Anisotropy and Particle Conservation for Trajectory-Based Deterministic Methods

Necessary and sufficient constraints are derived for the solid angle quadrature of a ray-tracing procedure to unconditionally ensure the particle conservation when anisotropic scattering is considered. As an application of this result, a discussion on the choice of a polar quadrature in two-dimensional (2-D) calculations with the method of characteristics is provided. A new quadrature based on the derived constraints is introduced and compared with other optimized quadratures on a simple 2-D benchmark.