This paper presents the construction of a conservative radiation hydrodynamics algorithm in two dimensional spherical geometry. We first discretize the radiation transport equation in that geometry. The discretization preserves the conservation of photons by integrating the original radiation transport equation in two dimensional spherical coordinates over both angular and spatial control volumes. Some numerical results are provided to verify the discretization for both optically thin and thick circumstances. We secondly formulate the staggered Lagrangian hydrodynamics in that geometry. The formulation preserves the conservation of mass, momentum and energy by integrating the original hydrodynamic equations in two dimensional spherical coordinates over their respective control volumes. The original edge-centered artificial viscosity in two dimensional cylindrical geometry is also extended to be capable of capturing shock waves in two dimensional spherical geometry. Several two dimensional benchmark cases are provided to verify the scheme. The subsequent construction of the conservative radiation hydrodynamics algorithm is accomplished by the combination of the staggered Lagrangian hydrodynamics scheme and the solution of the radiation transport equation in two dimensional spherical geometry. Several two dimensional problems are calculated to verify our radiation hydrodynamics algorithm at the end.

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