Nonlinear Evolution of Thermal Structures. Numerical Approach

Abstract

A numerical algorithm using a two stage, two level difference scheme has been developed to solve the heat transfer equation with nonlinear heat diffusion and bulk energy losses. The algorithm is an extension of the scheme developed by Meek and Norbury (1982). The first stage calculates an intermediate value which is used in a second stage to estimate a new value. The scheme is consistent, second-order convergent in space and almost second order in time. It has been applied to the nonlinear stability and time evolution of thermal structures constituted by optically thin plasmas with solar abundances. The configuration has been assumed to be heated at a rate ∼ Tm, cooled at a rate ∼ Tn and a thermal conduction coefficient ∼ Tk. In particular, the second order analytical approximation considered in previous papers (Ibanez and Rosenzweig, 1995; Steele and Ibanez, 1997) has been worked out for arbitrary amplitude of the initial temperature disturbance. Particular cases of interest in Astrophysics are considered.