The Simplified P₂ Approximation

The simplified P₂ (SP₂) approximation to the transport equation is derived by a formal procedure and by a variational analysis. The variational analysis yields the SP₂ equations, together with interface and Marshak-like boundary conditions. Numerical calculations show that the resulting SP₂ solution is generally more accurate than the P₁ solution for both integral quantities and detailed flux distributions, except near material interfaces, where the SP₂ solution is discontinuous.