Nonlinear hydrodynamics. Lecture 9

A very sophisticated method for calculating the stability and pulsations of stars which make contact with actual observations of the stellar behavior, hydrodynamic calculations are very simple in principle. Conservation of mass can be accounted for by having mass shells that are fixed with their mass for all time. Motions of these shells can be calculated by taking the difference between the external force of gravity and that from the local pressure gradient. The conservation of energy can be coupled to this momentum conservation equation to give the current temperatures, densities, pressures, and opacities at the shell centers, as well as the positions, velocities, and accelerations of the mass shell interfaces. Energy flow across these interfaces can be calculated from the current conditions, and this energy is partitioned between internal energy and the work done on or by the mass shell. We discuss here only the purely radial case for hydrodynamics because it is very useful for stellar pulsation studies