有限体积法求解立体角离散误差

为解决采用有限体积法求解辐射传输方程时引起离散误差的问题,从有限体积法立体角内热流密度的求解过程出发,运用泰勒级数推导了近似误差的表达式,并分析影响离散误差的各种因素,包括离散射线数,辐射强度分布,假散射及网格比.根据分析结果,采用辐射强度的连续分布模型,模拟了各种因素对误差的影响.结果表明,辐射强度的分布函数对于有限体积法的离散误差有一定程度影响.当增加网格数及减小网格尺寸比时,可以有效地减小离散误差.假散射与离散误差间呈较强的非线性耦合关系.

Angular discretization error produced in solving radiative transfer equation with finite volume method

Based on the solution process of heat flux within the solid angle of FVM,Taylor series was used to develop the expression of approximation error,and factors that affect the discretization error were analyzed,with include the number of discrete radiosity,the distribution of radiative intensity,the false scattering and the grid ratio. According to the analytical results,the influence of these factors on the error was simulated by adopting the continuous distribution model of intensity. Results show that the distribution model of radiative intensity affects the discretization error of FVM to a certain degree. When the number of grid is increased and the grid ratio is decreased,the error can be reduced effectively. The false scattering has strong non linear coupling relationship with discretization error.