Discontinuous Finite Element Approach for Transient Radiative Transfer Equation
Discontinuous Finite Element Approach for Transient Radiative Transfer Equation
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DOI：
10.1115/1.2737477
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发表时间：
2007-08
影响因子：
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通讯作者：
Liwu Liu;L. J. Liu
中科院分区：
文献类型：
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作者：
Liwu Liu;L. J. Liu
将基于离散纵坐标方程的间断有限元法推广到求解吸收、发射和散射介质中的瞬态辐射传输问题。采用全隐式格式对瞬态项进行离散。三个数值例子来说明这种间断有限元方法的性能。数值结果与其他基准近似解进行了比较。结果表明，间断有限元法具有计算效率高、精度高、稳定性好等优点，可用于求解参与介质中的瞬态辐射传输问题。由于在间断有限元离散化中，单元间边界的连续性被放松，使得场变量在单元边界上被视为间断的。这一特点使得间断有限元法能够正确预测介质内的传播速度，并准确捕捉入射辐射和辐射热通量在穿透前沿的急剧下降。
A discontinuous finite element method based on the discrete ordinates equation is extended to solve transient radiative transfer problems in absorbing, emitting, and scattering media. The fully implicit scheme is used to discretize the transient term. Three numerical examples are studied to illustrate the performance of this discontinuous finite element method. The numerical results are compared to the other benchmark approximate solutions. By comparison, the results show that the discontinuous finite element method is efficient, accurate, and stable, and can be used for solving transient radiative transfer problems in participating media. Because the continuity at interelement boundaries is relaxed in discontinuous finite element discretization so that field variable is considered discontinuous across the element boundaries. This feature makes the discontinuous finite element method able to predict the correct propagation speed within medium and accurately capture the sharp drop in the incident radiation and the radiative heat flux at the penetration front.