Nonlinear evolution of thermal structures. Numerical approach

A numerical algorithm using a two stage, two level difference scheme has be en developed to solve the heat transfer equation with nonlinear heat diffus ion and bulk energy losses. The algorithm is an extension of the scheme dev eloped by Meek and Norbury (1982). The first stage calculates an intermedia te value which is used in a second stage to estimate a new value. The schem e is consistent, second-order convergent in space and almost second order i n time. It has been applied to the nonlinear stability and time evolution o f thermal structures constituted by optically thin plasmas with solar abund ances. The configuration has been assumed to be heated at a rate similar to T-m, cooled at a rate similar to T-n and a thermal conduction coefficient similar to T-k. In particular, the second order analytical approximation co nsidered in previous papers (Ibanez and Rosenzweig, 1995; Steele and Ibanez , 1997) has been worked out for arbitrary amplitude of the initial temperat ure disturbance. Particular cases of interest in Astrophysics are considere d.