一维瞬态辐射传输的有限元法模拟

随着超短脉冲激光的快速发展,吸收散射性介质内的瞬态辐射传输引起了人们的广泛关注.本文基于离散坐标法和最小二乘有限元法(LSFEM),提出了模拟多维吸收散射性介质内瞬态辐射传输的数值模型.该模型有效地克服了在标准Galerkin有限元法(GFEM)中发生的伪振荡现象,在时间步长较大的情况下仍然可以得到光滑无振荡的解.而且,最小二乘法产生的求解系数矩阵是对称正定的,与GFEM中的系数矩阵相比,仅需要存储一半的非零系数,可以应用许多高效的迭代求解方法进行求解.为了检验模型,本文研究了一维吸收散射性介质内瞬态辐射传输问题,其结果与蒙特卡洛法(MCM)和积分模型法(IE)的结果进行了比较,结果证实:本文的方法可以精确、高效地模拟参与性介质内的瞬态辐射传输.

SIMULATION OF ONE-DIMENSIONAL TRANSIENT RADIATIVE TRANSFER BY FINITE ELEMENT METHOD

With the rapid progress on the ultra-short pulse laser, the transient radiative transfer in the absorbing and scattering media has attracted increasing attention. In present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate the transient radiative transfer. This model can overcome the spurious oscillation which be found in the standard Galerkin finite element method for radiative transfer. Under large time step, it can produce smooth results. In addition, the resulting coefficients' matrix produced by the present method is symmetric and positive-definite. Only half of a sparse matrix needs to be stored. Some robust iterative algorithms for symmetrical systems of equations can be successfully used. In order to validate this method, two one-dimensional transient radiative transfer problems are investigated and the results are compared with those by Monte-Carlo method and Integral Model' method. It indicates that the present model can simulate the transient radiative transfer in participating medium effectively and accurately.