Studies of hydrodynamic events in stellar evolution. I. Method of computation

We describe a numerical method of computation for hydrodynamic events in stellar evolution. The differential equations (spherical symmetry) of conservation of mass, momentum, and energy; energy transport by diffusion and convection; and the definition of velocity are replaced by finite-difference equations. By specifying a parameter 0 between 0 and 1, the time differences are expressed as a mixture of backward (0 = 1) and forward (0 = 0) differences relative to the time at which the mass differences are computed. The solution proceeds by Henyey's iterative method. The useful range of 0 lies between 0.5 and 1.0: For 0.5 < 0 < 1.0, deviations from equilibrium are artificially dampened; at 0 = 0.5, neither damping nor amplification occurs. No numerical restrictions are placed on the time step. Thus, one can either follow a star's evolution by using 0 = 1 and long time steps or investigate the details of hydrodynamic events by using 0 = 0.5 and short time steps. We describe several test applications: Numerical stability, propagation of a shock wave, free-fall collapse, and nova outburst. The results are in satisfactory agreement with either analytical solutions or with numerical solutions obtained with an independent computer code.