In this paper we present a multilevel projection-based iterative scheme for solving thermal radiative transfer problems that performs iteration cycles on the high-order Boltzmann transport equation (BTE) and low-order moment equations. Fully implicit temporal discretization based on the backward Euler time-integration method is used for all equations. The multilevel iterative scheme is designed to perform iteration cycles over collections of multiple time steps, each of which can be interpreted as a coarse time interval with a subgrid of time steps. This treatment is demonstrated to transform implicit temporal integrators to diagonally-implicit multi-step schemes on the coarse time grid formed with the amalgamated time intervals. A multilevel set of moment equations are formulated by the nonlinear projective approach. The Eddington tensor defined with the BTE solution provides exact closure for the moment equations. During each iteration, a number of chronological time steps are solved with the BTE alone, after which the same collection of time steps is solved with the moment equations and material energy balance. Numerical results are presented to demonstrate the effectiveness of this iterative scheme for simulating evolving radiation and heat waves in 2D geometry.

翻译：本文提出了一种多层级投影迭代格式，用于求解热辐射传输问题。该格式在高阶玻尔兹曼传输方程（BTE）与低阶矩方程之间执行迭代循环。所有方程均采用基于后向欧拉时间积分方法的全隐式时间离散。多层级迭代格式设计为在多个时间步的集合上进行迭代循环，每个集合可被解释为具有时间步子网格的粗时间区间。这一处理方法被证明能够将隐式时间积分器转化为对角隐式多步格式，该格式作用于由聚合时间区间形成的粗时间网格上。通过非线性投影方法构建了多层级矩方程组，其中利用BTE解定义的Eddington张量为矩方程提供了精确闭合。在每次迭代中，先单独使用BTE求解若干按时间顺序排列的时间步，随后使用矩方程和材料能量平衡求解同一时间步集合。数值结果展示了该迭代格式在二维几何中模拟演化辐射与热波的有效性。