为重要，同时由于高温气体辐射导致辐射特性的剧烈变化，将会呈现出多尺度的现象，增加了辐射计算的难度。文章通过稳态离散统一气体动力学格式（SDUGKS，Steady Discrete Unified Gas Kinetics Scheme）的思路实现稳态辐射问题的求解，SDUGKS格式通过特征线差分离散的方法实现单元界面的重构，通过某种迭代格式来实现单元数据的更新，这一过程实现了对网格内部的辐射特性的有效模拟，该过程可适用于任何具体的辐射尺度。因此就可以在任意网格条件下实现多尺度问题的计算。文章引入了修正的延迟修正法（Deferred-correction，DC）实现单元数据更新，对单一尺度和多尺度问题进行了计算，在单一尺度问题中，验证了SDUGKS格式求解稳态辐射问题的正确性，进一步构造多尺度问题进行求解，论证了SDUGKS在多尺度问题计算中的渐近保持性质和准确性。

Multiscale steady-state thermal radiation calculation based on gas kinetics method

With the increase of the gas temperature in the combustion chamber of the aero engine, the problem of radiation in the high temperature area will become more important. At the same time, the radiation characteristics will change drastically due to high temperature gas radiation, which will show a multi-scale phenomenon and thus increase the difficulty of radiation calculation. This paper uses the idea of steady discrete unified gas kinetics scheme (SDUGKS) to solve the steady-state radiation problem. SDUGKS schemes uses the method of differential discretization by characteristic line to achieve reconstruction of the unit interface, and realizes update of cell data through a certain iterative format. This process realizes effective simulation of the radiation characteristics inside the grid. The process can be applied to any specific radiation scale, so that the calculation of multi-scale problems can be realized under any grid condition. This paper introduces the deferred-correction (DC) method to update unit data, and calculates the single-scale and multi-scale problems. For the single-scale problem, the SDUGKS format is verified to be applicable for the steady-state radiation problem. The multi-scale problem is further constructed to be solved, which verifies the asymptotic preservation and accuracy of SDUGKS in calculation of multi-scale problems.