基于动态模态分解和序列奇异值分解的辐射传热数据加速计算
Data-Driven Acceleration of Thermal Radiation Transfer Calculations with the Dynamic Mode Decomposition and a Sequential Singular Value Decomposition
摘要：
我们提出了一种加速辐射转移离散坐标辐射转移计算的方法。与大多数加速方案相比，我们的方法适用于非线性正修复。该方法是基于动态模式分解（DMD），并使用一系列的秩一更新计算的奇异值分解所需的DMD。使用顺序方法允许我们自动确定要包括在DMD加速中的解向量的数量。我们目前的结果与标准的温度线性化的平板几何离散坐标计算。正源迭代相比，我们的研究结果表明，我们的加速方法减少了运输扫描的数量需要解决的问题，由一个标准的扩散Marshak波问题的一个因素约为3，一个因素的几千个冷却问题的有效散射比接近统一，和一个因素的20个改善在一个现实的，多材料的辐射冲击问题。
英文摘要：
We present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic mode decomposition (DMD) and using a sequence of rank-one updates to compute the singular value decomposition needed for DMD. Using a sequential method allows us to automatically determine the number of solution vectors to include in the DMD acceleration. We present results for slab geometry discrete ordinates calculations with the standard temperature linearization. Compared with positive source iteration, our results demonstrate that our acceleration method reduces the number of transport sweeps required to solve the problem by a factor of about 3 on a standard diffusive Marshak wave problem, a factor of several thousand on a cooling problem where the effective scattering ratio approaches unity, and a factor of 20 improvement in a realistic, multimaterial radiating shock problem.
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