基于矩方程与Eddington张量的POD/DMD的非线性辐射传输降阶模型
Reduced order models for nonlinear radiative transfer based on moment equations and POD/DMD of Eddington tensor
AI总结：
针对非线性热辐射传输问题，提出基于矩方程与Eddington张量数据驱动降阶近似的新型降阶模型，验证了低秩下的准确性及秩提升后的误差递减特性。
摘要：
本文提出了一类用于非线性热辐射传输（TRT）问题的新型降阶模型（ROMs）。这类模型通过非线性投影方法与数据压缩技术构建。对玻尔兹曼输运方程（BTE）应用非线性投影，推导得到低阶矩方程层级。为矩方程组提供精确闭合的Eddington（准扩散）张量，通过多种基于数据的模型降阶方法进行近似，这些方法包括：（i）本征正交分解（proper orthogonal decomposition）、（ii）动态模态分解（dynamic mode decomposition, DMD）、（iii）平衡扣除型DMD变体。数值结果展示了这些降阶模型在模拟演化辐射波与热波时的性能。结果表明，即便Eddington张量采用极低秩表示，这些模型仍具备准确性；随着近似秩的提升，降阶模型生成的解的误差会逐渐降低。
英文摘要：
A new group of reduced-order models (ROMs) for nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. The Eddington (quasidiffusion) tensor that provides exact closure for the system of moment equations is approximated via one of several data-based methods of model-order reduction. These methods are the (i) proper orthogonal decomposition, (ii) dynamic mode decomposition (DMD), (iii) an equilibrium-subtracted DMD variant. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be accurate even with very low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.
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