The necessity of conserving both scattered energy and asymmetry factor for ballistic incidence after either FVM or DOM discretization is convincingly shown by analyzing ultrafast laser radiative transfer in a cubic enclosure housing a participating medium. A phase-function normalization technique introduced previously by the present authors to correct for non-conservation of energy and asymmetry factor in diffuse radiant energy scattering is applied to scattering of ballistic incidence for the first time in 3-D FVM/DOM in order to improve treatment of anisotropic scattering through reduction of angular false scattering errors. Treatment of only the diffuse radiation will not conserve ballistic properties if the direction of ballistic incidence differs from a predetermined discrete direction. Our ultrafast radiative transfer predictions generated using the FVM and DOM are compared to benchmark Monte Carlo predictions in the literature to gauge accuracy and to illustrate the necessity of ballistic phase-function normalization. Additionally, numerical predictions of energy deposition in a tissue-phantom medium are analyzed to further clarify the importance of accurate numerical predictions. It is shown that the addition of proper ballistic phase-function treatment greatly improves predicted heat fluxes and energy deposition for anisotropic scattering and for situations where accurate numerical modeling is crucial.

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