The purpose of this paper is to present a High-Order/Low-Order radiation-hydrodynamics method that is second-order accurate in both space and time and uses the Variable Eddington Factor (VEF) method to couple a high-order set of 1-D slab-geometry grey S_n radiation transport equations with a low-order set of radiation moment and hydrodynamics equations. The S_n equations are spatially discretized with a lumped linear-discontinuous Galerkin scheme, while the low-order radiation-hydrodynamics equations are spatially discretized with a constant-linear mixed finite-element scheme. Both the high-order and low-order equations are discretized in time using a trapezoidal BDF-2 method. One manufactured solution is used to demonstrate that the scheme is second-order accurate for smooth solutions, and another one is used to demonstrate that the scheme is asymptotic-preserving in the equilibrium-diffusion limit. Calculations are performed for radiative shock problems and compared with semi-analytic solutions. In a previous paper it was shown that the pure radiative transfer scheme (the S_n equations coupled to the radiation moment equations and a material temperature equation rather than the hydrodynamics equations) is asymptotic-preserving in the equilibrium-diffusion limit, is well-behaved with unresolved spatial boundary layers in that limit, and yields accurate Marshak wave speeds even with strongly temperature-dependent opacities and relatively coarse meshes. These same properties carry over to our radiation-hydrodynamics scheme.

本文的目的是提出一种高阶/低阶辐射-流体动力学方法，该方法在空间和时间上都是二阶精确的，并且使用可变爱丁顿因子（VEF）方法来耦合1的高阶集合。具有低阶辐射矩集和流体动力学方程的-D平板几何灰色S _n辐射输运方程。在S _ñ方程组采用集总线性不连续Galerkin方案在空间上离散，而低阶辐射-流体动力学方程采用恒定线性混合有限元方案在空间上离散。使用梯形BDF-2方法可以及时离散高阶和低阶方程。一种制造的解用于证明该方案对于光滑解是二阶精确的，而另一种解被用于证明该方案在平衡扩散极限中是渐近保持的。对辐射冲击问题进行计算，并与半解析解进行比较。在先前的论文中表明，纯辐射传输方案（S _n与辐射矩方程式和材料温度方程式而不是流体动力学方程式耦合的方程式在平衡扩散极限中是渐近保持的，在该极限中具有未解析的空间边界层，并且即使在以下情况下也能产生准确的Marshak波速强烈依赖于温度的混浊度和相对较粗的网格。这些相同的特性延续到我们的辐射流体力学方案中。