The Numerical Modelling of Nonlinear Stellar Pulsations

This interdisciplinary meeting has brought together a group of astrophysicists with hands-on experience in the numerical computation of astrophysical fluid dynamics, in particular nonlinear stellar pulsations, and a group of applied mathematicians who are actively engaged with the development of novel and improved numerical methods. The goal of the workshop has been for the astrophysicists to discuss in detail the numerical problems encountered in the modelling of stellar pulsations and for the mathematicians to present a survey of recent developments in numerical techniques. This astrophysical-mathematical intercourse will help the astrophysicists in the future development of more reliable and efficient codes, on the one hand, and it has introduced the mathematicians to an unfamiliar area which is a tough testing ground for their techniques. Since the difficulties encountered are common to other fluid dynamics problems, and are in fact perhaps more severe, fluid dynamicists in other research areas may fmd the results of this workshop of interest as well. Much of our theoretical understanding of the intricate and interesting behavior of variable stars rests on our ability to perform accurate numerical hydrodynamical computations of stellar models. Extensive calculations of nonlinear radial stellar pulsations with the use of increasingly powerful computers are showing more and more clearly that the numerical codes in current use have serious deficiencies.

Inhalt

The Modelling of Nonlinear Stellar Pulsations.- Current Numerical Techniques for Pulsation.- The Numerical Calculation of Stellar Pulsation: A Review of Methods and Results.- Multiperiodic Stellar Oscillations.- Numerical Sensitivity of Nonlinear Stellar Pulsation Computations.- Time Dependent Convection in Stellar Pulsation.- Regular and Chaotic Pulsations of Convective Cepheid Envelopes.- Regular and Irregular Pulsations.- Resonances and Bifurcations.- Dynamical Phenomena in Pulsating Star Atmospheres.- Reminiscence of a Stellar Pulsation Theorist.- Modern Numerical Methods Applicable to Stellar Pulsation.- Numerical Methodologies for Solving Partial Differential Equations.- From Artificial Viscosity to ENO Schemes.- High Order Accurate Modern Numerical Methods Applicable to Stellar Pulsations.- Smooth Particle Hydrodynamics: A Review.- Simple Adaptive Grids for Astrophysical Problems.- Bifurcations in Non Oscillating Stars.- Experiments with Artificial Viscosity.- Toward a Generalized Riemann Problem for Pulsation.- Discrete Map Simulation of Stellar Oscillations.