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A two-step discrete method for reconstruction of temperature distribution in a three-dimensional participating medium

机译：二维参与介质中温度分布的两步离散方法

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摘要

A new two-step discrete method is proposed in this paper for reconstruction of three-dimensional temperature distribution in an absorbing, emitting and isotropically scattering medium. With this new method, the temperature of the wall is also considered. The local radiative source term is reconstructed in the first step through the discrete transfer method from the directional, exit radiation intensities measured by CCD cameras. Then, the temperature of each discrete element is calculated in the second step by subtracting the scattering contribution from the retrieved radiative source term through the discrete ordinate method. The least squares minimum residual algorithm is employed to solve the ill-posed reconstruction equations and the calculation is improved to reduce the computational cost. The performance of the proposed method is examined by numerical test problems with unimodal and bimodal temperature distributions. The ill-conditioning of the reconstruction problem is checked by the Picard condition. The effects of the measurement noise and the radiative properties on the reconstruction accuracy are discussed. The results show that the method proposed in this paper is capable of reconstructing the temperature distribution accurately in large, confined, participating media, even with noisy input data. The computation time reduction of this new method is significant when compared with other methods.
机译：本文提出了一种新的两步离散方法，用于重构吸收，发射和各向同性散射介质中的三维温度分布。使用这种新方法，还需要考虑墙的温度。第一步，通过离散转移方法，根据CCD摄像机测得的定向出射辐射强度，重建局部辐射源项。然后，在第二步中，通过离散纵坐标方法从检索的辐射源项中减去散射贡献，从而计算出每个离散元素的温度。采用最小二乘最小残差算法求解不适定的重建方程，并对计算结果进行改进以降低计算量。提出的方法的性能通过单峰和双峰温度分布的数值测试问题进行了检验。皮卡德条件检查重建问题的状况。讨论了测量噪声和辐射特性对重建精度的影响。结果表明，本文提出的方法即使在嘈杂的输入数据下也能够在大型，受限，参与的介质中准确地重建温度分布。与其他方法相比，此新方法的计算时间减少非常重要。

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