Evaluation of numerical scattering in finite volume method for solving radiative transfer equation by a central laser incidence model

The numerical scattering caused by spatial discretization in finite volume method is discussed. Based on an analysis of the generation process of numerical scattering, a physical model of central laser incidence to a two-dimensional rectangle containing semitransparent medium is established to validate the numerical scattering, with Monte Carlo method as benchmark, in which numerical scattering does not exist. Numerical scattering will be affected by spatial grid number, spatial differential schemes and spectral absorption coefficient. With the spatial grid number increasing, numerical scattering will be decreased. The accuracy of the diamond scheme is the highest, and the exponential scheme is a bit lower, the lowest accuracy of the three schemes is the step scheme. The tendency of numerical scattering is reverse, i.e., the step scheme produces minimum numerical scattering, and exponential scheme produces more, while the diamond scheme produces maximum among three methods. When the bias of absorption efficient is high, the numerical scattering cannot be eliminated only by increasing the grid number. If we set the direction of laser incidence as central axis, it can be seen that numerical scattering distributed symmetry along the axis, which can be called as symmetrical cross-scattering. All of the three schemes show symmetrical cross-scattering.