Simulation of stellar instabilities with vastly different time-scales using domain decomposition

Strange mode instabilities in the envelopes of massive stars lead to shock waves, which can oscillate on a much shorter time-scale than that associated with the primary instability. The phenomenon is studied by direct numerical simulation using a, with respect to time, implicit Lagrangian scheme, which allows for a variation of the dependent variables by several orders of magnitude. The time-step for the simulation of the system is reduced appreciably by the shock oscillations and prevents its long-term study. A procedure based on domain decomposition is proposed to surmount the difficulty of vastly different time-scales in various regions of the stellar envelope and thus to enable the desired long-term simulations. Criteria for domain decomposition are derived and the proper treatment of the resulting inner boundaries is discussed. Tests of the approach are presented and its viability is demonstrated by application to a model for the star P Cygni. In this investigation primarily the feasibility of domain decomposition for the problem considered is studied. We intend to use the results as the basis of an extension to two-dimensional simulations.