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A second-order maximum-entropy inspired interpolative closure for radiative heat transfer in gray participating media
Journal of Quantitative Spectroscopy and Radiative Transfer ( IF 2.3 ) Pub Date : 2020-08-04 , DOI: 10.1016/j.jqsrt.2020.107238
Joachim A.R. Sarr , Clinton P.T. Groth

A new interpolative-based approximation to the second-order maximum-entropy, M2, moment closure for predicting radiative heat transfer in gray participating media is proposed and described. In addition to preserving many of the desirable mathematical properties of the original M2 closure, the proposed interpolative approximation provides significant reductions in computational costs compared to the costs of the original M2 closure by avoiding repeated numerical solution of the corresponding optimization problem for entropy maximization. Theoretical details of the proposed interpolative-based closure, along with a description of an efficient Godunov-type finite-volume scheme that has been developed for the numerical solution of the resulting system of hyperbolic moment equations, are presented. The finite-volume method makes use of limited linear solution reconstruction, multi-block body-fitted quadrilateral meshes with anisotropic adaptive mesh refinement (AMR), and an efficient Newton-Krylov-Schwarz (NKS) iterative method for solution of the resulting non-linear algebraic equations arising from the spatial discretization procedure. The predictive capabilities of the proposed interpolative M2 closure are assessed by considering a number of model problems involving radiative heat transfer within one- and two-dimensional enclosures, the results for which are compared to solutions of the first-order maximum entropy, M1, moment closure, as well as those of the more commonly adopted spherical harmonic moment closure techniques (first-order P1 and third-order P3) and the popular discrete ordinates method (DOM). The latter is used as a benchmark for comparisons, whenever exact solutions are not available. The numerical results illustrate the promise of the proposed M2 closure, with the closure outperforming the M1, P1 and P3 closures for virtually all cases considered.



中文翻译:

灰色参与介质中辐射热传递的二阶最大熵启发插值闭包

提出并描述了一种新的基于插值的近似二阶最大熵M 2矩闭合,用于预测灰色参与介质中的辐射热传递。除了保留许多原来的M的理想的数学性质的2封,建议插值逼近提供了比原来的M的成本计算成本降低显著2通过避免为熵最大化而对相应的优化问题进行重复的数值解来进行闭合。介绍了拟议的基于插值的闭包的理论细节,并描述了一种有效的Godunov型有限体积方案,该方案已为双曲线矩方程组的数值解决方案开发。有限体积方法利用有限的线性解重建,具有各向异性自适应网格细化(AMR)的多块体拟合四边形网格以及有效的牛顿-克里洛夫-舒瓦兹(NKS)迭代方法来求解所得的非网格。由空间离散过程产生的线性代数方程。拟议内插M 2的预测能力通过考虑许多涉及一维和二维外壳内辐射热传递的模型问题来评估闭合,将其结果与一阶最大熵M 1,矩闭合以及较普遍采用的球谐矩闭合技术(一阶P 1和三阶P 3)以及流行的离散纵坐标方法(DOM)。只要没有确切的解决方案,后者就会用作比较的基准。数值结果说明了提出的M 2封闭的前景,其封闭性能优于M 1,P 1和P 3 几乎所有案例都被关闭。

更新日期:2020-08-04
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