Implicit radiation hydrodynamics for 1D-problems

A numerical method is reviewed and described in detail which allows an accurate solution of the equations of radiation hydrodynamics for one-dimensional spherical configurations. Such problems occur in a large variety of astrophysical situations where the interaction of matter with radiation (and vice versa) plays an important role (e.g. stellar structure, stellar pulsations, star and planet formation, radiation driven winds, stellar explosions, etc.). The method relies on a conservative formulation of the physical equations and uses an adaptive grid to resolve and trace any steep features developing within the flow. Due to the wide temporal as well as spatial range of physical time scales the solution is advanced in time by an implicit discretization scheme resulting in a nonlinear system of algebraic equations which has to be solved by a Newton–Raphson procedure. A few examples concerning stellar pulsations of a class of luminous blue stars closes this article.