Title: Mathematical and numerical validation of the simplified spherical harmonics approach for time-dependent anisotropic-scattering transport problems in homogeneous media,
Abstract: In this work, we extend the solid harmonics derivation, which was used by
Ackroyd et al to derive the steady-state SP$_N$ equations, to transient
problems. The derivation expands the angular flux in ordinary surface harmonics
but uses harmonic polynomials to generate additional surface spherical harmonic
terms to be used in Galerkin projection. The derivation shows the equivalence
between the SP$_N$ and the P$_N$ approximation. Also, we use the line source
problem and McClarren's "box" problem to demonstrate such equivalence
numerically. Both problems were initially proposed for isotropic scattering,
but here we add higher-order scattering moments to them. Results show that the
difference between the SP$_N$ and P$_N$ scalar flux solution is at the roundoff
level.