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

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.