MacBurn's cylinder test problem
This note describes test problem for MacBurn which illustrates its performance. The source is centered inside a cylinder with axial-extent-to-radius ratio s.t. each end receives 1/4 of the thermal energy. The source (fireball) is modeled as either a point or as disk of finite radius, as described by Marrs et al. For the latter, the disk is divided into 13 equal area segments, each approximated as a point source and models a partially occluded fireball. If the source is modeled as a single point, one obtains very nearly the expected deposition, e.g., 1/4 of the flux on each end and energy is conserved. If the source is modeled as a disk, both conservation and energy fraction degrade. However, errors decrease if the source radius to domain size ratio decreases. Modeling the source as a disk increases run-times.