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首页> 外文期刊>Computational thermal sciences >EXTENSION TO COMPLEX GEOMETRIES OF THE HYBRID FINITE VOLUME/FINITE ELEMENT METHOD FOR THE SOLUTION OF THE RADIATIVE TRANSFER EQUATION
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EXTENSION TO COMPLEX GEOMETRIES OF THE HYBRID FINITE VOLUME/FINITE ELEMENT METHOD FOR THE SOLUTION OF THE RADIATIVE TRANSFER EQUATION

机译：混合有限体积/有限元法复杂几何的辐射传递方程解。

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摘要

A hybrid finite volume/finite element method was recently developed to solve the radiative trans-fer equation (RTE). In this method, the radiation intensity is approximated as a linear com-bination of basis functions, dependent only on the angular direction. The coefficients of the approximation are unknown functions of the spatial coordinates. The spatial discretization is carried out using the finite volume method, transforming the differential equations into alge-braic equations. The angular discretization is accomplished using a methodology similar to that employed in the finite element method. The Galerkin-like approximation of the radiation intensity is introduced into the RTE, which is multiplied by the nth basis function and integrated over all directions. The basis functions are taken as bilinear basis functions, and a classical polar/azimuthal discretization is carried out, as in the finite volume and discrete transfer meth-ods. However, while in these methods the radiation intensity is constant over a control angle or a solid angle, respectively, in the present method the radiation intensity is a continuously varying function. Previous development and application of the method was limited to Cartesian coordinates. In the present work, the method is extended to complex geometries using a struc-tured body-fitted mesh. Radiative transfer is calculated for several two-dimensional enclosures containing emitting-absorbing, scattering, gray media, and the predicted results are compared with benchmark solutions published in the literature. It was found that the results are in good agreement with reference solutions, demonstrating the ability of the present method to handle complex geometries.
机译：最近开发了一种混合有限体积/有限元方法来求解辐射传递方程（RTE）。在这种方法中，辐射强度近似于基函数的线性组合，仅取决于角度方向。近似系数是空间坐标的未知函数。使用有限体积法进行空间离散，将微分方程转换为代数方程。角度离散化是使用类似于有限元方法的方法完成的。将辐射强度的类似于Galerkin的近似值引入RTE，然后将其乘以n基函数并在所有方向上积分。基函数被视为双线性基函数，并且进行了经典的极性/方位离散化，例如在有限体积法和离散转移法中。然而，尽管在这些方法中辐射强度分别在控制角或立体角上是恒定的，但是在本方法中，辐射强度是连续变化的函数。该方法的先前开发和应用仅限于笛卡尔坐标。在当前的工作中，该方法使用结构化的身体拟合网格扩展到复杂的几何形状。计算包含发射吸收，散射，灰色介质的几个二维外壳的辐射传递，并将预测结果与文献中发布的基准解决方案进行比较。发现该结果与参考解决方案非常吻合，证明了本方法处理复杂几何形状的能力。

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