球几何中子输运保正线性间断有限元格式

Positivity preserving linear discontinuous finite element scheme for spherical neutron transport equations

针对球几何中子输运方程线性间断有限元方法计算的负中子通量问题,构造了保正线性间断有限元格式,该格式保持中子角通量0阶矩和1阶矩。现有方法计算中子角通量非负时,采用传统的线性间断有限元方法,求解线性方程组;原方法计算出现负通量,则采用构造的保正格式,求解非线性方程组。编制了球几何中子输运问题保正格式程序模块,并集成到应用程序。数值算例表明构造的保正格式计算的中子通量非负,有效降低数值误差,提高数值计算的精度。

The linear discontinuous finite element method for the spherical neutron transport equation will give negative angular flux. A positivity preserving linear discontinuous finite element scheme has been constructed and this scheme can preserve zeroth order moment and first order moment of neutron angular flux. A program for the spherical neutron transport problem has been established by the positivity preserving linear discontinuous finite element scheme, which uses the classical scheme by solving linear system of equations when the neutron angular flux is non-negative and adopts the positivity preserving scheme by solving nonlinear system of equations when the neutron angular flux is negative. The numerical results show that the positivity preserving scheme can give non-negative neutron angular flux which reflects the corresponding physical meaning and can give more accurate neutron angular flux and reduce numerical error.