Adaptive radiation hydrodynamics of pulsating stars

In this review we present an effective numerical method to calculate non-linear radial stellar pulsations by the VIP94-code (for Vienna Pulsation code, version 1994). Employing an implicit adaptive grid method we solve the system of radiation hydrodynamics together with realistic constitutive relations and a variable Eddington factor determined by the static radiative transfer equation. In order to illustrate the general applicability of the numerical technique we choose both piston models of atmospheres of long period variable and self-excited models of RR-Lyrae and Cepheid stars as representative examples. At the end of the article some possible extensions and refinements are discussed.