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.
翻译:提出了一组非线性热辐射转移问题的新减序模型(ROMs),这些模型是通过非线性投影法和数据压缩技术开发的,非线性投影适用于Boltzmann运输方程(BTE),以得出低序瞬时方程的等级。Eddington(qusidifulation)振标,为瞬时方程系统提供精确封闭,通过若干基于数据的方法之一的模型-顺序缩减方法加以近似。这些方法有:(一) 正确的正态分解,(二) 动态模式分解,(三) 平衡分式DMD变方程,(三) 平衡分集式DMD变方程。提供了数值结果,以展示这些模型的性能,以模拟不断演变的辐射和热波。结果显示这些模型准确性能,即使Eddington 10or的表示非常低级。随着近值的上升,由ROM产生的溶液的误差也逐渐减少。