On the Numerical Stability of Computations of Stellar Evolution
Abstract
We discuss the numerical instability arising from the coupling between hydrostatic equilibrium and thermal processes in a star. Two alternative physical pictures are possible: the heat wave does or does not propagate through the adjacent shells in the star in a given time step (slow or rapid evolution). Correspondingly, we have two alternative approaches to the mathematical formulation. If the physical picture is wrong, we encounter a numerical instability. In practice, different physical pictures are necessary for a model because of a great difference in the time scale of heat conduction between the core and the envelope of the star when we compute an advanced phase of evolution. After analyzing the nature of the instability, we show that a single mathematical scheme is possible which akvays meets the necessary physical picture required by rapid or slow evolution in the stellar core or envelope. In this scheme it is essential that the difference equation for energy flow and the difference equation for energy conservation be off center in opposite directions in the limit of rapid evolution.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- February 1970
- DOI:
- 10.1086/150336
- Bibcode:
- 1970ApJ...159..619S